open source pkg v1
This commit is contained in:
Vijay Yadev
@@ -0,0 +1,9 @@
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function [RotFull] = AddOrthRow(RotSmall)
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% We can work out these values from the small version of the rotation matrix Rx * Ry * Rz (if you plug in values you can work it out, just slightly tedious)
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RotFull = zeros(3,3);
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RotFull(1:2, :) = RotSmall;
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RotFull(3,1) = RotSmall(1, 2) * RotSmall(2, 3) - RotSmall(1, 3) * RotSmall(2, 2);
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RotFull(3,2) = RotSmall(1, 3) * RotSmall(2, 1) - RotSmall(1, 1) * RotSmall(2, 3);
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RotFull(3,3) = RotSmall(1, 1) * RotSmall(2, 2) - RotSmall(1, 2) * RotSmall(2, 1);
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@@ -0,0 +1,22 @@
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function [ R, T ] = AlignShapesKabsch ( alignFrom, alignTo )
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%ALIGN3DSHAPES Summary of this function goes here
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% Detailed explanation goes here
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dims = size(alignFrom, 2);
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alignFromMean = alignFrom - repmat(mean(alignFrom), size(alignFrom,1),1);
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alignToMean = alignTo - repmat(mean(alignTo), size(alignTo,1),1);
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[U, ~, V] = svd( alignFromMean' * alignToMean);
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% make sure no reflection is there
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d = sign(det(V*U'));
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corr = eye(dims);
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corr(end,end) = d;
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R = V*corr*U';
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T = mean(alignTo) - (R * mean(alignFrom)')';
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T = T';
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end
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@@ -0,0 +1,30 @@
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function [ A, T, error, alignedShape, s ] = AlignShapesWithScale( alignFrom, alignTo )
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%ALIGNSHAPESWITHSCALE Summary of this function goes here
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% Detailed explanation goes here
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numPoints = size(alignFrom,1);
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meanFrom = mean(alignFrom);
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meanTo = mean(alignTo);
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alignFromMeanNormed = bsxfun(@minus, alignFrom, meanFrom);
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alignToMeanNormed = bsxfun(@minus, alignTo, meanTo);
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% scale now
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sFrom = sqrt(sum(alignFromMeanNormed(:).^2)/numPoints);
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sTo = sqrt(sum(alignToMeanNormed(:).^2)/numPoints);
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s = sTo / sFrom;
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alignFromMeanNormed = alignFromMeanNormed/sFrom;
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alignToMeanNormed = alignToMeanNormed/sTo;
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[R, t] = AlignShapesKabsch(alignFromMeanNormed, alignToMeanNormed);
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A = s * R;
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aligned = (A * alignFrom')';
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T = mean(alignTo - aligned);
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alignedShape = bsxfun(@plus, aligned, T);
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error = mean(sum((alignedShape - alignTo).^2,2));
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end
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@@ -0,0 +1,11 @@
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function [Rot] = AxisAngle2Rot(axisAngle)
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theta = norm(axisAngle, 2);
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nx = axisAngle / theta;
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nx = [ 0 -nx(3) nx(2);
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nx(3) 0 -nx(1);
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-nx(2) nx(1) 0 ];
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Rot = eye(3) + sin(theta) * nx + (1-cos(theta))*nx^2;
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@@ -0,0 +1,11 @@
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function [Rot] = Euler2Rot(euler)
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rx = euler(1);
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ry = euler(2);
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rz = euler(3);
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Rx = [1 0 0; 0 cos(rx) -sin(rx); 0 sin(rx) cos(rx)];
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Ry = [cos(ry) 0 sin(ry); 0 1 0; -sin(ry) 0 cos(ry)];
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Rz = [cos(rz) -sin(rz) 0; sin(rz) cos(rz) 0; 0 0 1];
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Rot = Rx * Ry * Rz;
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@@ -0,0 +1,7 @@
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function [shape3D] = GetShape3D(M, V, p)
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shape3D = M + V * p;
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shape3D = reshape(shape3D, numel(shape3D) / 3, 3);
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end
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@@ -0,0 +1,20 @@
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function [shape2D] = GetShapeOrtho(M, V, p, global_params)
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% M - mean shape vector
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% V - eigenvectors
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% p - parameters of non-rigid shape
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% V_exp
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% p_exp
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% global_params includes scale, euler rotation, translation,
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% R - rotation matrix
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% T - translation vector (tx, ty)
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R = Euler2Rot(global_params(2:4));
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T = [global_params(5:6); 0];
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a = global_params(1);
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shape3D = GetShape3D(M, V, p);
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shape2D = bsxfun(@plus, a * R*shape3D', T);
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shape2D = shape2D';
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end
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@@ -0,0 +1,103 @@
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function [normX, normY, meanShape, Transform] = ProcrustesAnalysis(x, y, options)
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% Translate all elements to origin and scale to 1
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normX = zeros(size(x));
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normY = zeros(size(y));
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for i = 1:size(x,1)
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offsetX = mean(x(i,:));
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offsetY = mean(y(i,:));
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Transform.offsetX(i) = offsetX;
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Transform.offsetY(i) = offsetY;
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normX(i,:) = x(i,:) - offsetX;
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normY(i,:) = y(i,:) - offsetY;
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% Get the Frobenius norm, to scale the shapes to unit size
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scale = norm([normX(i,:) normY(i,:)], 'fro');
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Transform.scale(i) = scale;
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normX(i,:) = normX(i,:)/scale;
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normY(i,:) = normY(i,:)/scale;
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end
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% Rotate elements untill all of them have the same orientation
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% the initial estimate of rotation would be the first element
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% if change is less than 1% stop (shouldn't take more than 2 steps)
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change = 0.1;
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meanShape = [ normX(1,:); normY(1,:) ]';
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Transform.Rotation = zeros(size(x,1),1);
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for i = 1:30
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% align all of the shapes to the mean shape
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% remember all orientations to get the mean one
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orientations = zeros(size(normX,1),1);
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for j = 1:size(x,1)
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% do SVD of mean * X'
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currentShape = [ normX(j,:); normY(j,:) ]';
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[U, ~, V] = svd( meanShape' * currentShape);
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rot = V*U';
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if(asin(rot(2,1)) > 0)
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orientations(j) = real(acos(rot(1,1)));
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else
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orientations(j) = real(-acos(rot(1,1)));
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end
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Transform.Rotation(j) = Transform.Rotation(j) + orientations(j);
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currentShape = currentShape * rot;
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normX(j,:) = currentShape(:,1)';
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normY(j,:) = currentShape(:,2)';
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end
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% recalculate the mean shape;
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oldMean = meanShape;
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meanShape = [mean(normX); mean(normY)]';
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% rotate the mean shape to mean rotation
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meanOrientation = mean(orientations);
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% Do this only the first time
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if(i==1)
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rotM = [ cos(-meanOrientation) -sin(-meanOrientation); sin(-meanOrientation) cos(-meanOrientation) ];
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meanShape = meanShape * rotM;
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end
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% scale mean shape to unit
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meanScale = norm(meanShape, 'fro');
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meanShape = meanShape*(1/meanScale);
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% find frobenious norm
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diff = norm(oldMean - meanShape, 'fro');
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if(diff/norm(oldMean,'fro') < change)
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break;
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end
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end
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% transform to tangent space to preserve linearities
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% get the scaling factors for each shape
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if(options.TangentSpaceTransform)
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scaling = [ normX normY ] * [ meanShape(:,1)' meanShape(:,2)']';
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for i=1:size(x,1)
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normX(i,:) = normX(i,:) * (1 / scaling(i));
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normY(i,:) = normY(i,:) * (1 / scaling(i));
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end
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end
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@@ -0,0 +1,139 @@
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function [ normX, normY, normZ, meanShape, Transform ] = ProcrustesAnalysis3D( x, y, z, tangentSpace, meanShape )
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%PROCRUSTESANALYSIS3D Summary of this function goes here
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% Detailed explanation goes here
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meanProvided = false;
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if(nargin > 4)
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meanProvided = true;
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end
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% Translate all elements to origin
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normX = zeros(size(x));
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normY = zeros(size(y));
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normZ = zeros(size(z));
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for i = 1:size(x,1)
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offsetX = mean(x(i,:));
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offsetY = mean(y(i,:));
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offsetZ = mean(z(i,:));
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Transform.offsetX(i) = offsetX;
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Transform.offsetY(i) = offsetY;
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Transform.offsetZ(i) = offsetZ;
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normX(i,:) = x(i,:) - offsetX;
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normY(i,:) = y(i,:) - offsetY;
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normZ(i,:) = z(i,:) - offsetZ;
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end
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% Rotate elements untill all of them have the same orientation
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% the initial estimate of rotation would be the first element
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% if change is less than 1% stop (shouldn't take more than 2 steps)
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change = 0.1;
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if(~meanProvided)
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meanShape = [ mean(normX); mean(normY); mean(normZ) ]';
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end
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% scale all the shapes to mean shape
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% Get the Frobenius norm, to scale the shapes to mean size (still want to
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% retain mm)
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meanScale = norm(meanShape, 'fro');
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for i = 1:size(x,1)
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scale = norm([normX(i,:) normY(i,:) normZ(i,:)], 'fro')/meanScale;
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normX(i,:) = normX(i,:)/scale;
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normY(i,:) = normY(i,:)/scale;
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normZ(i,:) = normZ(i,:)/scale;
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end
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Transform.RotationX = zeros(size(x,1),1);
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Transform.RotationY = zeros(size(x,1),1);
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Transform.RotationZ = zeros(size(x,1),1);
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for i = 1:30
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% align all of the shapes to the mean shape
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% remember all orientations to get the mean one (in euler angle form, pitch, yaw roll)
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orientationsX = zeros(size(normX,1),1);
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orientationsY = zeros(size(normX,1),1);
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orientationsZ = zeros(size(normX,1),1);
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for j = 1:size(x,1)
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currentShape = [normX(j,:); normY(j,:); normZ(j,:)]';
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% we want to align the current shape to the mean one
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[ R, T ] = AlignShapesKabsch(currentShape, meanShape);
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eulers = Rot2Euler(R);
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orientationsX(j) = eulers(1);
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orientationsY(j) = eulers(2);
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orientationsZ(j) = eulers(3);
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Transform.RotationX(j) = eulers(1);
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Transform.RotationY(j) = eulers(2);
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Transform.RotationZ(j) = eulers(3);
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currentShape = R * currentShape';
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normX(j,:) = currentShape(1,:);
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normY(j,:) = currentShape(2,:);
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normZ(j,:) = currentShape(3,:);
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end
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% recalculate the mean shape
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% if(~meanProvided)
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oldMean = meanShape;
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meanShape = [mean(normX); mean(normY); mean(normZ)]';
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meanScale = norm(meanShape, 'fro');
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% end
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for j = 1:size(x,1)
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scale = norm([normX(j,:) normY(j,:) normZ(j,:)], 'fro')/meanScale;
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normX(j,:) = normX(j,:)/scale;
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normY(j,:) = normY(j,:)/scale;
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normZ(j,:) = normZ(j,:)/scale;
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end
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if(i==1 && ~meanProvided)
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% rotate the mean shape to mean rotation
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meanOrientationX = mean(orientationsX);
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meanOrientationY = mean(orientationsY);
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meanOrientationZ = mean(orientationsZ);
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R = Euler2Rot([meanOrientationX, meanOrientationY, meanOrientationZ]);
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meanShape = (R * meanShape')';
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end
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% find frobenious norm
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diff = norm(oldMean - meanShape, 'fro');
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if(diff/norm(oldMean,'fro') < change)
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break;
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end
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end
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% transform to tangent space to preserve linearities
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% get the scaling factors for each shape
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if(tangentSpace)
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[ normX, normY, normZ] = TangentSpaceTransform(normX, normY, normZ, meanShape);
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end
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end
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@@ -0,0 +1,11 @@
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function [ axisAngle ] = Rot2AxisAngle( Rot )
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%ROT2AXISANGLE Summary of this function goes here
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% Detailed explanation goes here
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theta = acos((trace(Rot) - 1) / 2);
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vec = 1.0/(2*sin(theta));
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vec = vec * [Rot(3,2) - Rot(2,3), Rot(1,3) - Rot(3,1), Rot(2,1) - Rot(1,2)];
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axisAngle = vec * theta;
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end
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@@ -0,0 +1,16 @@
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function [euler] = Rot2Euler(R)
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q0 = sqrt( 1 + R(1,1) + R(2,2) + R(3,3) ) / 2;
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if(q0 ~= 0)
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q1 = (R(3,2) - R(2,3)) / (4*q0) ;
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q2 = (R(1,3) - R(3,1)) / (4*q0) ;
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q3 = (R(2,1) - R(1,2)) / (4*q0) ;
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yaw = asin(2*(q0*q2 + q1*q3));
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pitch= atan2(2*(q0*q1-q2*q3), q0*q0-q1*q1-q2*q2+q3*q3);
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roll = atan2(2*(q0*q3-q1*q2), q0*q0+q1*q1-q2*q2-q3*q3);
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euler = [pitch, yaw, roll];
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else
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euler = [0, 0, 0];
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end
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@@ -0,0 +1,17 @@
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function [ transformedX, transformedY, transformedZ ] = TangentSpaceTransform( x, y, z, meanShape )
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%TANGENTSPACETRANSFORM Summary of this function goes here
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% Detailed explanation goes here
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scaling = [ x y z] * [ meanShape(:,1)' meanShape(:,2)' meanShape(:,3)']';
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for i=1:size(x,1)
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x(i,:) = x(i,:) * (1 / scaling(i));
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y(i,:) = y(i,:) * (1 / scaling(i));
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z(i,:) = z(i,:) * (1 / scaling(i));
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end
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transformedX = x * mean(scaling);
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transformedY = y * mean(scaling);
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transformedZ = z * mean(scaling);
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end
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@@ -0,0 +1,373 @@
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function [ a, R, T, T3D, params, error, shapeOrtho ] = fit_PDM_ortho_proj_to_2D( M, E, V, shape2D, f, cx, cy)
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%FITPDMTO2DSHAPE Summary of this function goes here
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% Detailed explanation goes here
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params = zeros(size(E));
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hidden = false;
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% if some of the points are unavailable modify M, V, and shape2D (can
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% later infer the actual shape from this)
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if(sum(shape2D(:)==0) > 0)
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hidden = true;
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% which indices to remove
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inds_to_rem = shape2D(:,1) == 0 | shape2D(:,2) == 0;
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shape2D = shape2D(~inds_to_rem,:);
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inds_to_rem = repmat(inds_to_rem, 3, 1);
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M_old = M;
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V_old = V;
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M = M(~inds_to_rem);
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V = V(~inds_to_rem,:);
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end
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num_points = numel(M) / 3;
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m = reshape(M, num_points, 3)';
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width_model = max(m(1,:)) - min(m(1,:));
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height_model = max(m(2,:)) - min(m(2,:));
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bounding_box = [min(shape2D(:,1)), min(shape2D(:,2)),...
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max(shape2D(:,1)), max(shape2D(:,2))];
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a = (((bounding_box(3) - bounding_box(1)) / width_model) + ((bounding_box(4) - bounding_box(2))/ height_model)) / 2;
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tx = (bounding_box(3) + bounding_box(1))/2;
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ty = (bounding_box(4) + bounding_box(2))/2;
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% correct it so that the bounding box is just around the minimum
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% and maximum point in the initialised face
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tx = tx - a*(min(m(1,:)) + max(m(1,:)))/2;
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ty = ty - a*(min(m(2,:)) + max(m(2,:)))/2;
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% To deal with really extreme cases of roll
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M3D = cat(2, M(1:end/3), M(end/3+1:2*end/3), zeros(numel(M(1:end/3)),1));
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shape3D = cat(2, shape2D, zeros(numel(M(1:end/3)),1));
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[ A, T, error, alignedShape, s ] = AlignShapesWithScale(M3D, shape3D);
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R = A/s;
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% R = eye(3);
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T = [tx; ty];
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||||
|
||||
currShape = getShapeOrtho(M, V, params, R, T, a);
|
||||
|
||||
currError = getRMSerror(currShape, shape2D);
|
||||
|
||||
reg_rigid = zeros(6,1);
|
||||
regFactor = 20;
|
||||
regularisations = [reg_rigid; regFactor ./ E]; % the above version, however, does not perform as well
|
||||
regularisations = diag(regularisations)*diag(regularisations);
|
||||
|
||||
red_in_a_row = 0;
|
||||
|
||||
for i=1:1000
|
||||
|
||||
shape3D = M + V * params;
|
||||
shape3D = reshape(shape3D, numel(shape3D) / 3, 3);
|
||||
|
||||
% Now find the current residual error
|
||||
currShape = a * R(1:2,:)*shape3D' + repmat(T, 1, numel(M)/3);
|
||||
currShape = currShape';
|
||||
|
||||
error_res = shape2D - currShape;
|
||||
|
||||
eul = Rot2Euler(R);
|
||||
|
||||
p_global = [a; eul'; T];
|
||||
|
||||
% get the Jacobians
|
||||
J = CalcJacobian(M, V, params, p_global);
|
||||
|
||||
% RLMS style update
|
||||
p_delta = (J'*J + regularisations) \ (J'*error_res(:) - regularisations*[p_global;params]);
|
||||
|
||||
% Take smaller steps
|
||||
p_delta = 0.25 * p_delta;
|
||||
|
||||
[params, p_global] = CalcReferenceUpdate(p_delta, params, p_global);
|
||||
|
||||
% Make sure the params do not get out of hand
|
||||
params = ClampPDM(params, E);
|
||||
|
||||
a = p_global(1);
|
||||
R = Euler2Rot(p_global(2:4));
|
||||
T = p_global(5:6);
|
||||
|
||||
shape3D = M + V * params;
|
||||
shape3D = reshape(shape3D, numel(shape3D) / 3, 3);
|
||||
currShape = a * R(1:2,:)*shape3D' + repmat(T, 1, numel(M)/3);
|
||||
currShape = currShape';
|
||||
|
||||
error = getRMSerror(currShape, shape2D);
|
||||
|
||||
if(0.999 * currError < error)
|
||||
red_in_a_row = red_in_a_row + 1;
|
||||
if(red_in_a_row == 5)
|
||||
break;
|
||||
end
|
||||
end
|
||||
|
||||
currError = error;
|
||||
|
||||
end
|
||||
|
||||
if(hidden)
|
||||
shapeOrtho = getShapeOrtho(M_old, V_old, params, R, T, a);
|
||||
else
|
||||
shapeOrtho = currShape;
|
||||
end
|
||||
if(nargin == 7)
|
||||
|
||||
Zavg = f / a;
|
||||
Xavg = (T(1) - cx) / a;
|
||||
Yavg = (T(2) - cy) / a;
|
||||
|
||||
T3D = [Xavg;Yavg;Zavg];
|
||||
else
|
||||
T3D = [0;0;0];
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
function [shape2D] = getShapeOrtho(M, V, p, R, T, a)
|
||||
|
||||
% M - mean shape vector
|
||||
% V - eigenvectors
|
||||
% p - parameters of non-rigid shape
|
||||
% R - rotation matrix
|
||||
% T - translation vector (tx, ty)
|
||||
shape3D = getShape3D(M, V, p);
|
||||
shape2D = a * R(1:2,:)*shape3D' + repmat(T, 1, numel(M)/3);
|
||||
shape2D = shape2D';
|
||||
end
|
||||
|
||||
function [shape2D] = getShapeOrthoFull(M, V, p, R, T, a)
|
||||
|
||||
% M - mean shape vector
|
||||
% V - eigenvectors
|
||||
% p - parameters of non-rigid shape
|
||||
% R - rotation matrix
|
||||
% T - translation vector (tx, ty)
|
||||
T = [T; 0];
|
||||
shape3D = getShape3D(M, V, p);
|
||||
shape2D = a * R*shape3D' + repmat(T, 1, numel(M)/3);
|
||||
shape2D = shape2D';
|
||||
end
|
||||
|
||||
function [shape3D] = getShape3D(M, V, params)
|
||||
|
||||
shape3D = M + V * params;
|
||||
shape3D = reshape(shape3D, numel(shape3D) / 3, 3);
|
||||
|
||||
end
|
||||
|
||||
function [error] = getRMSerror(shape2Dv1, shape2Dv2)
|
||||
|
||||
error = sqrt(mean(reshape(shape2Dv1 - shape2Dv2, numel(shape2Dv1), 1).^2));
|
||||
|
||||
end
|
||||
|
||||
% This calculates the combined rigid with non-rigid Jacobian
|
||||
function J = CalcJacobian(M, V, p, p_global)
|
||||
|
||||
n = size(M, 1)/3;
|
||||
|
||||
non_rigid_modes = size(V,2);
|
||||
|
||||
J = zeros(n*2, 6 + non_rigid_modes);
|
||||
|
||||
|
||||
% now the layour is
|
||||
% ---------- Rigid part -------------------|----Non rigid part--------|
|
||||
% dx_1/ds, dx_1/dr1, ... dx_1/dtx, dx_1/dty dx_1/dp_1 ... dx_1/dp_m
|
||||
% dx_2/ds, dx_2/dr1, ... dx_2/dtx, dx_2/dty dx_2/dp_1 ... dx_2/dp_m
|
||||
% ...
|
||||
% dx_n/ds, dx_n/dr1, ... dx_n/dtx, dx_n/dty dx_n/dp_1 ... dx_n/dp_m
|
||||
% dy_1/ds, dy_1/dr1, ... dy_1/dtx, dy_1/dty dy_1/dp_1 ... dy_1/dp_m
|
||||
% ...
|
||||
% dy_n/ds, dy_n/dr1, ... dy_n/dtx, dy_n/dty dy_n/dp_1 ... dy_n/dp_m
|
||||
|
||||
% getting the rigid part
|
||||
J(:,1:6) = CalcRigidJacobian(M, V, p, p_global);
|
||||
|
||||
% constructing the non-rigid part
|
||||
R = Euler2Rot(p_global(2:4));
|
||||
s = p_global(1);
|
||||
|
||||
% 'rotate' and 'scale' the principal components
|
||||
|
||||
% First reshape to 3D
|
||||
V_X = V(1:n,:);
|
||||
V_Y = V(n+1:2*n,:);
|
||||
V_Z = V(2*n+1:end,:);
|
||||
|
||||
J_x_non_rigid = s*(R(1,1)*V_X + R(1,2)*V_Y + R(1,3)*V_Z);
|
||||
J_y_non_rigid = s*(R(2,1)*V_X + R(2,2)*V_Y + R(2,3)*V_Z);
|
||||
|
||||
J(1:n, 7:end) = J_x_non_rigid;
|
||||
J(n+1:end, 7:end) = J_y_non_rigid;
|
||||
|
||||
end
|
||||
|
||||
function J = CalcRigidJacobian(M, V, p, p_global)
|
||||
|
||||
n = size(M, 1)/3;
|
||||
|
||||
% Get the current 3D shape (not affected by global transform, as this
|
||||
% is how the Jacobian was derived (for derivation please see
|
||||
% ../derivations/orthoJacobian
|
||||
shape3D = GetShape3D(M, V, p);
|
||||
|
||||
% Get the rotation matrix corresponding to current global orientation
|
||||
R = Euler2Rot(p_global(2:4));
|
||||
s = p_global(1);
|
||||
|
||||
% Rigid Jacobian is laid out as follows
|
||||
% dx_1/ds, dx_1/dr1, dx_1/dr2, dx_1/dr3, dx_1/dtx, dx_1/dty
|
||||
% dx_2/ds, dx_2/dr1, dx_2/dr2, dx_2/dr3, dx_2/dtx, dx_2/dty
|
||||
% ...
|
||||
% dx_n/ds, dx_n/dr1, dx_n/dr2, dx_n/dr3, dx_n/dtx, dx_n/dty
|
||||
% dy_1/ds, dy_1/dr1, dy_1/dr2, dy_1/dr3, dy_1/dtx, dy_1/dty
|
||||
% ...
|
||||
% dy_n/ds, dy_n/dr1, dy_n/dr2, dy_n/dr3, dy_n/dtx, dy_n/dty
|
||||
|
||||
J = zeros(n*2, 6);
|
||||
|
||||
% dx/ds = X * r11 + Y * r12 + Z * r13
|
||||
% dx/dr1 = s*(r13 * Y - r12 * Z)
|
||||
% dx/dr2 = -s*(r13 * X - r11 * Z)
|
||||
% dx/dr3 = s*(r12 * X - r11 * Y)
|
||||
% dx/dtx = 1
|
||||
% dx/dty = 0
|
||||
|
||||
% dy/ds = X * r21 + Y * r22 + Z * r23
|
||||
% dy/dr1 = s * (r23 * Y - r22 * Z)
|
||||
% dy/dr2 = -s * (r23 * X - r21 * Z)
|
||||
% dy/dr3 = s * (r22 * X - r21 * Y)
|
||||
% dy/dtx = 0
|
||||
% dy/dty = 1
|
||||
|
||||
% set the Jacobian for x's
|
||||
|
||||
% with respect to scaling factor
|
||||
J(1:n,1) = shape3D * R(1,:)';
|
||||
|
||||
% with respect to angular rotation around x, y, and z axes
|
||||
|
||||
% Change of x with respect to change in axis angle rotation
|
||||
dxdR = [ 0, R(1,3), -R(1,2);
|
||||
-R(1,3), 0, R(1,1);
|
||||
R(1,2), -R(1,1), 0];
|
||||
|
||||
J(1:n,2:4) = s*(dxdR * shape3D')';
|
||||
|
||||
% with respect to translation
|
||||
J(1:n,5) = 1;
|
||||
J(1:n,6) = 0;
|
||||
|
||||
% set the Jacobian for y's
|
||||
|
||||
% with respect to scaling factor
|
||||
J(n+1:end,1) = shape3D * R(2,:)';
|
||||
|
||||
% with respect to angular rotation around x, y, and z axes
|
||||
|
||||
% Change of y with respect to change in axis angle rotation
|
||||
dydR = [ 0, R(2,3), -R(2,2);
|
||||
-R(2,3), 0, R(2,1);
|
||||
R(2,2), -R(2,1), 0];
|
||||
|
||||
J(n+1:end,2:4) = s*(dydR * shape3D')';
|
||||
|
||||
% with respect to translation
|
||||
J(n+1:end,5) = 0;
|
||||
J(n+1:end,6) = 1;
|
||||
|
||||
end
|
||||
|
||||
% This updates the parameters based on the updates from the RLMS
|
||||
function [non_rigid, rigid] = CalcReferenceUpdate(params_delta, current_non_rigid, current_global)
|
||||
|
||||
|
||||
rigid = zeros(6, 1);
|
||||
% Same goes for scaling and translation parameters
|
||||
rigid(1) = current_global(1) + params_delta(1);
|
||||
rigid(5) = current_global(5) + params_delta(5);
|
||||
rigid(6) = current_global(6) + params_delta(6);
|
||||
|
||||
% for rotation however, we want to make sure that the rotation matrix
|
||||
% approximation we have
|
||||
% R' = [1, -wz, wy
|
||||
% wz, 1, -wx
|
||||
% -wy, wx, 1]
|
||||
% is a legal rotation matrix, and then we combine it with current
|
||||
% rotation (through matrix multiplication) to acquire the new rotation
|
||||
|
||||
R = Euler2Rot(current_global(2:4));
|
||||
|
||||
wx = params_delta(2);
|
||||
wy = params_delta(3);
|
||||
wz = params_delta(4);
|
||||
|
||||
R_delta = [1, -wz, wy;
|
||||
wz, 1, -wx;
|
||||
-wy, wx, 1];
|
||||
|
||||
% Make sure R_delta is orthonormal
|
||||
R_delta = double(OrthonormaliseRotation(R_delta));
|
||||
|
||||
% Combine rotations
|
||||
R_final = R * R_delta;
|
||||
|
||||
% Extract euler angle
|
||||
euler = real(Rot2Euler(R_final));
|
||||
|
||||
rigid(2:4) = euler;
|
||||
|
||||
if(length(params_delta) > 6)
|
||||
% non-rigid parameters can just be added together
|
||||
non_rigid = params_delta(7:end) + current_non_rigid;
|
||||
else
|
||||
non_rigid = current_non_rigid;
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
function R_ortho = OrthonormaliseRotation(R)
|
||||
|
||||
% U * V' is basically what we want, as it's guaranteed to be
|
||||
% orthonormal
|
||||
[U, ~, V] = svd(R);
|
||||
|
||||
% We also want to make sure no reflection happened
|
||||
|
||||
% get the orthogonal matrix from the initial rotation matrix
|
||||
X = U*V';
|
||||
|
||||
% This makes sure that the handedness is preserved and no reflection happened
|
||||
% by making sure the determinant is 1 and not -1
|
||||
W = eye(3);
|
||||
W(3,3) = det(X);
|
||||
R_ortho = U*W*V';
|
||||
end
|
||||
|
||||
% This clamps the non-rigid parameters to stay within +- 3 standard
|
||||
% deviations
|
||||
function [non_rigid_params] = ClampPDM(non_rigid, E)
|
||||
|
||||
stds = sqrt(E);
|
||||
|
||||
non_rigid_params = non_rigid;
|
||||
|
||||
lower = non_rigid_params < -3 * stds;
|
||||
non_rigid_params(lower) = -3*stds(lower);
|
||||
|
||||
higher = non_rigid_params > 3 * stds;
|
||||
non_rigid_params(higher) = 3*stds(higher);
|
||||
|
||||
end
|
||||
@@ -0,0 +1,16 @@
|
||||
% for easier readibility write them row by row
|
||||
function writeMatrix(fileID, M, type)
|
||||
|
||||
fprintf(fileID, '%d\r\n', size(M,1));
|
||||
fprintf(fileID, '%d\r\n', size(M,2));
|
||||
fprintf(fileID, '%d\r\n', type);
|
||||
|
||||
for i=1:size(M,1)
|
||||
if(type == 4 || type == 0)
|
||||
fprintf(fileID, '%d ', M(i,:));
|
||||
else
|
||||
fprintf(fileID, '%.9f ', M(i,:));
|
||||
end
|
||||
fprintf(fileID, '\r\n');
|
||||
end
|
||||
end
|
||||
50
pkg/OpenFace/model_training/pdm_generation/Readme.txt
Normal file
50
pkg/OpenFace/model_training/pdm_generation/Readme.txt
Normal file
@@ -0,0 +1,50 @@
|
||||
Creating the Point Distribution Model.
|
||||
|
||||
---------------------------------------------------------------
|
||||
To create a model from 300W training data use the Matlab script:
|
||||
|
||||
./Wild_data_pdm/Create_pdm_wild.m (This might take up to a couple of hours, depending on the machine used, and if you compiled computeH - see readme in nrsfm-em folder)
|
||||
|
||||
You need the training data which can be acquired from (http://ibug.doc.ic.ac.uk/resources/facial-point-annotations/), to run the script from scratch. Alternatively the data is collected in 'wild_68_pts.mat', so you can skip the Collect_wild_annotations step.
|
||||
|
||||
The script will produce "./Wild_data_pdm/pdm_68_aligned_wild.mat" and "./Wild_data_pdm/pdm_68_aligned_wild.txt" which can be used for landmark detection.
|
||||
|
||||
---------------------------------------------------------------
|
||||
To create a model from Menpo + 300W training data use the Matlab script:
|
||||
|
||||
First convert menpo to train/validation folds (PDM training is done on training fold):
|
||||
'./menpo_pdm/split_menpo_data.m'
|
||||
|
||||
Followed by:
|
||||
Collect_menpo_annotations;
|
||||
Collect_menpo_annotations_valid;
|
||||
|
||||
To train the actual PDM:
|
||||
'./menpo_pdm/Create_pdm_wild.m' (This might take up to a couple of hours, depending on the machine used, and if you compiled computeH - see readme in nrsfm-em folder)
|
||||
|
||||
You need the training data which can be acquired from (https://ibug.doc.ic.ac.uk/resources/300-W/, and https://ibug.doc.ic.ac.uk/resources/2nd-facial-landmark-tracking-competition-menpo-ben/), to run the script from scratch. Alternatively the data is collected in 'menpo_68_pts.mat', so you can skip the Collect_wild_annotations step.
|
||||
|
||||
The script will produce "./menpo_pdm/pdm_68_aligned_menpo.mat" and "./menpo_pdm/pdm_68_aligned_menpo.txt" which can be used for landmark detection.
|
||||
|
||||
-------
|
||||
As Menpo challenge expects profile faces to have chin outline, so to learn the conversion to Menpo format use "menpo_chin/learn_menpo_profile_mapping.m" (to get data you will also need to run Collect_menpo_annotations_profile_train.m, Collect_menpo_annotations_profile_valid.m)
|
||||
|
||||
---------------------------------------------------------------
|
||||
To visualise the results use:
|
||||
visualise_PDMs.m
|
||||
|
||||
The PDM triangulation was created using the Delaunay triangulation algorithm, with manual hole cutting for eyes and mouth. Same can be done on any other annotated face dataset.
|
||||
|
||||
The pdm used in "in-the-wild" and "menpo" experiments is already included as:
|
||||
./Wild_data_pdm/pdm_68_aligned_wild
|
||||
./Wild_data_pdm/pdm_68_aligned_wild.txt
|
||||
|
||||
./menpo_pdm/pdm_68_aligned_menpo.mat
|
||||
./menpo_pdm/pdm_68_aligned_menpo.txt
|
||||
|
||||
The same model should be generated using the Matlab script as well (overwriting the data).
|
||||
|
||||
--------------------------------------------------------------
|
||||
We use the non-rigid structure from motion approach by Lorenzo Torresani, Aaron Hertzmann, Chris Bregler, "Learning Non-Rigid 3D Shape from 2D Motion", NIPS 16, 2003
|
||||
http://cs.stanford.edu/~ltorresa/projects/learning-nr-shape/
|
||||
Please cite their work and ours if you use this code.
|
||||
@@ -0,0 +1,6 @@
|
||||
%% Torresani visualisation of in-the wild PDM
|
||||
load './Wild_data_pdm/pdm_10_brows.mat';
|
||||
|
||||
T = delaunay(M(1:10), M(11:20));
|
||||
% Visualise it
|
||||
visualisePDM(M, E, V, T-1, 5, 5)
|
||||
@@ -0,0 +1,27 @@
|
||||
% collect the training data annotations (from the 300 faces in the wild
|
||||
% challenge)
|
||||
|
||||
test_data_loc = '../../../';
|
||||
|
||||
dataset_locs = {[test_data_loc, '/test data/helen/trainset/'];
|
||||
[test_data_loc, '/test data/lfpw/trainset/']};
|
||||
|
||||
all_pts = [];
|
||||
for i=1:numel(dataset_locs)
|
||||
landmarkLabels = dir([dataset_locs{i} '\*.pts']);
|
||||
|
||||
for p=1:numel(landmarkLabels)
|
||||
landmarks = importdata([dataset_locs{i}, landmarkLabels(p).name], ' ', 3);
|
||||
landmarks = landmarks.data;
|
||||
all_pts = cat(3, all_pts, landmarks);
|
||||
end
|
||||
end
|
||||
|
||||
%%
|
||||
|
||||
xs = squeeze(all_pts(:,1,:));
|
||||
ys = squeeze(all_pts(:,2,:));
|
||||
|
||||
all_pts = cat(2,xs,ys)';
|
||||
|
||||
save('wild_68_pts', 'all_pts');
|
||||
@@ -0,0 +1,122 @@
|
||||
clear;
|
||||
|
||||
addpath('../PDM_helpers/');
|
||||
|
||||
%% Create the PDM using PCA, from the recovered 3D data
|
||||
clear
|
||||
load('Torr_wild');
|
||||
|
||||
% need to still perform procrustes though
|
||||
|
||||
x = P3(1:end/3,:);
|
||||
y = P3(end/3+1:2*end/3,:);
|
||||
|
||||
% To make sure that PDM faces the right way (positive Z towards the screen)
|
||||
z = -P3(2*end/3+1:end,:);
|
||||
|
||||
brow_ids = 18:27;
|
||||
|
||||
%%
|
||||
[ normX, normY, normZ, meanShape, Transform ] = ProcrustesAnalysis3D(x,y,z, true);
|
||||
|
||||
normX = normX(:, brow_ids);
|
||||
normY = normY(:, brow_ids);
|
||||
normZ = normZ(:, brow_ids);
|
||||
meanShape = meanShape(brow_ids,:);
|
||||
% make it zero centered now?
|
||||
offsets = mean(meanShape);
|
||||
|
||||
normX = normX - offsets(1);
|
||||
normY = normY - offsets(1);
|
||||
normZ = normZ - offsets(1);
|
||||
|
||||
observations = [normX normY normZ];
|
||||
|
||||
[princComp, score, eigenVals] = princomp(observations,'econ');
|
||||
% Keeping most variation
|
||||
totalSum = sum(eigenVals);
|
||||
count = numel(eigenVals);
|
||||
for i=1:numel(eigenVals)
|
||||
if ((sum(eigenVals(1:i)) / totalSum) >= 0.999)
|
||||
count = i;
|
||||
break;
|
||||
end
|
||||
end
|
||||
|
||||
load('pdm_68_multi_pie.mat', 'M');
|
||||
M_full = M;
|
||||
|
||||
V = princComp(:,1:count);
|
||||
E = eigenVals(1:count);
|
||||
M = meanShape(:);
|
||||
|
||||
left_corner = [M(1); M(1+10)];
|
||||
right_corner = [M(10); M(10+10)];
|
||||
|
||||
dist_norm = norm(left_corner - right_corner,2);
|
||||
|
||||
left_corner_full = [M_full(18); M_full(18+68)];
|
||||
right_corner_full = [M_full(27); M_full(27+68)];
|
||||
|
||||
dist_norm_full = norm(left_corner_full - right_corner_full,2);
|
||||
|
||||
% average human interocular distance is 65mm
|
||||
scaling = dist_norm_full / dist_norm;
|
||||
|
||||
% normalise the mean values as well
|
||||
M(1:end/3) = M(1:end/3) - mean(M(1:end/3));
|
||||
M(end/3+1:2*end/3) = M(end/3+1:2*end/3) - mean(M(end/3+1:2*end/3));
|
||||
M(2*end/3+1:end) = M(2*end/3+1:end) - mean(M(2*end/3+1:end));
|
||||
|
||||
M = M * scaling;
|
||||
E = E * scaling .^ 2;
|
||||
|
||||
% orthonormalise V
|
||||
scalingV = sqrt(sum(V.^2));
|
||||
V = V ./ repmat(scalingV, numel(M),1);
|
||||
|
||||
E = E .* (scalingV') .^ 2;
|
||||
|
||||
%% Also align the model to a Multi-PIE one for accurate head orientation
|
||||
% also align the mean shape model (an aligned 68 point PDM from Multi-PIE dataset)
|
||||
M_mouth = M;
|
||||
|
||||
load('pdm_68_multi_pie.mat', 'M');
|
||||
M_align = M;
|
||||
|
||||
n_points = numel(M)/3;
|
||||
M_mouth_full = reshape(M_align, n_points,3);
|
||||
M_mouth_full = M_mouth_full(brow_ids, :);
|
||||
|
||||
n_points_mouth = numel(brow_ids);
|
||||
|
||||
M_mouth = reshape(M_mouth, n_points_mouth, 3);
|
||||
|
||||
% work out the translation and rotation needed
|
||||
[ R, T ] = AlignShapesKabsch(M_mouth, M_mouth_full);
|
||||
|
||||
% Transform the wild one to be in the same reference as the Multi-PIE one
|
||||
M_aligned = (R * M_mouth')';
|
||||
|
||||
M_aligned = M_aligned(:);
|
||||
V_aligned = V;
|
||||
|
||||
% need to align the principal components as well
|
||||
for i=1:size(V,2)
|
||||
|
||||
V_aligned_pie_curr = (R * reshape(V(:,i), n_points_mouth, 3)')';
|
||||
V_aligned(:,i) = V_aligned_pie_curr(:);
|
||||
|
||||
end
|
||||
|
||||
V = V_aligned;
|
||||
M = M_aligned;
|
||||
|
||||
save('pdm_10_brows.mat', 'E', 'M', 'V');
|
||||
|
||||
writePDM(V, E, M, 'pdm_10_brows.txt');
|
||||
|
||||
% also save this to model location
|
||||
if(exist('../../models/pdm/', 'file'))
|
||||
save('../../models/pdm/pdm_10_brows.mat', 'E', 'M', 'V');
|
||||
end
|
||||
@@ -0,0 +1,118 @@
|
||||
clear;
|
||||
|
||||
addpath('../PDM_helpers/');
|
||||
|
||||
%% Create the PDM using PCA, from the recovered 3D data
|
||||
clear
|
||||
load('Torr_wild');
|
||||
|
||||
% need to still perform procrustes though
|
||||
|
||||
x = P3(1:end/3,:);
|
||||
y = P3(end/3+1:2*end/3,:);
|
||||
|
||||
% To make sure that PDM faces the right way (positive Z towards the screen)
|
||||
z = -P3(2*end/3+1:end,:);
|
||||
|
||||
inner_ids = 18:68;
|
||||
|
||||
%%
|
||||
[ normX, normY, normZ, meanShape, Transform ] = ProcrustesAnalysis3D(x,y,z, true);
|
||||
|
||||
normX = normX(:, inner_ids);
|
||||
normY = normY(:, inner_ids);
|
||||
normZ = normZ(:, inner_ids);
|
||||
meanShape = meanShape(inner_ids,:);
|
||||
% make it zero centered now?
|
||||
offsets = mean(meanShape);
|
||||
|
||||
normX = normX - offsets(1);
|
||||
normY = normY - offsets(1);
|
||||
normZ = normZ - offsets(1);
|
||||
|
||||
observations = [normX normY normZ];
|
||||
|
||||
[princComp, score, eigenVals] = princomp(observations,'econ');
|
||||
% Keeping most variation
|
||||
totalSum = sum(eigenVals);
|
||||
count = numel(eigenVals);
|
||||
for i=1:numel(eigenVals)
|
||||
if ((sum(eigenVals(1:i)) / totalSum) >= 0.999)
|
||||
count = i;
|
||||
break;
|
||||
end
|
||||
end
|
||||
|
||||
load('pdm_68_multi_pie.mat', 'M');
|
||||
M_full = M;
|
||||
|
||||
V = princComp(:,1:count);
|
||||
E = eigenVals(1:count);
|
||||
M = meanShape(:);
|
||||
|
||||
% Now normalise it to have actual world scale
|
||||
lPupil = [(M(20) + M(23))/2; (M(20 + 51) + M(23 + 51))/2];
|
||||
rPupil = [(M(26) + M(29))/2; (M(26 + 51) + M(29 + 51))/2];
|
||||
|
||||
dist = norm(lPupil - rPupil,2);
|
||||
|
||||
% average human interocular distance is 65mm
|
||||
scaling = 65 / dist;
|
||||
|
||||
% normalise the mean values as well
|
||||
M(1:end/3) = M(1:end/3) - mean(M(1:end/3));
|
||||
M(end/3+1:2*end/3) = M(end/3+1:2*end/3) - mean(M(end/3+1:2*end/3));
|
||||
M(2*end/3+1:end) = M(2*end/3+1:end) - mean(M(2*end/3+1:end));
|
||||
|
||||
M = M * scaling;
|
||||
E = E * scaling .^ 2;
|
||||
|
||||
% orthonormalise V
|
||||
scalingV = sqrt(sum(V.^2));
|
||||
V = V ./ repmat(scalingV, numel(M),1);
|
||||
|
||||
E = E .* (scalingV') .^ 2;
|
||||
|
||||
%% Also align the model to a Multi-PIE one for accurate head orientation
|
||||
% also align the mean shape model (an aligned 68 point PDM from Multi-PIE dataset)
|
||||
M_inner = M;
|
||||
|
||||
load('pdm_68_multi_pie.mat', 'M');
|
||||
M_align = M;
|
||||
|
||||
n_points = numel(M)/3;
|
||||
M_inner_full = reshape(M_align, n_points,3);
|
||||
M_inner_full = M_inner_full(inner_ids, :);
|
||||
|
||||
n_points_mouth = numel(inner_ids);
|
||||
|
||||
M_inner = reshape(M_inner, n_points_mouth, 3);
|
||||
|
||||
% work out the translation and rotation needed
|
||||
[ R, T ] = AlignShapesKabsch(M_inner, M_inner_full);
|
||||
|
||||
% Transform the wild one to be in the same reference as the Multi-PIE one
|
||||
M_aligned = (R * M_inner')';
|
||||
|
||||
M_aligned = M_aligned(:);
|
||||
V_aligned = V;
|
||||
|
||||
% need to align the principal components as well
|
||||
for i=1:size(V,2)
|
||||
|
||||
V_aligned_pie_curr = (R * reshape(V(:,i), n_points_mouth, 3)')';
|
||||
V_aligned(:,i) = V_aligned_pie_curr(:);
|
||||
|
||||
end
|
||||
|
||||
V = V_aligned;
|
||||
M = M_aligned;
|
||||
|
||||
save('pdm_51_inner.mat', 'E', 'M', 'V');
|
||||
|
||||
writePDM(V, E, M, 'pdm_51_inner.txt');
|
||||
|
||||
% also save this to model location
|
||||
if(exist('../../models/pdm/', 'file'))
|
||||
save('../../models/pdm/pdm_51_inner.mat', 'E', 'M', 'V');
|
||||
end
|
||||
@@ -0,0 +1,122 @@
|
||||
clear;
|
||||
|
||||
addpath('../PDM_helpers/');
|
||||
|
||||
%% Create the PDM using PCA, from the recovered 3D data
|
||||
clear
|
||||
load('Torr_wild');
|
||||
|
||||
% need to still perform procrustes though
|
||||
|
||||
x = P3(1:end/3,:);
|
||||
y = P3(end/3+1:2*end/3,:);
|
||||
|
||||
% To make sure that PDM faces the right way (positive Z towards the screen)
|
||||
z = -P3(2*end/3+1:end,:);
|
||||
|
||||
mouth_ids = 49:68;
|
||||
|
||||
%%
|
||||
[ normX, normY, normZ, meanShape, Transform ] = ProcrustesAnalysis3D(x,y,z, true);
|
||||
|
||||
normX = normX(:, mouth_ids);
|
||||
normY = normY(:, mouth_ids);
|
||||
normZ = normZ(:, mouth_ids);
|
||||
meanShape = meanShape(mouth_ids,:);
|
||||
% make it zero centered now?
|
||||
offsets = mean(meanShape);
|
||||
|
||||
normX = normX - offsets(1);
|
||||
normY = normY - offsets(1);
|
||||
normZ = normZ - offsets(1);
|
||||
|
||||
observations = [normX normY normZ];
|
||||
|
||||
[princComp, score, eigenVals] = princomp(observations,'econ');
|
||||
% Keeping most variation
|
||||
totalSum = sum(eigenVals);
|
||||
count = numel(eigenVals);
|
||||
for i=1:numel(eigenVals)
|
||||
if ((sum(eigenVals(1:i)) / totalSum) >= 0.999)
|
||||
count = i;
|
||||
break;
|
||||
end
|
||||
end
|
||||
|
||||
load('pdm_68_multi_pie.mat', 'M');
|
||||
M_full = M;
|
||||
|
||||
V = princComp(:,1:count);
|
||||
E = eigenVals(1:count);
|
||||
M = meanShape(:);
|
||||
|
||||
left_corner = [M(1); M(1+20)];
|
||||
right_corner = [M(7); M(7+20)];
|
||||
|
||||
dist_norm = norm(left_corner - right_corner,2);
|
||||
|
||||
left_corner_full = [M_full(49); M_full(49+68)];
|
||||
right_corner_full = [M_full(55); M_full(55+68)];
|
||||
|
||||
dist_norm_full = norm(left_corner_full - right_corner_full,2);
|
||||
|
||||
% average human interocular distance is 65mm
|
||||
scaling = dist_norm_full / dist_norm;
|
||||
|
||||
% normalise the mean values as well
|
||||
M(1:end/3) = M(1:end/3) - mean(M(1:end/3));
|
||||
M(end/3+1:2*end/3) = M(end/3+1:2*end/3) - mean(M(end/3+1:2*end/3));
|
||||
M(2*end/3+1:end) = M(2*end/3+1:end) - mean(M(2*end/3+1:end));
|
||||
|
||||
M = M * scaling;
|
||||
E = E * scaling .^ 2;
|
||||
|
||||
% orthonormalise V
|
||||
scalingV = sqrt(sum(V.^2));
|
||||
V = V ./ repmat(scalingV, numel(M),1);
|
||||
|
||||
E = E .* (scalingV') .^ 2;
|
||||
|
||||
%% Also align the model to a Multi-PIE one for accurate head orientation
|
||||
% also align the mean shape model (an aligned 68 point PDM from Multi-PIE dataset)
|
||||
M_mouth = M;
|
||||
|
||||
load('pdm_68_multi_pie.mat', 'M');
|
||||
M_align = M;
|
||||
|
||||
n_points = numel(M)/3;
|
||||
M_mouth_full = reshape(M_align, n_points,3);
|
||||
M_mouth_full = M_mouth_full(mouth_ids, :);
|
||||
|
||||
n_points_mouth = numel(mouth_ids);
|
||||
|
||||
M_mouth = reshape(M_mouth, n_points_mouth, 3);
|
||||
|
||||
% work out the translation and rotation needed
|
||||
[ R, T ] = AlignShapesKabsch(M_mouth, M_mouth_full);
|
||||
|
||||
% Transform the wild one to be in the same reference as the Multi-PIE one
|
||||
M_aligned = (R * M_mouth')';
|
||||
|
||||
M_aligned = M_aligned(:);
|
||||
V_aligned = V;
|
||||
|
||||
% need to align the principal components as well
|
||||
for i=1:size(V,2)
|
||||
|
||||
V_aligned_pie_curr = (R * reshape(V(:,i), n_points_mouth, 3)')';
|
||||
V_aligned(:,i) = V_aligned_pie_curr(:);
|
||||
|
||||
end
|
||||
|
||||
V = V_aligned;
|
||||
M = M_aligned;
|
||||
|
||||
save('pdm_20_mouth.mat', 'E', 'M', 'V');
|
||||
|
||||
writePDM(V, E, M, 'pdm_20_mouth.txt');
|
||||
|
||||
% also save this to model location
|
||||
if(exist('../../models/pdm/', 'file'))
|
||||
save('../../models/pdm/pdm_20_mouth.mat', 'E', 'M', 'V');
|
||||
end
|
||||
@@ -0,0 +1,104 @@
|
||||
clear;
|
||||
|
||||
addpath('../PDM_helpers/');
|
||||
|
||||
Collect_wild_annotations;
|
||||
|
||||
Reconstruct_Torresani;
|
||||
|
||||
%% Create the PDM using PCA, from the recovered 3D data
|
||||
clear
|
||||
load('Torr_wild');
|
||||
|
||||
% need to still perform procrustes though
|
||||
|
||||
x = P3(1:end/3,:);
|
||||
y = P3(end/3+1:2*end/3,:);
|
||||
|
||||
% To make sure that PDM faces the right way (positive Z towards the screen)
|
||||
z = -P3(2*end/3+1:end,:);
|
||||
|
||||
[ normX, normY, normZ, meanShape, Transform ] = ProcrustesAnalysis3D(x,y,z, true);
|
||||
observations = [normX normY normZ];
|
||||
|
||||
[princComp, score, eigenVals] = princomp(observations,'econ');
|
||||
% Keeping most variation
|
||||
totalSum = sum(eigenVals);
|
||||
count = numel(eigenVals);
|
||||
for i=1:numel(eigenVals)
|
||||
if ((sum(eigenVals(1:i)) / totalSum) >= 0.999)
|
||||
count = i;
|
||||
break;
|
||||
end
|
||||
end
|
||||
|
||||
V = princComp(:,1:count);
|
||||
E = eigenVals(1:count);
|
||||
M = meanShape(:);
|
||||
|
||||
% Now normalise it to have actual world scale
|
||||
lPupil = [(M(37) + M(40))/2; (M(37 + 68) + M(40 + 68))/2];
|
||||
rPupil = [(M(43) + M(46))/2; (M(43 + 68) + M(46 + 68))/2];
|
||||
|
||||
dist = norm(lPupil - rPupil,2);
|
||||
|
||||
% average human interocular distance is 65mm
|
||||
scaling = 65 / dist;
|
||||
|
||||
% normalise the mean values as well
|
||||
M(1:end/3) = M(1:end/3) - mean(M(1:end/3));
|
||||
M(end/3+1:2*end/3) = M(end/3+1:2*end/3) - mean(M(end/3+1:2*end/3));
|
||||
M(2*end/3+1:end) = M(2*end/3+1:end) - mean(M(2*end/3+1:end));
|
||||
|
||||
M = M * scaling;
|
||||
E = E * scaling .^ 2;
|
||||
|
||||
% orthonormalise V
|
||||
scalingV = sqrt(sum(V.^2));
|
||||
V = V ./ repmat(scalingV, numel(M),1);
|
||||
|
||||
E = E .* (scalingV') .^ 2;
|
||||
|
||||
%% Also align the model to a Multi-PIE one for accurate head orientation
|
||||
% also align the mean shape model (an aligned 68 point PDM from Multi-PIE dataset)
|
||||
M_wild = M;
|
||||
|
||||
load('pdm_68_multi_pie.mat', 'M');
|
||||
M_align = M;
|
||||
|
||||
n_points = numel(M)/3;
|
||||
|
||||
M_wild = reshape(M_wild, n_points, 3);
|
||||
|
||||
% work out the translation and rotation needed
|
||||
[ R, T ] = AlignShapesKabsch(M_wild, reshape(M_align, n_points,3));
|
||||
|
||||
% Transform the wild one to be in the same reference as the Multi-PIE one
|
||||
M_aligned = (R * M_wild')';
|
||||
|
||||
M_aligned(:,1) = M_aligned(:,1) + T(1);
|
||||
M_aligned(:,2) = M_aligned(:,2) + T(2);
|
||||
M_aligned(:,3) = M_aligned(:,3) + T(3);
|
||||
|
||||
M_aligned = M_aligned(:);
|
||||
V_aligned = V;
|
||||
|
||||
% need to align the principal components as well
|
||||
for i=1:size(V,2)
|
||||
|
||||
V_aligned_pie_curr = (R * reshape(V(:,i), n_points, 3)')';
|
||||
V_aligned(:,i) = V_aligned_pie_curr(:);
|
||||
|
||||
end
|
||||
|
||||
V = V_aligned;
|
||||
M = M_aligned;
|
||||
|
||||
save('pdm_68_aligned_wild.mat', 'E', 'M', 'V');
|
||||
|
||||
writePDM(V, E, M, 'pdm_68_aligned_wild.txt');
|
||||
|
||||
% also save this to model location
|
||||
if(exist('../../models/pdm/', 'file'))
|
||||
save('../../models/pdm/pdm_68_aligned_wild.mat', 'E', 'M', 'V');
|
||||
end
|
||||
@@ -0,0 +1,155 @@
|
||||
clear;
|
||||
|
||||
addpath('../PDM_helpers/');
|
||||
|
||||
%% Create the PDM using PCA, from the recovered 3D data
|
||||
clear
|
||||
load('Torr_wild');
|
||||
|
||||
% need to still perform procrustes though
|
||||
|
||||
x = P3(1:end/3,:);
|
||||
y = P3(end/3+1:2*end/3,:);
|
||||
|
||||
% To make sure that PDM faces the right way (positive Z towards the screen)
|
||||
z = -P3(2*end/3+1:end,:);
|
||||
|
||||
%% Replacing and augmenting eye models with synth
|
||||
num_samples = size(x, 1);
|
||||
to_augment_ratio = 0.2;
|
||||
rng(0);
|
||||
% Take half of the samples and replace either their left or right eye with
|
||||
% a synthetic one from an eye PDM but with same alignment and scaling
|
||||
to_augment = randperm(num_samples);
|
||||
to_augment = to_augment(1:round(end * to_augment_ratio));
|
||||
|
||||
left_eye_inds = [37,38,39,40,41,42];
|
||||
right_eye_inds = [43,44,45,46,47,48];
|
||||
|
||||
load('pdm_l_eye.mat');
|
||||
M_l_eye = M;
|
||||
V_l_eye = V;
|
||||
E_l_eye = E;
|
||||
|
||||
load('pdm_r_eye.mat');
|
||||
M_r_eye = M;
|
||||
V_r_eye = V;
|
||||
E_r_eye = E;
|
||||
num_points = numel(M) / 3;
|
||||
|
||||
for i = to_augment
|
||||
|
||||
shape_3D = cat(1, x(i,:), y(i,:), z(i,:))';
|
||||
|
||||
eye_shape_l = shape_3D(left_eye_inds, :);
|
||||
eye_shape_r = shape_3D(right_eye_inds, :);
|
||||
|
||||
[ R_l, T_l ] = AlignShapesWithScale ( reshape(M_l_eye, num_points, 3), eye_shape_l );
|
||||
[ R_r, T_r ] = AlignShapesWithScale ( reshape(M_r_eye, num_points, 3), eye_shape_r );
|
||||
|
||||
params_left = randn(size(E)) .* sqrt(E);
|
||||
params_right = params_left;
|
||||
% Third of samples with left and right eye done independently
|
||||
if(mod(i,3) == 0)
|
||||
params_right = randn(size(E)) .* sqrt(E);
|
||||
end
|
||||
shape_l_unaligned = M_l_eye + V_l_eye * params_left;
|
||||
shape_r_unaligned = M_r_eye + V_r_eye * params_right;
|
||||
|
||||
shape_l = (R_l * reshape(shape_l_unaligned, num_points, 3)' + repmat(T_l', 1, num_points))';
|
||||
shape_r = (R_r * reshape(shape_r_unaligned, num_points, 3)' + repmat(T_r', 1, num_points))';
|
||||
|
||||
shape_3D(left_eye_inds, :) = shape_l;
|
||||
shape_3D(right_eye_inds, :) = shape_r;
|
||||
|
||||
x(i,:) = shape_3D(:,1);
|
||||
y(i,:) = shape_3D(:,2);
|
||||
z(i,:) = shape_3D(:,3);
|
||||
end
|
||||
|
||||
%%
|
||||
|
||||
[ normX, normY, normZ, meanShape, Transform ] = ProcrustesAnalysis3D(x,y,z, true);
|
||||
observations = [normX normY normZ];
|
||||
|
||||
[princComp, score, eigenVals] = princomp(observations,'econ');
|
||||
% Keeping most variation
|
||||
totalSum = sum(eigenVals);
|
||||
count = numel(eigenVals);
|
||||
for i=1:numel(eigenVals)
|
||||
if ((sum(eigenVals(1:i)) / totalSum) >= 0.999)
|
||||
count = i;
|
||||
break;
|
||||
end
|
||||
end
|
||||
|
||||
V = princComp(:,1:count);
|
||||
E = eigenVals(1:count);
|
||||
M = meanShape(:);
|
||||
|
||||
% Now normalise it to have actual world scale
|
||||
lPupil = [(M(37) + M(40))/2; (M(37 + 68) + M(40 + 68))/2];
|
||||
rPupil = [(M(43) + M(46))/2; (M(43 + 68) + M(46 + 68))/2];
|
||||
|
||||
dist = norm(lPupil - rPupil,2);
|
||||
|
||||
% average human interocular distance is 65mm
|
||||
scaling = 65 / dist;
|
||||
|
||||
% normalise the mean values as well
|
||||
M(1:end/3) = M(1:end/3) - mean(M(1:end/3));
|
||||
M(end/3+1:2*end/3) = M(end/3+1:2*end/3) - mean(M(end/3+1:2*end/3));
|
||||
M(2*end/3+1:end) = M(2*end/3+1:end) - mean(M(2*end/3+1:end));
|
||||
|
||||
M = M * scaling;
|
||||
E = E * scaling .^ 2;
|
||||
|
||||
% orthonormalise V
|
||||
scalingV = sqrt(sum(V.^2));
|
||||
V = V ./ repmat(scalingV, numel(M),1);
|
||||
|
||||
E = E .* (scalingV') .^ 2;
|
||||
|
||||
%% Also align the model to a Multi-PIE one for accurate head orientation
|
||||
% also align the mean shape model (an aligned 68 point PDM from Multi-PIE dataset)
|
||||
M_wild = M;
|
||||
|
||||
load('pdm_68_multi_pie.mat', 'M');
|
||||
M_align = M;
|
||||
|
||||
n_points = numel(M)/3;
|
||||
|
||||
M_wild = reshape(M_wild, n_points, 3);
|
||||
|
||||
% work out the translation and rotation needed
|
||||
[ R, T ] = AlignShapesKabsch(M_wild, reshape(M_align, n_points,3));
|
||||
|
||||
% Transform the wild one to be in the same reference as the Multi-PIE one
|
||||
M_aligned = (R * M_wild')';
|
||||
|
||||
M_aligned(:,1) = M_aligned(:,1) + T(1);
|
||||
M_aligned(:,2) = M_aligned(:,2) + T(2);
|
||||
M_aligned(:,3) = M_aligned(:,3) + T(3);
|
||||
|
||||
M_aligned = M_aligned(:);
|
||||
V_aligned = V;
|
||||
|
||||
% need to align the principal components as well
|
||||
for i=1:size(V,2)
|
||||
|
||||
V_aligned_pie_curr = (R * reshape(V(:,i), n_points, 3)')';
|
||||
V_aligned(:,i) = V_aligned_pie_curr(:);
|
||||
|
||||
end
|
||||
|
||||
V = V_aligned;
|
||||
M = M_aligned;
|
||||
|
||||
save('pdm_68_aligned_wild_eyes.mat', 'E', 'M', 'V');
|
||||
|
||||
writePDM(V, E, M, 'pdm_68_aligned_wild_eyes.txt');
|
||||
|
||||
% also save this to model location
|
||||
if(exist('../../models/pdm/', 'file'))
|
||||
save('../../models/pdm/pdm_68_aligned_wild_eyes.mat', 'E', 'M', 'V');
|
||||
end
|
||||
@@ -0,0 +1,21 @@
|
||||
clear
|
||||
|
||||
load('wild_68_pts');
|
||||
|
||||
%% Perform NRSFM by Torresani
|
||||
addpath('../nrsfm-em');
|
||||
% (T is the number of frames, J is the number of points)
|
||||
|
||||
J = size(all_pts,2);
|
||||
T = size(all_pts,1)/2;
|
||||
|
||||
use_lds = 0; % not modeling a linear dynamic system here
|
||||
max_em_iter = 100;
|
||||
tol = 0.001;
|
||||
K = 25; % number of deformation shapes
|
||||
|
||||
MD = zeros(T,J);
|
||||
|
||||
[P3, S_hat, V, RO, Tr, Z] = em_sfm(all_pts, MD, K, use_lds, tol, max_em_iter);
|
||||
|
||||
save('Torr_wild', 'P3', 'S_hat', 'V', 'RO', 'Tr', 'Z');
|
||||
Binary file not shown.
Binary file not shown.
@@ -0,0 +1,73 @@
|
||||
# The mean values of the components (in mm)
|
||||
30
|
||||
1
|
||||
6
|
||||
-59.311715
|
||||
-49.656374
|
||||
-36.519342
|
||||
-23.114109
|
||||
-11.102775
|
||||
11.746394
|
||||
24.272337
|
||||
36.926413
|
||||
49.187656
|
||||
57.571516
|
||||
7.522611
|
||||
-1.285248
|
||||
-4.120274
|
||||
-2.909300
|
||||
1.505526
|
||||
0.953260
|
||||
-3.468254
|
||||
-4.431070
|
||||
-1.204565
|
||||
7.437314
|
||||
12.922686
|
||||
6.081795
|
||||
-0.356387
|
||||
-6.878823
|
||||
-11.698406
|
||||
-11.384541
|
||||
-6.725768
|
||||
-0.455801
|
||||
6.014541
|
||||
12.480705
|
||||
# The principal components (eigenvectors) of identity or combined identity and expression model
|
||||
30
|
||||
17
|
||||
6
|
||||
-0.115855 0.017675 0.112381 -0.224780 0.190237 0.268706 -0.202754 -0.251027 0.118283 -0.011289 0.051905 -0.350571 0.432091 -0.155808 -0.136110 -0.312021 -0.000891
|
||||
-0.126893 0.076077 0.174580 -0.213429 -0.051257 0.371169 -0.076506 -0.203451 -0.127792 0.124594 -0.077901 -0.097071 0.121576 -0.002685 -0.027058 0.071460 -0.182244
|
||||
-0.067791 0.100813 0.162427 -0.272724 -0.096811 0.298594 0.122696 -0.020401 -0.103738 0.138066 0.020532 -0.017299 -0.085616 -0.057392 -0.073484 0.242107 -0.106554
|
||||
0.005156 0.105515 0.109714 -0.335677 -0.045955 0.188574 0.293137 0.140266 -0.073797 0.087543 0.119352 0.015805 -0.040730 0.015911 0.036457 0.040209 -0.027342
|
||||
0.077455 0.126081 0.063141 -0.328804 0.019409 0.051795 0.417376 0.280580 -0.143234 0.095648 0.269801 0.135384 -0.003168 0.026857 0.192486 -0.156261 0.263948
|
||||
-0.116213 0.152100 -0.062003 0.348108 -0.040849 0.209698 -0.067181 -0.134663 0.017338 0.096037 0.525527 0.074738 0.048981 -0.002296 0.054737 0.426044 -0.096395
|
||||
-0.049418 0.122147 -0.126200 0.342430 -0.009263 0.269805 0.039364 -0.068249 0.009306 0.088701 0.263921 -0.077076 -0.059729 -0.064601 0.133011 -0.056771 0.108044
|
||||
0.038429 0.092866 -0.188981 0.263755 0.012096 0.266189 0.169712 0.010751 0.119147 0.024392 0.081671 -0.187201 -0.075470 0.107591 0.062809 -0.324099 0.058920
|
||||
0.112376 0.025656 -0.216436 0.193946 -0.016660 0.232772 0.282141 0.158978 0.136351 0.002089 -0.118733 -0.142104 0.097955 0.059410 -0.154689 -0.194049 -0.031804
|
||||
0.114188 -0.130170 -0.174169 0.191762 -0.195103 0.190258 0.279139 0.281720 -0.066004 0.123975 -0.396257 0.053729 0.361327 -0.177745 -0.057390 0.168402 -0.201155
|
||||
0.288166 -0.194473 -0.015827 0.009077 0.418086 -0.022613 0.117649 0.059021 -0.224545 -0.403229 0.317470 0.048014 0.232258 -0.262646 -0.058026 0.096080 -0.034383
|
||||
0.225211 -0.196106 0.090749 0.095635 0.179941 0.163486 -0.067404 -0.027071 -0.346387 -0.173432 0.018340 -0.005431 0.045333 0.110366 0.167530 -0.165334 -0.041722
|
||||
0.188859 -0.228777 0.178728 0.115005 -0.055599 0.265779 -0.136571 0.000687 -0.317056 -0.035217 -0.164134 -0.059464 -0.270511 0.096234 0.046649 0.011434 -0.114439
|
||||
0.187690 -0.194656 0.239892 0.089220 -0.158710 0.230462 -0.144633 0.079202 -0.051936 -0.040858 -0.051375 -0.107937 -0.178707 0.016844 -0.095587 0.155152 0.237757
|
||||
0.213731 -0.118216 0.260832 -0.018525 -0.203527 0.090306 -0.081522 0.183138 0.298107 -0.148661 0.144778 -0.086354 0.075695 0.359077 -0.003220 0.123004 0.153235
|
||||
0.213879 -0.005454 0.292498 0.027878 -0.181921 -0.110158 -0.046454 0.179035 0.346801 -0.019625 0.186584 -0.072762 0.237652 0.127243 -0.090293 -0.142916 -0.125680
|
||||
0.214223 0.083728 0.299734 0.137942 -0.134027 -0.095215 -0.076392 0.047619 0.056303 0.227987 0.094137 0.167932 0.120995 -0.345791 -0.077045 -0.080997 -0.124563
|
||||
0.223947 0.142542 0.265080 0.155541 -0.040785 -0.104679 -0.011702 -0.101953 -0.083393 0.293108 -0.009030 0.178206 -0.014665 -0.255405 0.133083 -0.123141 0.002706
|
||||
0.289425 0.186506 0.150883 0.087257 0.150744 -0.025223 0.097930 -0.291791 0.016561 0.179223 -0.158765 0.005175 -0.071000 0.037704 0.240156 -0.213779 -0.007066
|
||||
0.377715 0.228925 0.027876 -0.035904 0.329561 -0.004865 0.296091 -0.344762 0.271084 -0.058106 -0.168470 -0.037769 -0.107151 0.170890 -0.234930 0.364336 -0.043925
|
||||
0.235989 -0.283437 -0.237426 -0.155858 0.192605 -0.065912 -0.164298 0.130180 0.108647 0.509874 0.063963 -0.413621 -0.076361 -0.176039 0.127326 0.201274 0.230766
|
||||
0.092079 -0.224911 -0.190272 -0.113577 0.206179 0.030213 -0.144149 0.082893 0.103292 0.304112 0.074765 0.230037 0.121414 0.177928 0.081006 0.034475 -0.335870
|
||||
-0.026560 -0.187708 -0.043189 -0.027055 0.187650 0.162367 -0.077148 -0.007240 0.063007 0.228144 0.082818 0.402834 -0.144065 0.307619 -0.251945 -0.251016 -0.155876
|
||||
-0.121468 -0.157968 0.088559 0.042820 0.191345 0.237663 -0.018577 0.014077 0.185760 0.047000 -0.039870 0.404833 -0.023480 -0.172314 -0.283046 -0.017858 0.427597
|
||||
-0.209385 -0.115827 0.193175 0.025027 0.227926 0.213845 0.022273 0.112581 0.457201 -0.200956 -0.228230 0.126375 -0.090472 -0.255162 0.528110 0.087333 -0.035752
|
||||
-0.233912 0.055439 0.289612 0.137137 0.344491 -0.103428 0.091358 0.373419 0.011601 0.057748 0.088048 -0.302169 -0.307677 0.014112 -0.079806 -0.043797 -0.400862
|
||||
-0.163184 0.194211 0.196784 0.204193 0.265118 -0.062938 -0.053343 0.247213 -0.169242 0.123571 -0.145108 -0.053310 0.149120 -0.007818 -0.342120 0.109687 0.175742
|
||||
-0.045597 0.261653 0.064937 0.093595 0.217729 0.009227 -0.160526 0.160531 -0.152289 0.128235 -0.161239 -0.010860 0.166935 0.315001 0.164770 0.034697 0.327473
|
||||
0.106052 0.338850 -0.094366 -0.061863 0.088697 0.088872 -0.290121 0.203536 -0.028585 -0.078035 -0.077293 0.157792 0.273036 0.186534 0.258076 0.140811 -0.109532
|
||||
0.282952 0.410848 -0.266993 -0.170966 -0.022985 0.190222 -0.373867 0.268300 0.077488 -0.189009 -0.012222 0.046526 -0.337083 -0.288010 -0.187752 -0.113879 -0.067014
|
||||
# The variances of the components (eigenvalues) of identity or combined identity and expression model
|
||||
1
|
||||
17
|
||||
6
|
||||
164.070338 100.330032 77.401188 56.832204 40.964240 19.493408 16.009887 12.486359 7.371305 6.830343 4.189282 1.404434 0.923250 0.609166 0.436453 0.301253 0.194100
|
||||
Binary file not shown.
@@ -0,0 +1,133 @@
|
||||
# The mean values of the components (in mm)
|
||||
60
|
||||
1
|
||||
6
|
||||
-27.309204
|
||||
-16.673318
|
||||
-6.578808
|
||||
-0.031483
|
||||
7.373878
|
||||
17.055620
|
||||
26.162515
|
||||
17.182703
|
||||
7.856005
|
||||
-0.084508
|
||||
-7.325182
|
||||
-17.297781
|
||||
-23.090940
|
||||
-6.802599
|
||||
-0.091174
|
||||
7.412170
|
||||
22.173029
|
||||
7.400285
|
||||
-0.232695
|
||||
-7.098512
|
||||
-1.302487
|
||||
-6.404651
|
||||
-8.882681
|
||||
-7.233405
|
||||
-8.835055
|
||||
-6.134308
|
||||
-1.601907
|
||||
6.682756
|
||||
10.199776
|
||||
10.945969
|
||||
10.339322
|
||||
6.955241
|
||||
-1.078341
|
||||
-3.026630
|
||||
-2.432167
|
||||
-3.121466
|
||||
-1.236794
|
||||
1.729259
|
||||
2.535530
|
||||
1.902040
|
||||
13.567256
|
||||
0.581842
|
||||
-5.720740
|
||||
-6.631154
|
||||
-5.739922
|
||||
1.094403
|
||||
12.948823
|
||||
2.509050
|
||||
-4.340145
|
||||
-5.300401
|
||||
-4.281023
|
||||
2.203722
|
||||
11.242974
|
||||
-3.745466
|
||||
-4.899801
|
||||
-3.792054
|
||||
10.632832
|
||||
-3.147113
|
||||
-4.282539
|
||||
-2.900542
|
||||
# The principal components (eigenvectors) of identity or combined identity and expression model
|
||||
60
|
||||
20
|
||||
6
|
||||
-0.165214 0.138338 -0.098396 -0.182077 -0.036920 0.196885 -0.112468 0.062690 -0.068589 0.151029 -0.304435 -0.187718 -0.094117 -0.083526 -0.015422 0.172666 -0.028301 -0.112210 -0.145189 -0.005009
|
||||
-0.126987 0.073810 -0.007203 -0.114765 0.008483 0.211387 -0.105068 0.009514 -0.032689 -0.006602 -0.117184 0.055068 -0.086664 0.018451 -0.021731 0.105376 -0.077804 0.069339 0.207213 0.061348
|
||||
-0.042344 0.024330 -0.007160 -0.040110 0.054025 0.202127 -0.090701 -0.044548 -0.011013 -0.154445 -0.045996 0.132794 0.021742 0.201215 0.130358 0.049175 -0.222597 0.099316 0.098293 0.064004
|
||||
0.003891 -0.001155 0.003515 -0.003888 -0.025761 0.038245 -0.128850 -0.043337 0.002551 -0.041481 -0.067797 0.008049 0.050227 0.145299 0.137046 0.000959 -0.155304 0.057728 0.136098 -0.055146
|
||||
0.060204 -0.044485 0.028127 0.018733 -0.125445 -0.149271 -0.158316 -0.003378 -0.012674 0.111552 -0.095160 -0.204882 0.012177 0.167283 0.086429 0.015356 -0.204352 0.076149 0.185512 -0.004423
|
||||
0.132414 -0.087891 0.023702 0.074097 -0.210859 -0.129062 -0.144445 -0.000314 0.037166 0.049620 -0.170658 0.018315 -0.054434 -0.021413 -0.037237 -0.010009 -0.092485 -0.005519 0.044136 0.006572
|
||||
0.159973 -0.161485 0.075196 0.121630 -0.277616 -0.000003 -0.098117 0.016514 0.027402 -0.065585 -0.098367 0.401008 -0.021273 -0.001244 -0.059493 0.153559 0.017401 -0.265928 -0.203277 -0.055127
|
||||
0.134339 -0.092107 0.015163 0.060664 -0.293648 -0.058517 -0.193437 0.020743 0.054338 0.061998 -0.080932 0.042332 0.003617 -0.079148 -0.097813 -0.040087 0.138819 0.077572 -0.077943 -0.004550
|
||||
0.061524 -0.054792 0.001422 -0.009066 -0.246421 -0.057970 -0.248311 0.028463 0.031433 0.100672 0.051067 -0.196588 0.084177 -0.008046 -0.084231 -0.116763 0.151484 0.072879 0.051415 0.041114
|
||||
-0.000904 -0.012828 -0.012623 -0.032618 -0.133137 0.129187 -0.219322 -0.000064 0.048106 -0.053279 0.078892 -0.004008 0.106879 -0.013008 -0.036618 -0.189677 0.184362 0.043216 0.074391 0.036553
|
||||
-0.055834 0.009987 -0.018853 -0.063349 -0.054161 0.294646 -0.207149 0.007256 0.020483 -0.139071 0.110680 0.134791 0.091089 0.009279 -0.023321 -0.159300 0.098352 0.057060 0.062556 0.041476
|
||||
-0.143429 0.063622 -0.020066 -0.135267 -0.051886 0.279550 -0.188802 0.042156 -0.000222 0.007284 -0.064904 0.042402 -0.038245 -0.134157 -0.173434 -0.045077 0.162619 -0.013236 0.094182 0.097204
|
||||
-0.164957 0.140850 -0.104438 -0.192367 -0.099801 0.204798 -0.112534 0.029542 -0.010473 0.124158 -0.314390 -0.089466 -0.066191 -0.155595 -0.094322 0.197666 -0.026093 -0.171786 -0.135991 -0.065891
|
||||
-0.043385 0.020607 -0.017086 -0.033613 0.068484 0.212011 -0.139364 -0.029423 0.006118 -0.167088 0.021744 0.092548 0.046266 0.226600 0.104019 0.007327 -0.156935 0.039961 -0.073728 0.008618
|
||||
0.002969 -0.004663 -0.001380 0.000213 -0.020040 0.046675 -0.158368 -0.032203 0.023413 -0.062642 -0.019694 -0.013859 0.065324 0.164943 0.132424 -0.012187 -0.096348 -0.025338 -0.039500 -0.039641
|
||||
0.057634 -0.048651 0.022452 0.027305 -0.120552 -0.142154 -0.193425 0.004595 0.013431 0.092191 -0.046018 -0.232401 0.017817 0.192463 0.088429 0.001980 -0.149024 0.018052 -0.015598 -0.022181
|
||||
0.166057 -0.155216 0.088923 0.103196 -0.297425 0.009419 -0.072244 0.069074 -0.020015 -0.046613 -0.088876 0.341200 -0.094173 -0.032241 0.029553 0.096727 -0.064822 -0.201811 0.124770 0.108857
|
||||
0.061711 -0.053620 0.008151 0.010580 -0.139611 -0.117541 -0.231305 0.028215 0.033461 0.105218 -0.003816 -0.242275 0.087275 0.168979 0.036062 -0.004422 -0.007056 0.059875 -0.142222 0.015443
|
||||
-0.000051 -0.010291 -0.008546 -0.010835 -0.039883 0.075465 -0.197283 -0.009065 0.044428 -0.050742 0.019328 -0.042687 0.129778 0.137582 0.084759 -0.078423 0.076894 0.022389 -0.125670 -0.036013
|
||||
-0.054251 0.015211 -0.019037 -0.040277 0.051132 0.235184 -0.179568 -0.009527 0.036643 -0.166700 0.058953 0.072856 0.113652 0.202300 0.072753 -0.047844 -0.008505 0.075833 -0.161318 -0.003104
|
||||
-0.117118 0.203894 -0.041094 0.109391 -0.137184 0.060799 -0.027204 -0.165541 0.302696 0.266142 0.251682 0.037832 -0.071214 -0.111438 0.062406 0.031708 -0.126158 0.095581 0.001912 -0.092178
|
||||
-0.136290 0.128312 0.110127 0.138673 -0.106760 0.100003 0.008324 0.134972 0.035183 0.023122 0.227144 -0.063203 -0.060541 -0.010547 0.000710 0.099622 0.091436 -0.155304 0.084842 0.050883
|
||||
-0.119535 0.090543 0.190827 0.146689 -0.069520 0.048896 -0.021264 0.268198 -0.154852 -0.023393 0.147493 -0.091208 -0.025496 0.028589 -0.064418 0.030925 0.108773 -0.027214 0.059608 -0.006907
|
||||
-0.121652 0.092003 0.182460 0.165002 -0.055652 0.007413 -0.001054 0.275066 -0.157740 -0.024372 0.059435 -0.112037 0.037738 0.093191 -0.018301 -0.005120 0.088542 0.012711 0.016992 0.007801
|
||||
-0.120667 0.096027 0.185093 0.157265 -0.021747 0.010923 0.009790 0.283755 -0.172288 -0.013184 0.011181 -0.061444 0.059456 0.133417 -0.059922 -0.091063 0.046852 -0.070944 0.059908 0.011668
|
||||
-0.139344 0.135119 0.101530 0.156911 -0.000782 -0.002797 0.086705 0.163796 -0.032404 0.041915 -0.091706 0.002948 0.101716 0.238055 -0.060332 -0.044009 0.177401 -0.146656 -0.045753 0.030878
|
||||
-0.122205 0.201711 -0.044720 0.148915 0.024646 -0.075754 0.066659 -0.100980 0.217465 0.255989 -0.202482 0.168588 0.197263 0.158509 -0.061798 -0.219756 0.030649 -0.055627 -0.214743 0.035437
|
||||
0.075966 0.189620 -0.164338 0.178415 0.024778 0.029777 0.082997 -0.119644 -0.033496 -0.044324 -0.307699 0.126508 0.115832 0.032790 -0.026536 -0.178844 0.120253 0.058184 0.339680 0.048642
|
||||
0.171269 0.172195 -0.222833 0.167783 -0.012430 0.009154 0.029608 -0.088405 -0.080788 -0.160437 -0.210014 -0.061813 0.000343 0.041509 -0.009968 0.050423 0.179128 0.079614 0.134192 -0.052075
|
||||
0.184449 0.163949 -0.225532 0.159700 -0.031285 -0.007983 -0.013325 -0.081786 -0.080491 -0.178183 -0.077742 -0.177989 -0.035773 0.022056 -0.031337 0.139994 0.136624 -0.014130 0.026403 -0.095971
|
||||
0.175166 0.163168 -0.226234 0.158860 -0.037138 0.025148 -0.038151 -0.112141 -0.055069 -0.203861 0.086416 -0.138912 -0.007856 0.025976 0.010887 0.174693 0.125283 -0.069140 -0.092362 -0.152360
|
||||
0.081701 0.171954 -0.167853 0.144460 -0.062239 0.062659 -0.076015 -0.175230 0.061535 -0.109617 0.350035 -0.033369 0.068365 -0.004124 0.071919 0.092104 0.102486 -0.211342 0.036673 0.025002
|
||||
-0.099243 0.187943 -0.012460 0.130958 -0.135446 0.062536 -0.019156 -0.154103 0.255364 0.199504 0.236757 -0.005349 -0.071191 -0.068761 -0.006979 0.128886 -0.124707 0.001938 0.188615 0.161965
|
||||
-0.136579 0.119726 0.116893 0.193986 -0.123871 -0.014572 -0.005930 0.047068 0.078813 -0.218378 -0.037452 0.032506 -0.037667 -0.235302 0.110313 0.074713 -0.150191 0.219429 -0.058809 -0.132775
|
||||
-0.131812 0.112981 0.125667 0.198457 -0.114171 -0.051228 0.018124 0.082502 0.038912 -0.208008 -0.109996 -0.003093 -0.011409 -0.191063 0.114530 0.001152 -0.109834 0.148087 -0.059075 -0.084447
|
||||
-0.138314 0.123890 0.106302 0.200754 -0.095531 -0.052098 0.053139 0.072025 0.051365 -0.196080 -0.183752 0.055611 0.030403 -0.116086 0.137609 0.000901 -0.176404 0.201225 -0.056097 -0.037470
|
||||
-0.102241 0.194776 -0.022325 0.164948 0.020658 -0.057896 0.062456 -0.101567 0.166055 0.177161 -0.145174 0.076312 0.184185 0.171013 -0.040175 -0.066336 -0.017244 -0.136124 -0.154641 0.157774
|
||||
0.168984 0.146858 -0.143228 0.129361 0.053077 0.084254 -0.046097 0.124540 -0.261892 0.200821 -0.051044 0.159245 -0.128653 -0.038895 -0.030591 -0.176560 -0.099498 0.180485 0.007082 0.092484
|
||||
0.181620 0.139462 -0.140905 0.123248 0.055152 0.053057 -0.089998 0.149301 -0.273534 0.199619 0.064442 0.023025 -0.152344 -0.043166 -0.027494 -0.089195 -0.181976 0.032106 -0.112558 0.071071
|
||||
0.172811 0.139611 -0.139514 0.119176 0.068143 0.071850 -0.104034 0.115039 -0.232227 0.166959 0.190007 0.070013 -0.125923 -0.028105 0.035670 -0.014323 -0.238995 -0.072535 -0.192671 -0.014436
|
||||
0.211817 -0.102382 0.130761 0.098762 -0.121867 0.327473 0.245143 -0.037055 0.013081 0.038818 -0.032146 -0.183385 0.376428 -0.100767 -0.376967 0.243645 -0.217240 0.043700 -0.000501 0.148479
|
||||
0.137399 0.049821 0.230437 -0.030529 -0.050402 0.164105 0.208789 -0.127676 -0.130675 0.012646 -0.029679 -0.021004 -0.139298 0.158657 0.383239 0.124091 0.096647 -0.110886 -0.176205 0.345885
|
||||
0.056389 0.137105 0.272979 -0.099404 -0.085052 0.014908 -0.011534 -0.217331 -0.168226 0.167543 -0.008911 0.053499 -0.091396 -0.008675 0.053801 -0.125789 0.063029 -0.021515 0.262300 -0.149909
|
||||
0.035899 0.141570 0.261650 -0.062387 0.011453 0.007417 -0.082129 -0.208338 -0.155465 0.059055 0.017798 0.138071 -0.017871 -0.043291 -0.087840 -0.136899 0.049175 -0.020713 -0.017076 -0.311678
|
||||
0.044348 0.138092 0.263521 -0.033239 0.123163 -0.106653 -0.152702 -0.204702 -0.156196 0.048833 0.087994 0.202133 0.107690 0.138321 -0.207329 0.173887 -0.039737 0.024640 0.049511 -0.085651
|
||||
0.092829 0.065152 0.241323 0.052732 0.196494 -0.013391 -0.149758 -0.104225 0.031934 0.152485 -0.070635 0.039713 -0.122304 0.048438 -0.087186 0.397237 0.299360 0.473880 -0.117227 -0.002554
|
||||
0.158053 -0.101186 0.156712 0.215453 0.339646 0.191924 -0.151986 0.111721 0.258211 0.091504 -0.101779 -0.142292 -0.013019 -0.162528 0.128016 -0.089405 0.095266 -0.204595 -0.035294 -0.336480
|
||||
0.188516 0.082941 0.069982 -0.009706 0.159551 -0.068643 -0.154058 0.166783 0.305500 -0.067861 -0.039627 0.058385 -0.241467 -0.098176 0.090395 -0.057780 0.190590 0.112858 -0.091243 0.450396
|
||||
0.140762 0.220921 0.016074 -0.159415 0.074844 -0.164230 -0.059170 0.203815 0.186257 -0.176954 0.022749 0.042020 -0.022450 0.000533 -0.285248 0.005403 -0.060779 -0.093700 0.196549 0.152982
|
||||
0.133395 0.226433 -0.010707 -0.230464 -0.059869 -0.040571 0.050888 0.169524 0.160922 -0.128840 0.075728 0.058027 -0.099835 0.083377 -0.182640 -0.033985 -0.110493 0.030869 -0.151127 -0.173059
|
||||
0.141192 0.210974 0.008052 -0.236000 -0.148708 -0.006984 0.143058 0.142625 0.145189 -0.028687 0.006157 -0.068735 -0.116293 0.146256 -0.075127 -0.184362 -0.126478 0.117311 -0.017960 -0.117790
|
||||
0.194816 0.077450 0.057706 -0.119500 -0.199164 0.160135 0.297202 0.119818 0.195158 0.023858 -0.016339 0.020867 -0.164792 0.345639 0.006437 0.100508 0.122376 0.035187 0.001808 -0.234999
|
||||
0.245836 -0.106971 0.120251 0.071136 -0.044177 0.311010 0.161058 -0.072139 0.006055 0.005484 0.054567 -0.094933 0.140048 -0.118908 -0.088061 -0.313039 -0.033682 0.248989 -0.177996 0.049038
|
||||
0.051138 0.127016 0.184698 -0.064446 -0.117282 0.021123 0.033572 -0.228811 -0.042348 -0.094835 -0.088508 -0.233492 -0.129506 -0.095787 0.094395 -0.183820 -0.060330 -0.105878 0.066953 0.194516
|
||||
0.035780 0.139162 0.190771 -0.045610 -0.014853 -0.018465 -0.041855 -0.218615 -0.027237 -0.184942 -0.048642 -0.112175 -0.156972 -0.147516 -0.043889 -0.241342 0.002376 -0.240789 -0.186848 -0.031317
|
||||
0.037228 0.127624 0.194696 0.006552 0.129864 -0.122606 -0.131251 -0.170038 -0.033162 -0.194869 -0.027183 -0.168875 0.003183 0.072068 -0.200457 0.062314 -0.193679 -0.083199 -0.095265 0.173709
|
||||
0.201029 -0.083106 0.138055 0.173335 0.277821 0.178579 -0.072555 0.107889 0.241164 0.075336 -0.112203 -0.072009 -0.097806 0.069757 0.027092 0.018868 -0.184103 -0.191984 0.297183 -0.096902
|
||||
0.152897 0.177724 0.057093 -0.132735 0.144986 -0.138582 -0.119123 0.129211 -0.019119 -0.037618 0.012867 0.060035 0.421622 -0.173865 0.058724 0.096386 -0.058369 -0.086065 -0.012869 0.082874
|
||||
0.149118 0.186737 0.039840 -0.192782 -0.007293 -0.040932 -0.013722 0.120472 -0.001574 0.040954 0.025753 0.096957 0.301644 -0.202047 0.246000 0.065756 0.003742 -0.018442 -0.026361 -0.117320
|
||||
0.159851 0.161593 0.053412 -0.206175 -0.106257 -0.001689 0.070771 0.120813 -0.033887 0.155037 -0.029883 -0.032399 0.256918 -0.104441 0.385746 0.075412 0.108663 0.012296 0.128341 0.022908
|
||||
# The variances of the components (eigenvalues) of identity or combined identity and expression model
|
||||
1
|
||||
20
|
||||
6
|
||||
287.523387 166.988429 105.780078 38.958658 30.091307 22.252112 15.728614 10.954751 7.749462 6.920441 2.405751 1.883367 1.088821 0.989291 0.666215 0.519866 0.435068 0.317623 0.231609 0.191709
|
||||
Binary file not shown.
@@ -0,0 +1,319 @@
|
||||
# The mean values of the components (in mm)
|
||||
153
|
||||
1
|
||||
6
|
||||
-61.487065
|
||||
-51.509332
|
||||
-37.921431
|
||||
-24.057516
|
||||
-11.630855
|
||||
12.064575
|
||||
25.080979
|
||||
38.237788
|
||||
50.986671
|
||||
59.712693
|
||||
0.585413
|
||||
0.765027
|
||||
0.986699
|
||||
1.246623
|
||||
-15.032333
|
||||
-7.411138
|
||||
0.343475
|
||||
8.042640
|
||||
14.960422
|
||||
-46.398983
|
||||
-37.943690
|
||||
-28.132841
|
||||
-19.916545
|
||||
-28.549994
|
||||
-38.380366
|
||||
19.002468
|
||||
27.657580
|
||||
37.180192
|
||||
44.841001
|
||||
37.909841
|
||||
28.497442
|
||||
-29.562845
|
||||
-17.967543
|
||||
-7.015967
|
||||
0.052801
|
||||
8.043929
|
||||
18.433173
|
||||
28.157774
|
||||
18.519833
|
||||
8.494683
|
||||
-0.070888
|
||||
-7.892087
|
||||
-18.695338
|
||||
-24.992703
|
||||
-7.290790
|
||||
-0.039765
|
||||
8.052638
|
||||
23.868342
|
||||
8.019854
|
||||
-0.212622
|
||||
-7.631916
|
||||
-37.103038
|
||||
-46.958179
|
||||
-50.611833
|
||||
-50.104582
|
||||
-46.101873
|
||||
-46.640281
|
||||
-50.673103
|
||||
-50.958467
|
||||
-46.902842
|
||||
-37.264890
|
||||
-31.676015
|
||||
-21.117514
|
||||
-10.737646
|
||||
0.158715
|
||||
12.338379
|
||||
14.273187
|
||||
15.946075
|
||||
14.281476
|
||||
12.541686
|
||||
-25.706010
|
||||
-31.203003
|
||||
-31.244206
|
||||
-25.361289
|
||||
-23.810857
|
||||
-23.539489
|
||||
-25.401771
|
||||
-31.558920
|
||||
-31.146069
|
||||
-25.831501
|
||||
-23.695860
|
||||
-23.829951
|
||||
39.570821
|
||||
32.160420
|
||||
28.582469
|
||||
30.231097
|
||||
28.688419
|
||||
32.668615
|
||||
39.377912
|
||||
46.579784
|
||||
49.241136
|
||||
49.857061
|
||||
49.336194
|
||||
46.680342
|
||||
39.469109
|
||||
35.142334
|
||||
35.627156
|
||||
35.092954
|
||||
39.393934
|
||||
40.374411
|
||||
41.028762
|
||||
40.536741
|
||||
27.039832
|
||||
20.931821
|
||||
14.543527
|
||||
7.608953
|
||||
2.074720
|
||||
2.333803
|
||||
7.566715
|
||||
14.068191
|
||||
20.304220
|
||||
25.944547
|
||||
-0.320469
|
||||
-8.941564
|
||||
-17.912415
|
||||
-26.452684
|
||||
-10.746347
|
||||
-14.216881
|
||||
-16.665096
|
||||
-14.180856
|
||||
-11.109900
|
||||
19.097556
|
||||
15.606980
|
||||
14.061942
|
||||
12.235130
|
||||
11.967495
|
||||
13.450376
|
||||
12.176099
|
||||
13.685622
|
||||
15.227482
|
||||
18.115394
|
||||
13.233978
|
||||
11.664752
|
||||
4.879596
|
||||
-8.128708
|
||||
-14.406876
|
||||
-15.587202
|
||||
-14.334949
|
||||
-7.381702
|
||||
4.647518
|
||||
-7.847965
|
||||
-15.774312
|
||||
-16.972084
|
||||
-15.841250
|
||||
-8.462756
|
||||
2.392204
|
||||
-13.202273
|
||||
-14.479181
|
||||
-13.135758
|
||||
2.088533
|
||||
-13.195614
|
||||
-14.587587
|
||||
-13.062554
|
||||
# The principal components (eigenvectors) of identity or combined identity and expression model
|
||||
153
|
||||
32
|
||||
6
|
||||
0.048215 0.005826 0.019250 0.055175 0.004152 -0.240330 -0.093805 0.065577 -0.028184 0.043409 0.171981 0.101208 0.077786 -0.095916 0.166254 0.029127 0.009577 0.016140 0.053935 0.072393 -0.052710 -0.000041 -0.149995 0.088505 -0.021293 0.097688 -0.043028 0.145707 -0.058863 -0.018754 -0.055098 0.283637
|
||||
0.058869 0.003249 0.041189 -0.001982 0.025312 -0.192894 -0.025140 -0.032292 -0.197517 0.118099 0.225632 0.096284 0.114517 -0.081005 0.139197 -0.078138 -0.126771 -0.136139 -0.046585 0.090782 -0.008204 -0.019328 -0.091391 0.060952 0.007995 0.018184 0.028784 0.048866 -0.015436 0.006046 -0.004828 0.138112
|
||||
0.031959 -0.001668 0.061660 -0.005340 0.003024 -0.169106 0.025180 -0.033297 -0.250054 0.214220 0.125180 0.023097 0.034194 0.014102 0.146834 -0.076318 -0.060218 -0.123413 -0.083792 0.072286 0.019266 0.024247 -0.000997 0.006645 0.024498 0.012834 0.062842 -0.003123 -0.023415 -0.025680 0.048748 -0.026094
|
||||
-0.001316 0.001415 0.073054 0.021599 -0.024599 -0.145333 0.048714 0.025206 -0.239694 0.291975 0.015222 -0.075696 -0.069737 0.103674 0.137956 -0.059660 0.017648 -0.060510 -0.113918 0.036965 0.012494 0.050988 -0.008944 -0.006526 0.024140 0.036188 0.105884 0.010739 -0.032776 -0.034197 0.114925 -0.102668
|
||||
-0.035824 0.001344 0.096519 0.024048 -0.043021 -0.102931 0.068178 0.077011 -0.175251 0.344608 -0.084700 -0.152937 -0.159712 0.163325 0.067623 -0.042989 0.040499 -0.059369 -0.151509 -0.008246 -0.025670 0.086600 -0.038968 -0.005819 0.081015 0.001095 0.078814 0.006911 -0.081881 -0.006646 0.188712 -0.148058
|
||||
0.071337 -0.000209 0.075707 -0.111516 0.029058 0.178910 -0.041829 0.002022 0.098852 -0.063920 0.157150 0.263712 0.153704 -0.143048 0.009165 0.169592 -0.042091 -0.015215 0.060386 0.092701 -0.011412 0.161957 -0.030557 -0.139962 0.185329 -0.000155 0.099424 0.016836 -0.080710 -0.067204 -0.083318 -0.183333
|
||||
0.043699 0.001130 0.048352 -0.082623 0.002693 0.222765 -0.007747 0.047357 0.126133 -0.011240 0.105147 0.176046 0.204156 -0.110730 0.095212 0.125733 -0.031262 -0.051717 -0.001980 0.069208 -0.016668 0.102606 -0.038347 -0.050735 0.155753 0.053377 0.085219 0.033941 -0.041428 -0.049227 0.078802 -0.077253
|
||||
-0.000141 0.006490 0.026936 -0.034005 -0.031528 0.243222 0.012922 0.092152 0.109157 0.056328 0.024020 0.073186 0.199754 -0.021186 0.166785 0.110435 0.009385 0.023913 -0.038320 0.060664 -0.013926 0.021366 -0.027649 -0.048182 0.088896 0.101399 0.136039 0.002153 -0.049570 0.002814 0.149871 0.053358
|
||||
-0.037555 0.007528 -0.015415 -0.002718 -0.057838 0.252132 0.053336 0.097507 0.077208 0.131023 -0.029302 -0.019790 0.160928 0.085102 0.145761 0.072649 0.053385 0.059314 -0.043048 -0.043633 0.018455 -0.049962 0.049462 -0.020626 0.000124 0.070969 0.074913 -0.085165 -0.038757 0.006930 0.199282 0.169772
|
||||
-0.042029 -0.013263 -0.114522 -0.009277 -0.033006 0.258765 0.109871 -0.001142 -0.002636 0.149950 0.001402 -0.063005 0.088768 0.097316 0.002668 -0.002525 0.002781 -0.066426 -0.007422 -0.173785 0.089002 -0.120039 0.113624 0.105707 -0.131966 -0.016829 -0.129686 -0.122573 0.009302 -0.009441 0.268861 0.192443
|
||||
0.010409 0.013506 0.115140 -0.057538 0.000108 0.025111 0.001272 0.021442 -0.008698 0.104583 0.019203 0.062144 -0.047550 0.036312 -0.079895 0.037948 0.014438 0.028186 0.030253 -0.010434 -0.021469 0.041396 -0.008376 -0.037902 0.095982 0.072764 0.102068 -0.046223 -0.057926 -0.054192 -0.040118 -0.116187
|
||||
0.011661 0.013580 0.098244 -0.054918 0.000709 0.017404 0.001459 0.017449 -0.007090 0.090928 0.008597 0.053388 -0.045450 0.027417 -0.104294 0.029068 0.016816 0.046028 0.008358 0.022175 -0.079674 -0.015467 0.041264 0.004870 0.095541 0.095869 0.038536 -0.024476 -0.035445 -0.051161 -0.010636 -0.090827
|
||||
0.012751 0.015901 0.091476 -0.053662 0.002269 0.011829 -0.001927 0.013682 -0.007728 0.075101 0.000009 0.047226 -0.044783 0.019237 -0.126011 0.015673 0.014294 0.065277 -0.017321 0.050151 -0.128723 -0.063789 0.084937 0.044485 0.109595 0.123454 -0.026538 -0.003911 -0.017052 -0.057302 0.012244 -0.069566
|
||||
0.012417 0.019872 0.090561 -0.054278 0.002424 0.009509 -0.003024 0.010002 -0.011042 0.060431 -0.010603 0.041663 -0.043785 0.017712 -0.146990 -0.005398 0.014213 0.074732 -0.050802 0.070873 -0.175363 -0.107205 0.125943 0.076813 0.124051 0.144704 -0.081053 0.023938 0.006968 -0.065779 0.037234 -0.039172
|
||||
0.024544 -0.041070 0.054915 -0.002156 0.020605 0.005506 0.033788 0.023038 -0.009453 -0.020991 0.027501 0.016838 -0.023416 -0.038269 -0.172593 0.100604 -0.087956 0.115924 -0.195525 0.149607 -0.119504 -0.086585 0.062174 -0.075038 0.035110 0.067295 0.018243 0.037127 -0.065788 0.114307 0.008766 0.013420
|
||||
0.015769 -0.016706 0.051135 -0.016355 0.023331 0.007524 0.007242 0.013630 -0.003853 -0.008421 -0.000527 0.001986 -0.030917 -0.012734 -0.145835 0.055688 -0.050414 0.097692 -0.122883 0.116419 -0.123293 -0.072748 0.065772 -0.026490 0.050794 0.080157 -0.001588 0.030216 -0.002659 0.090274 0.014294 0.008209
|
||||
0.006896 0.010273 0.040574 -0.028175 0.009177 -0.002727 -0.014177 0.003932 0.004489 0.006152 -0.014778 0.011313 -0.036673 0.012083 -0.116775 -0.004415 0.017024 0.042082 -0.017831 0.056364 -0.122120 -0.059416 0.060239 0.041547 0.076702 0.078139 -0.024391 0.022113 0.041986 0.029818 0.006180 -0.008338
|
||||
0.003970 0.033635 0.031624 -0.039688 -0.009931 -0.013688 -0.027612 -0.006537 0.014283 0.026041 -0.027827 0.007531 -0.035935 0.028010 -0.090291 -0.066369 0.095570 -0.004022 0.073400 -0.005364 -0.106538 -0.056168 0.061509 0.078550 0.094586 0.045250 -0.003615 0.025884 0.050964 -0.059244 -0.004008 -0.021368
|
||||
-0.001030 0.051101 0.012729 -0.044712 -0.018779 -0.019594 -0.042435 -0.019121 0.024428 0.034846 -0.034286 -0.007933 -0.033382 0.048139 -0.059376 -0.110934 0.139720 -0.028230 0.159201 -0.068088 -0.091597 -0.048485 0.074228 0.104849 0.077415 -0.003190 -0.011414 0.014616 0.051647 -0.131379 -0.016369 -0.029576
|
||||
0.013276 0.015196 0.059348 0.005177 -0.027902 -0.170695 -0.014038 0.150670 0.011873 0.000786 -0.001627 -0.017240 0.060415 -0.071933 -0.072809 0.194452 0.009800 0.022712 0.090550 -0.052535 0.048687 0.036304 -0.081877 0.107825 -0.019121 0.088373 0.006745 -0.001877 0.027214 0.037692 0.066350 -0.032024
|
||||
0.008368 0.021960 0.054532 0.000311 -0.013304 -0.136478 -0.005637 0.144631 -0.012116 0.036030 0.009154 -0.004242 0.045998 -0.045201 -0.104791 0.181210 -0.014972 0.008238 0.103363 -0.104654 0.090328 0.075697 -0.047151 0.056470 -0.047856 0.042860 0.048666 -0.031566 0.031284 0.039040 0.059929 -0.077071
|
||||
0.010395 0.003713 0.046220 0.009379 -0.018544 -0.083031 -0.013386 0.114954 -0.018702 0.037856 -0.002239 0.007356 0.059607 0.038771 -0.131230 0.159333 -0.105685 0.035886 0.067892 -0.054718 0.165788 0.105141 0.029341 0.082812 -0.059462 0.015944 0.035767 -0.047746 0.012667 0.050158 0.039094 -0.047357
|
||||
-0.004435 0.007758 0.022257 0.036260 -0.024646 -0.070379 -0.043482 0.069648 -0.017559 0.045113 -0.011125 0.031216 0.049811 0.049932 -0.155766 0.134651 -0.112632 0.006918 0.065349 -0.047570 0.144378 0.096402 0.099483 0.065001 -0.044072 -0.028810 -0.014239 -0.088588 -0.014730 0.076246 0.021813 -0.019431
|
||||
0.002165 0.006150 0.029380 0.029537 -0.025415 -0.100095 -0.017928 0.118446 -0.004248 0.030562 -0.006585 0.000532 0.058398 0.009221 -0.126284 0.163929 -0.090164 0.029112 0.068156 -0.063123 0.109314 0.090377 -0.005534 0.070883 -0.043083 -0.006742 -0.002886 -0.037771 0.001431 0.081963 0.004436 -0.032697
|
||||
0.005906 0.023652 0.032288 0.016417 -0.016369 -0.150461 -0.008210 0.140340 0.006951 0.032729 0.002817 -0.014571 0.043576 -0.085898 -0.093828 0.197874 0.009255 -0.010440 0.104221 -0.102783 0.013114 0.047952 -0.099076 0.069836 -0.028903 0.044003 0.014956 -0.013531 0.002087 0.064351 0.058261 -0.052773
|
||||
0.031500 -0.016588 -0.023311 -0.051803 0.020577 0.076264 0.056423 -0.050173 0.058645 0.086870 0.049525 0.017849 -0.103044 0.016589 0.058592 0.011828 0.079540 -0.004367 0.086692 -0.046516 -0.016537 0.071956 -0.138565 0.010325 -0.021842 0.083975 0.110326 0.083204 -0.010803 -0.126543 0.008570 -0.065688
|
||||
0.008613 -0.007233 -0.020573 -0.036715 0.011967 0.087079 0.019123 -0.079108 0.053694 0.138972 0.045043 0.066957 -0.125703 0.038948 0.052634 0.035588 0.066490 -0.058129 0.093071 -0.057940 -0.003968 0.124034 -0.079225 0.027754 -0.038168 0.004876 0.053321 0.063399 -0.004495 -0.056661 -0.007469 -0.016110
|
||||
0.010708 -0.022508 -0.031270 -0.026205 0.011524 0.141469 0.005171 -0.103210 0.057169 0.134168 0.035399 0.074052 -0.116274 0.110813 0.023736 0.016900 -0.015217 -0.013920 0.071146 -0.012837 0.055448 0.151531 -0.015708 0.005826 -0.049828 -0.042618 0.063884 0.047747 -0.001527 -0.018317 -0.022828 0.028414
|
||||
-0.002105 -0.020003 -0.064424 -0.013765 0.020781 0.174297 0.001852 -0.122246 0.043849 0.126361 0.045295 0.070262 -0.111656 0.134767 -0.017164 -0.026720 -0.057077 -0.037401 0.057190 -0.048382 0.069101 0.117167 0.012271 -0.038779 -0.039332 -0.077244 0.048794 -0.029942 0.009972 0.030621 -0.034125 0.032811
|
||||
0.013969 -0.027246 -0.057345 -0.015140 0.008990 0.148608 0.002683 -0.100291 0.049046 0.118726 0.042351 0.076792 -0.099641 0.130512 -0.001439 -0.013800 -0.045290 0.013326 0.049555 0.028980 0.100417 0.164552 0.016949 -0.001374 -0.021085 -0.071477 0.006962 0.059649 0.027692 -0.007030 -0.078989 0.038859
|
||||
0.019008 -0.012928 -0.046256 -0.036644 0.012116 0.098313 0.022292 -0.078736 0.050100 0.118315 0.047233 0.058065 -0.103981 0.053660 0.031135 0.009987 0.035686 -0.022567 0.066701 -0.005730 0.033996 0.126479 -0.062315 0.021035 -0.001091 -0.013353 0.002995 0.076257 0.009807 -0.058127 -0.042979 -0.004986
|
||||
-0.007601 -0.177175 0.017727 0.125761 0.005688 -0.003353 0.147590 0.073022 -0.018688 -0.204710 0.010150 0.031133 0.001801 0.030364 0.023092 -0.004181 0.085187 0.005926 0.087355 0.072482 -0.021998 -0.032687 0.046765 -0.055522 -0.177677 -0.034217 0.213318 0.017704 0.014570 -0.055193 0.030444 0.001590
|
||||
-0.016541 -0.130310 0.005113 0.039399 -0.015097 -0.002729 0.084226 0.039798 -0.038451 -0.160923 0.067103 -0.036395 -0.025994 0.076883 0.025661 0.022379 0.057800 -0.007792 -0.055764 0.012615 -0.000495 -0.017802 0.043257 -0.012918 -0.076865 0.029916 0.111351 0.026562 -0.043756 -0.072868 -0.014045 -0.005620
|
||||
-0.006580 -0.041018 0.011956 0.014998 0.000740 -0.005472 0.032329 0.006822 -0.020124 -0.131024 0.077596 -0.043507 -0.025592 0.112554 -0.034348 0.040738 0.060708 -0.001484 -0.155825 -0.070616 -0.011748 0.005651 0.000251 0.005087 0.038106 0.066154 0.082256 0.091179 -0.065226 -0.023005 -0.061362 -0.058155
|
||||
0.004961 0.001648 -0.003877 -0.006108 0.014598 -0.019228 -0.004263 -0.016762 0.000237 -0.074099 -0.025521 -0.041570 -0.009358 0.010684 -0.001844 0.010927 0.012393 -0.017579 -0.043086 -0.029781 -0.001323 0.002201 0.067935 -0.021949 0.012852 0.077330 0.032354 0.036728 -0.058971 -0.032938 -0.001410 -0.051522
|
||||
0.010249 0.058570 -0.030749 -0.037553 0.017103 -0.045825 -0.032816 -0.033532 0.023519 -0.005390 -0.142192 -0.028903 0.005856 -0.119621 0.037848 -0.030546 -0.049052 -0.044563 0.084150 0.025508 0.033239 0.010978 0.157710 -0.068468 -0.065812 0.111109 0.080771 0.000044 -0.000183 -0.031588 0.026364 -0.072106
|
||||
0.019855 0.127731 -0.069824 -0.036148 0.034849 -0.043347 -0.088673 -0.073093 0.049751 0.013844 -0.144983 -0.063823 0.020675 -0.110435 0.051877 -0.041482 -0.071095 0.014502 0.034872 0.022648 -0.049292 0.007571 0.075833 -0.065256 -0.069651 -0.001051 0.095846 0.062248 -0.062551 -0.005565 0.031314 -0.030085
|
||||
-0.002875 0.164839 -0.124720 -0.071759 0.017265 -0.043992 -0.148503 -0.111790 0.051584 0.012064 -0.084883 -0.131572 -0.001352 -0.044408 -0.003920 -0.047574 -0.034283 0.058068 -0.088753 -0.010707 -0.048508 0.013425 -0.024586 -0.044085 0.017545 -0.168004 0.085244 0.029133 -0.109995 -0.062934 -0.001407 0.004682
|
||||
0.017838 0.126359 -0.098394 -0.019146 0.037082 -0.045881 -0.088216 -0.093730 0.054146 -0.034776 -0.152958 -0.093546 0.040898 -0.099978 0.077336 -0.047936 -0.073395 -0.008478 0.035327 0.016668 -0.011878 0.031888 0.029670 -0.010671 0.013279 -0.059562 0.097616 -0.001442 -0.123286 0.033179 0.093989 -0.017493
|
||||
0.003354 0.057470 -0.070587 -0.005011 0.030120 -0.048761 -0.033225 -0.056017 0.022933 -0.077317 -0.170237 -0.073664 0.040276 -0.107085 0.099220 -0.034965 -0.061435 -0.077366 0.069545 -0.000936 0.069153 0.082774 0.086736 -0.021770 0.048952 -0.005926 0.014456 -0.045143 -0.062652 0.092136 0.133381 -0.040747
|
||||
-0.005090 -0.003703 -0.040158 0.017871 0.020138 -0.024901 -0.002366 -0.032407 -0.001883 -0.147184 -0.047234 -0.089613 0.020124 0.020696 0.065435 0.004741 -0.007643 -0.052853 -0.055641 -0.066739 0.032675 0.071221 -0.008619 0.042968 0.104527 -0.033912 -0.035940 0.001701 -0.099441 0.094234 0.101317 -0.019024
|
||||
-0.020413 -0.053520 -0.023649 0.035117 0.005981 -0.015046 0.027253 -0.008273 -0.021301 -0.215940 0.053858 -0.103258 0.002494 0.109283 0.037848 0.037581 0.055486 -0.042429 -0.157384 -0.081131 0.031650 0.072109 -0.075592 0.080851 0.143183 -0.044277 -0.015440 0.051076 -0.114670 0.079007 0.058218 -0.007329
|
||||
-0.029800 -0.143867 -0.013745 0.053673 -0.009247 -0.010775 0.087729 0.033939 -0.038123 -0.226383 0.051127 -0.072732 -0.003050 0.087211 0.077594 0.019810 0.059918 -0.024133 -0.041687 0.001805 0.000908 0.031197 -0.029281 0.024243 -0.029099 -0.078006 0.068409 0.023726 -0.060584 0.003392 0.082980 -0.001526
|
||||
-0.003562 -0.182306 -0.002510 0.134236 0.020593 -0.001022 0.150457 0.051751 -0.021379 -0.197171 -0.001357 0.011236 0.017400 0.037123 0.026165 -0.017637 0.090818 0.025239 0.074023 0.040654 -0.048912 -0.012247 0.059420 -0.037121 -0.191095 -0.060883 0.188357 0.054443 0.012178 -0.065544 0.013102 -0.027796
|
||||
-0.010711 -0.038978 0.021641 0.018128 0.003540 -0.003594 0.029128 0.000882 -0.023613 -0.158293 0.065713 -0.056117 -0.021144 0.110963 -0.022237 0.034373 0.061360 -0.018439 -0.167422 -0.072410 0.011021 0.030154 -0.039910 -0.005807 0.092278 0.022426 0.060858 0.072149 -0.046708 -0.000397 -0.017953 -0.017121
|
||||
0.001604 0.002832 0.000803 -0.005274 0.015109 -0.016136 -0.006531 -0.023165 -0.000438 -0.092850 -0.035022 -0.048312 -0.007273 0.013002 0.003632 -0.000217 0.014076 -0.024655 -0.057671 -0.039153 0.008338 0.025209 0.033618 -0.034396 0.059088 0.041641 0.012819 0.035200 -0.035564 -0.014626 0.032340 -0.025766
|
||||
0.006185 0.058475 -0.024893 -0.037175 0.019107 -0.042798 -0.037553 -0.041913 0.024837 -0.025511 -0.153636 -0.038780 0.010843 -0.117604 0.043591 -0.044371 -0.050973 -0.050976 0.069347 0.015835 0.052084 0.035582 0.124825 -0.086511 -0.028588 0.074993 0.066821 -0.007952 0.018917 -0.012518 0.062130 -0.033156
|
||||
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|
||||
0.134227 0.041096 -0.061485 0.054966 -0.056764 0.084437 0.213343 0.055314 -0.052393 0.011308 -0.027370 0.021602 -0.013330 -0.140458 0.009733 -0.079107 -0.082394 0.100616 -0.025509 -0.086411 0.004174 -0.036076 0.009054 0.186944 -0.031461 0.053258 0.150028 0.014613 0.049660 0.122103 0.020441 0.011679
|
||||
0.091513 0.134030 -0.116428 0.016728 -0.080013 0.082029 0.104084 0.018085 -0.027354 0.032150 0.078124 -0.022941 0.044163 -0.037802 -0.084995 -0.134114 -0.091533 0.133474 -0.008039 -0.109529 -0.007892 -0.148899 0.041573 0.097925 0.048025 0.040445 0.199117 -0.109140 -0.047717 -0.038369 0.062078 -0.039950
|
||||
0.039624 0.253230 -0.100188 -0.082036 -0.064970 0.016263 -0.088788 0.010698 -0.013891 -0.041645 0.138828 -0.069040 0.112394 0.174971 -0.109718 0.055792 -0.043798 0.025729 -0.054612 -0.027360 0.036663 0.001664 -0.042717 0.175052 0.041398 -0.063698 0.045263 0.022938 -0.035608 0.013511 0.027593 -0.009450
|
||||
0.107480 0.009787 -0.060226 -0.083488 -0.074567 0.034945 0.059688 0.035237 -0.019732 -0.013617 -0.023118 -0.014135 0.041612 0.026587 -0.059716 0.051098 -0.073035 -0.121685 -0.039252 -0.051624 -0.049556 -0.068248 0.055507 -0.058828 -0.149640 0.107282 -0.027147 0.087519 0.153781 0.055056 0.036505 -0.031854
|
||||
0.106622 -0.003861 -0.021348 -0.099473 -0.070178 0.052940 0.061288 0.031461 -0.019104 -0.020812 -0.018499 -0.044968 0.000296 0.018823 -0.027740 0.095604 -0.048958 -0.112997 -0.102798 -0.035527 -0.071991 0.001553 0.025803 -0.115849 -0.127057 0.024527 -0.124135 0.145897 0.129750 0.085928 0.040547 -0.017936
|
||||
0.099110 0.010502 0.036882 -0.130805 -0.078845 0.027013 0.053483 0.004597 -0.037911 -0.001205 -0.036378 -0.035327 -0.044486 -0.011252 0.014448 0.110590 -0.005294 -0.106933 -0.100168 -0.008829 -0.039386 0.052912 0.051532 -0.215856 -0.091016 0.055316 -0.098031 0.095330 0.149157 0.121476 0.032213 -0.016403
|
||||
0.028004 0.226894 0.023564 -0.130075 -0.083078 0.026565 -0.107154 -0.001028 -0.031965 -0.082441 0.154939 -0.156561 0.011600 0.088391 0.059746 -0.043768 0.117637 0.096381 0.031384 -0.037298 -0.019471 -0.011911 -0.082806 -0.023826 -0.035251 0.152668 0.054600 0.036817 0.086273 0.096746 -0.042278 0.077595
|
||||
0.134031 0.066380 0.033211 -0.032357 -0.052881 0.055878 0.125886 0.036614 -0.086323 -0.015670 -0.071590 0.038155 -0.125581 -0.112508 0.087640 0.043625 0.069072 0.062524 -0.018971 0.019054 -0.005686 0.107858 0.030051 0.104346 0.099672 -0.109073 -0.122930 -0.020258 -0.095912 0.104783 -0.177058 -0.071379
|
||||
0.136503 0.052062 -0.025896 0.007574 -0.042908 0.068754 0.150283 0.049774 -0.067584 -0.033491 -0.036563 0.046275 -0.076289 -0.108802 0.035446 -0.013211 0.035519 0.074173 0.001881 0.011113 0.029676 0.032394 0.039140 0.168346 0.109882 -0.092465 -0.106862 -0.037770 -0.143106 0.047406 -0.169767 -0.087501
|
||||
0.128717 0.065942 -0.069026 0.010173 -0.058821 0.055130 0.146527 0.062138 -0.051715 -0.023275 -0.042414 0.062661 -0.040407 -0.097958 -0.000170 -0.056738 0.005825 0.052625 0.081622 0.015050 0.039520 -0.053590 0.084135 0.214255 0.067782 -0.036374 -0.005244 -0.128133 -0.144167 0.012225 -0.152893 -0.083695
|
||||
# The variances of the components (eigenvalues) of identity or combined identity and expression model
|
||||
1
|
||||
32
|
||||
6
|
||||
440.568563 348.267724 258.176898 158.822108 129.944287 110.045102 74.920301 64.103548 54.641760 39.545215 36.676344 31.215370 29.972900 22.199493 20.407369 17.614554 12.651972 10.796969 9.472633 9.060509 7.384158 5.845468 4.290567 3.094468 2.205294 2.103393 1.662684 1.186149 0.669309 0.585443 0.354509 0.307398
|
||||
@@ -0,0 +1,421 @@
|
||||
# The mean values of the components (in mm)
|
||||
204
|
||||
1
|
||||
6
|
||||
-74.907476
|
||||
-73.885990
|
||||
-71.489258
|
||||
-67.482519
|
||||
-60.629789
|
||||
-49.691406
|
||||
-35.497591
|
||||
-18.891692
|
||||
0.105636
|
||||
19.085146
|
||||
35.647665
|
||||
49.792618
|
||||
60.675798
|
||||
67.467724
|
||||
71.412137
|
||||
73.748052
|
||||
74.707721
|
||||
-58.458668
|
||||
-49.527553
|
||||
-38.577366
|
||||
-27.361808
|
||||
-16.609493
|
||||
16.437446
|
||||
27.173888
|
||||
38.379921
|
||||
49.329869
|
||||
58.272633
|
||||
-0.044580
|
||||
-0.019917
|
||||
0.004603
|
||||
0.028615
|
||||
-12.698018
|
||||
-6.535473
|
||||
0.041603
|
||||
6.612439
|
||||
12.762422
|
||||
-43.886056
|
||||
-36.751464
|
||||
-28.218240
|
||||
-21.229092
|
||||
-28.717232
|
||||
-36.629921
|
||||
21.119565
|
||||
28.093004
|
||||
36.622605
|
||||
43.765142
|
||||
36.521022
|
||||
28.611100
|
||||
-26.653333
|
||||
-19.053937
|
||||
-9.906007
|
||||
0.059738
|
||||
10.017459
|
||||
19.165211
|
||||
26.764528
|
||||
19.820436
|
||||
10.655324
|
||||
0.089141
|
||||
-10.485863
|
||||
-19.676019
|
||||
-20.099832
|
||||
-10.413211
|
||||
0.066036
|
||||
10.540162
|
||||
20.221242
|
||||
10.704606
|
||||
0.073169
|
||||
-10.566624
|
||||
-28.812217
|
||||
-9.662052
|
||||
9.454018
|
||||
28.239136
|
||||
45.813647
|
||||
60.982433
|
||||
73.280172
|
||||
82.547123
|
||||
85.839987
|
||||
82.491573
|
||||
73.176472
|
||||
60.837946
|
||||
45.637786
|
||||
28.043667
|
||||
9.247651
|
||||
-9.875205
|
||||
-29.028947
|
||||
-57.238019
|
||||
-63.739913
|
||||
-66.320592
|
||||
-65.657067
|
||||
-62.730330
|
||||
-62.772247
|
||||
-65.732441
|
||||
-66.431039
|
||||
-63.884164
|
||||
-57.408209
|
||||
-43.494093
|
||||
-32.323206
|
||||
-21.219201
|
||||
-10.154099
|
||||
1.865699
|
||||
3.812307
|
||||
4.550229
|
||||
3.795547
|
||||
1.833301
|
||||
-39.575745
|
||||
-44.012326
|
||||
-44.271766
|
||||
-40.257729
|
||||
-37.775364
|
||||
-37.398870
|
||||
-40.324420
|
||||
-44.356723
|
||||
-44.121200
|
||||
-39.703605
|
||||
-37.507475
|
||||
-37.862166
|
||||
30.198595
|
||||
23.732715
|
||||
19.281161
|
||||
19.985394
|
||||
19.255417
|
||||
23.681657
|
||||
30.124395
|
||||
37.039208
|
||||
41.464305
|
||||
42.768918
|
||||
41.494874
|
||||
37.095259
|
||||
29.677178
|
||||
26.828533
|
||||
26.647927
|
||||
26.799121
|
||||
29.618278
|
||||
31.751934
|
||||
32.973459
|
||||
31.783409
|
||||
64.083586
|
||||
59.604237
|
||||
55.630937
|
||||
51.270408
|
||||
45.264067
|
||||
38.374113
|
||||
30.298802
|
||||
21.248638
|
||||
16.868691
|
||||
21.260056
|
||||
30.328419
|
||||
38.423826
|
||||
45.328428
|
||||
51.345204
|
||||
55.721454
|
||||
59.708635
|
||||
64.196230
|
||||
14.422033
|
||||
8.686064
|
||||
2.801790
|
||||
-2.729174
|
||||
-7.926259
|
||||
-7.862783
|
||||
-2.662158
|
||||
2.869104
|
||||
8.753808
|
||||
14.496714
|
||||
-20.448168
|
||||
-30.505334
|
||||
-40.604505
|
||||
-50.582207
|
||||
-32.451571
|
||||
-35.110317
|
||||
-36.937315
|
||||
-35.089217
|
||||
-32.412092
|
||||
5.389048
|
||||
2.570176
|
||||
0.218247
|
||||
-2.269159
|
||||
-0.023830
|
||||
2.115026
|
||||
-2.270098
|
||||
0.239954
|
||||
2.611755
|
||||
5.453688
|
||||
2.158551
|
||||
-0.000314
|
||||
-13.185956
|
||||
-22.510052
|
||||
-29.160533
|
||||
-32.817646
|
||||
-29.120915
|
||||
-22.445438
|
||||
-13.108197
|
||||
-20.287321
|
||||
-26.767387
|
||||
-29.589010
|
||||
-26.786669
|
||||
-20.332165
|
||||
-18.723657
|
||||
-27.229468
|
||||
-31.286473
|
||||
-27.203927
|
||||
-18.701761
|
||||
-23.325596
|
||||
-25.935592
|
||||
-23.339431
|
||||
# The principal components (eigenvectors) of identity or combined identity and expression model
|
||||
204
|
||||
23
|
||||
6
|
||||
0.091320 0.067697 -0.110358 0.031348 -0.109998 -0.043192 -0.136032 -0.076720 0.087824 0.044042 -0.013550 0.008589 -0.048083 -0.092181 0.092934 -0.015199 0.030018 0.050299 -0.164361 -0.135929 -0.022901 0.070813 0.074105
|
||||
0.090053 0.056855 -0.105143 0.048205 -0.137315 -0.027200 -0.087300 -0.073239 0.091754 0.044206 0.000382 0.024519 -0.033513 -0.072470 0.101305 -0.035842 0.021397 0.073502 -0.106065 -0.105874 0.013498 0.075177 0.084792
|
||||
0.089704 0.037096 -0.101815 0.061521 -0.160838 -0.001992 -0.034754 -0.069785 0.082533 0.047880 0.022942 0.050803 -0.009335 -0.040937 0.098634 -0.041056 0.000610 0.080194 -0.043046 -0.069439 0.052146 0.067026 0.101416
|
||||
0.092485 0.016520 -0.097276 0.072709 -0.162872 0.033565 0.019760 -0.045184 0.045705 0.052218 0.056124 0.061649 0.014402 0.018886 0.066230 -0.029254 -0.042334 0.079689 0.017926 -0.003587 0.072472 0.044603 0.107001
|
||||
0.088267 -0.001223 -0.083113 0.089495 -0.137565 0.075158 0.064326 -0.008052 -0.005583 0.053838 0.085757 0.042769 0.035269 0.069824 0.027312 -0.002588 -0.087080 0.069913 0.071855 0.081360 0.051892 0.017443 0.115903
|
||||
0.064175 -0.005923 -0.058178 0.096330 -0.095137 0.075500 0.064835 0.007740 -0.035258 0.050938 0.080419 0.003705 0.045576 0.073251 0.009771 0.007396 -0.093796 0.041737 0.075597 0.127960 0.018923 0.003372 0.125910
|
||||
0.032382 -0.002427 -0.034665 0.084426 -0.047610 0.038783 0.041234 0.015571 -0.038826 0.063202 0.043756 -0.026921 0.039418 0.037133 0.004837 -0.005497 -0.064320 -0.007338 0.030904 0.107632 -0.007177 0.006613 0.123277
|
||||
0.005362 0.001106 -0.015642 0.055153 -0.011213 0.004162 0.013564 0.007189 -0.023601 0.083772 0.018270 -0.025876 0.032027 0.004950 0.005615 -0.010527 -0.007367 -0.061217 -0.009623 0.033935 -0.007461 0.039074 0.142511
|
||||
0.001031 -0.000548 -0.000264 -0.000520 0.000206 0.000378 -0.000761 0.000710 0.001245 0.111872 0.001626 -0.001134 0.022890 0.003820 0.001163 0.006304 0.030369 -0.102361 -0.013169 -0.024623 -0.002881 0.005597 0.149742
|
||||
-0.003832 -0.001882 0.015328 -0.055899 0.011886 -0.003668 -0.014712 -0.005913 0.026117 0.082582 -0.014875 0.024610 0.032341 0.001382 -0.004014 0.016624 -0.006765 -0.061810 -0.002180 0.034345 -0.035194 -0.029396 0.143895
|
||||
-0.031542 0.001959 0.034646 -0.084730 0.048614 -0.038748 -0.041976 -0.014182 0.041330 0.060347 -0.040502 0.026823 0.041509 -0.031785 -0.004173 0.002464 -0.061396 -0.003610 -0.022907 0.114465 -0.084218 0.000325 0.122210
|
||||
-0.064081 0.005685 0.058498 -0.096256 0.096384 -0.075900 -0.065480 -0.005899 0.037385 0.046327 -0.077663 -0.002871 0.049507 -0.068448 -0.010635 -0.016896 -0.089363 0.049733 -0.053557 0.137522 -0.121203 0.001117 0.119090
|
||||
-0.088811 0.001207 0.083734 -0.089214 0.138583 -0.076308 -0.065254 0.010207 0.007104 0.049076 -0.084949 -0.041488 0.036841 -0.065810 -0.029573 -0.009323 -0.083644 0.074085 -0.046499 0.087602 -0.112927 -0.015765 0.105258
|
||||
-0.093338 -0.016415 0.097998 -0.072403 0.163322 -0.035482 -0.020914 0.047214 -0.044929 0.049145 -0.057297 -0.060576 0.009516 -0.016434 -0.068860 0.020221 -0.042707 0.072140 0.001044 -0.010845 -0.064012 -0.044385 0.097207
|
||||
-0.090565 -0.036989 0.102454 -0.061241 0.160693 -0.000469 0.033575 0.071524 -0.082226 0.047179 -0.025410 -0.050431 -0.019105 0.041642 -0.100474 0.036418 -0.003779 0.063417 0.054843 -0.091093 0.012150 -0.066716 0.097995
|
||||
-0.090943 -0.056818 0.105747 -0.047844 0.136781 0.024578 0.086293 0.074901 -0.092023 0.045773 -0.003807 -0.024785 -0.043866 0.071633 -0.102204 0.033835 0.016933 0.048663 0.112631 -0.132337 0.082004 -0.074648 0.089125
|
||||
-0.092315 -0.067689 0.110953 -0.030883 0.109131 0.040413 0.135033 0.078171 -0.088581 0.047146 0.009482 -0.009455 -0.056966 0.090377 -0.093138 0.014716 0.029261 0.018026 0.163776 -0.157569 0.142363 -0.070135 0.085600
|
||||
0.058537 -0.009903 -0.067255 -0.026008 0.081110 0.164341 -0.233081 0.078101 -0.035015 -0.070783 -0.017167 -0.007394 0.057358 0.086467 -0.024547 0.048349 -0.056198 -0.134009 -0.137372 0.093417 0.125693 -0.105378 0.088218
|
||||
0.046783 -0.016744 -0.042635 -0.030362 0.097473 0.186509 -0.142013 0.054124 -0.007578 -0.077677 -0.104050 -0.023043 0.074340 0.107853 0.023404 0.029266 -0.109087 -0.173086 -0.100872 0.070859 0.073751 -0.043594 0.051411
|
||||
0.037822 -0.005621 -0.030037 -0.008652 0.096784 0.166748 -0.015735 0.022319 0.027049 -0.077875 -0.182382 -0.011177 0.056973 0.098715 0.025433 -0.017646 -0.127515 -0.145490 -0.063487 0.052270 0.023116 0.010355 0.004992
|
||||
0.031842 0.009393 -0.022501 0.023745 0.092844 0.127249 0.111292 -0.002709 0.062522 -0.074558 -0.240922 0.020053 0.018223 0.074236 -0.000653 -0.085055 -0.126882 -0.098866 -0.032713 0.044542 -0.001878 0.040214 -0.038295
|
||||
0.025897 0.024767 -0.016090 0.053409 0.087370 0.086632 0.228057 -0.019734 0.095009 -0.069126 -0.280723 0.055079 -0.031099 0.041694 -0.034314 -0.154088 -0.120209 -0.049792 -0.004835 0.039939 -0.002989 0.053665 -0.080922
|
||||
-0.025121 -0.024547 0.015906 -0.054217 -0.088611 -0.084702 -0.226637 0.016001 -0.096775 -0.066004 0.280947 -0.056431 -0.052690 -0.040980 0.037382 0.140352 -0.159988 -0.048371 0.008326 -0.029439 0.020611 -0.055817 -0.075779
|
||||
-0.031357 -0.009150 0.022403 -0.024551 -0.093357 -0.125288 -0.110483 -0.000880 -0.064012 -0.071461 0.243276 -0.021425 0.003947 -0.072350 0.002305 0.072303 -0.149766 -0.104665 0.027648 -0.002234 0.007948 -0.039321 -0.035070
|
||||
-0.037606 0.005877 0.030041 0.007887 -0.096660 -0.164799 0.016030 -0.025726 -0.028324 -0.075031 0.186386 0.009802 0.051448 -0.096129 -0.025004 0.006258 -0.133735 -0.157940 0.049371 0.014843 -0.026932 -0.006537 0.004774
|
||||
-0.046785 0.017013 0.042753 0.029687 -0.096933 -0.184665 0.142032 -0.057164 0.006361 -0.075000 0.108881 0.021820 0.078163 -0.105623 -0.023812 -0.038141 -0.105804 -0.190414 0.079450 0.006308 -0.084686 0.049972 0.047392
|
||||
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0.040054 -0.009456 -0.022462 -0.028115 0.047836 -0.117620 -0.065581 0.152750 0.055895 0.086537 -0.001878 -0.094304 0.011719 0.000015 0.009484 0.010397 -0.077566 -0.098392 0.027748 -0.026350 -0.007136 0.028195 0.046831
|
||||
0.028104 -0.000077 -0.033499 0.014610 0.020788 -0.111121 0.030766 0.102595 0.056098 0.074833 -0.047232 -0.031991 0.049281 -0.027794 0.043929 0.027004 -0.066940 -0.048824 0.029001 -0.028601 0.021125 0.010895 0.091682
|
||||
0.012155 0.015544 -0.048047 0.059015 -0.003318 -0.104891 0.127691 0.045621 0.064996 0.063929 -0.099510 0.026920 0.071451 -0.062437 0.090102 0.043826 -0.066716 0.014832 0.033433 -0.048268 0.041771 0.001523 0.104638
|
||||
-0.010877 0.038806 -0.059631 0.093351 -0.036183 -0.103090 0.207613 -0.003086 0.062073 0.051161 -0.141758 0.079719 0.082879 -0.125936 0.093635 0.016578 -0.076075 0.043583 0.064284 -0.071153 0.027988 0.027119 0.103745
|
||||
-0.023959 -0.137903 -0.080850 -0.060032 0.073312 -0.031378 -0.106882 0.020766 0.009786 -0.002862 -0.028036 0.060861 -0.000014 0.072971 -0.084363 0.025088 -0.004714 0.009233 -0.110683 -0.011912 -0.056593 0.043849 0.000641
|
||||
-0.037140 -0.136200 -0.069400 -0.044426 0.127977 -0.059538 -0.085921 -0.028756 0.039860 -0.001850 -0.002636 0.063634 0.001342 0.026201 -0.091779 -0.032647 -0.000111 0.010259 -0.100253 0.008011 0.013583 0.070065 0.002899
|
||||
-0.048171 -0.132511 -0.059535 -0.024365 0.173715 -0.094460 -0.050715 -0.072405 0.073443 -0.000908 0.028076 0.053480 0.002074 0.003532 -0.095691 -0.102774 0.004379 0.012898 -0.108440 0.025000 0.076983 0.090541 0.004194
|
||||
-0.054686 -0.123766 -0.049335 -0.002926 0.218068 -0.135937 -0.007285 -0.103413 0.102512 -0.000119 0.066645 0.034567 0.001043 0.019243 -0.103623 -0.167941 0.006374 0.016401 -0.129772 0.035759 0.144799 0.120774 0.005008
|
||||
-0.064440 -0.118578 -0.004198 -0.001748 0.133252 0.118524 0.041641 -0.067077 -0.013124 -0.053822 0.118057 0.094445 0.108177 -0.083605 0.005961 -0.075387 0.079248 0.051165 -0.010494 -0.050608 0.028079 0.062593 0.150046
|
||||
-0.073679 -0.150260 -0.021981 -0.006050 0.145897 0.134784 0.053016 -0.063419 -0.005730 -0.025810 0.120418 0.090408 0.051217 -0.115461 0.052448 -0.025060 0.042889 0.022018 0.010738 -0.013007 0.034217 0.038088 0.075510
|
||||
-0.079875 -0.171924 -0.034483 -0.006044 0.155372 0.138780 0.066200 -0.053912 0.021308 0.004772 0.119585 0.082952 0.001345 -0.134491 0.077247 0.021979 0.002031 0.001109 0.022022 0.029910 0.034486 0.018476 0.000749
|
||||
-0.072287 -0.150978 -0.023675 -0.007608 0.142526 0.133172 0.053803 -0.066554 -0.002453 0.035124 0.115662 0.090207 -0.050494 -0.117441 0.056971 -0.025114 -0.036881 -0.021474 0.009983 0.052581 0.029244 0.035705 -0.075933
|
||||
-0.061777 -0.120140 -0.007713 -0.005110 0.126328 0.115569 0.043616 -0.073854 -0.006740 0.061979 0.107821 0.094221 -0.110452 -0.087307 0.014580 -0.075909 -0.074807 -0.050769 -0.014213 0.054450 0.024681 0.058030 -0.152882
|
||||
-0.022909 -0.019395 -0.040768 -0.075768 -0.119237 0.027971 0.010659 -0.128561 -0.132629 -0.104986 -0.036319 -0.023027 0.089380 0.064479 -0.023504 0.018677 0.008200 -0.069494 -0.099452 -0.140264 0.011754 -0.078184 -0.038726
|
||||
-0.011663 -0.012721 -0.015117 -0.078467 -0.071783 0.060507 0.006642 -0.105244 -0.081065 -0.076170 0.018144 -0.008068 0.029019 0.030540 0.002642 -0.017086 -0.029254 -0.046645 0.031060 -0.131388 -0.026875 -0.076424 -0.080200
|
||||
-0.012700 -0.020601 -0.014420 -0.080627 -0.068679 0.064607 -0.002786 -0.098847 -0.069667 -0.055799 0.020490 -0.015505 -0.010174 0.017321 -0.010725 -0.036045 -0.067074 -0.050202 0.073231 -0.093054 -0.002462 -0.058533 -0.119619
|
||||
-0.022216 -0.036533 -0.027628 -0.074864 -0.070484 0.042078 -0.019854 -0.113556 -0.069907 -0.041478 0.001313 -0.043331 -0.033593 -0.011060 -0.055672 -0.023027 -0.061931 -0.048030 0.117328 -0.039059 0.013910 0.032313 -0.113835
|
||||
-0.027296 -0.030028 -0.029386 -0.076219 -0.087638 0.021374 0.003870 -0.110062 -0.077782 -0.069674 -0.020143 -0.042802 0.028886 0.015273 -0.033187 0.002833 -0.016759 -0.057456 0.047262 -0.067098 0.002935 0.013527 -0.064547
|
||||
-0.026952 -0.025091 -0.034229 -0.079231 -0.100988 0.020407 0.011670 -0.110003 -0.097099 -0.082711 -0.029875 -0.031535 0.052469 0.040561 -0.017033 0.005566 0.003046 -0.081933 -0.015501 -0.098325 0.004758 -0.025428 -0.063197
|
||||
-0.024397 -0.033849 -0.022893 -0.069851 -0.064326 0.039641 -0.024282 -0.098773 -0.074091 0.044909 0.005768 -0.043196 0.030214 -0.014564 -0.061464 -0.015939 0.072864 0.025274 0.117331 0.021832 0.002672 0.032547 0.114817
|
||||
-0.013506 -0.018713 -0.011192 -0.076740 -0.064517 0.061248 -0.005771 -0.086178 -0.071570 0.060003 0.023383 -0.015642 0.005106 0.012858 -0.014423 -0.024426 0.077165 0.031334 0.077874 0.065428 -0.041374 -0.056843 0.118114
|
||||
-0.011771 -0.011460 -0.013058 -0.075249 -0.069583 0.054681 0.005956 -0.094395 -0.080802 0.080655 0.016568 -0.008488 -0.033029 0.023791 0.000018 -0.007143 0.034423 0.035382 0.050271 0.095798 -0.066996 -0.072290 0.075636
|
||||
-0.022185 -0.019104 -0.040197 -0.073881 -0.119383 0.021090 0.011975 -0.121001 -0.129652 0.108788 -0.042105 -0.023165 -0.087195 0.056911 -0.023261 0.024658 -0.011866 0.087048 -0.067562 0.141774 -0.042892 -0.076388 0.033233
|
||||
-0.027568 -0.023977 -0.032179 -0.076207 -0.098956 0.014736 0.011406 -0.100164 -0.096467 0.085564 -0.033132 -0.031380 -0.051423 0.034695 -0.019175 0.008240 -0.002948 0.083988 0.011173 0.081654 -0.025127 -0.024077 0.059653
|
||||
-0.028620 -0.028286 -0.026167 -0.072465 -0.084045 0.017229 0.001719 -0.098825 -0.079353 0.072429 -0.020945 -0.042761 -0.029173 0.010234 -0.035955 0.005873 0.020289 0.048886 0.058934 0.047219 -0.014606 0.012955 0.062687
|
||||
0.075805 -0.005394 0.168063 0.078607 -0.054244 0.058215 -0.006478 0.042799 0.001152 0.103007 -0.044958 0.018539 0.184649 -0.071353 0.019894 0.087271 -0.072213 -0.022852 0.055259 0.111090 0.078729 0.026963 -0.145646
|
||||
0.031030 -0.035872 0.148024 0.024897 -0.055144 0.051231 -0.000210 0.072150 0.048963 0.067141 0.003158 -0.005183 0.101734 -0.034460 0.007489 0.069011 -0.063569 0.008931 0.037548 0.097309 -0.011873 0.074967 -0.095813
|
||||
-0.036427 -0.064730 0.129730 0.007194 -0.061675 0.024125 -0.007446 0.060846 0.100609 0.028191 0.024440 -0.020667 0.039865 -0.005541 0.008106 0.074845 -0.042588 0.028918 -0.026261 0.049327 -0.037593 0.094940 -0.047102
|
||||
-0.063163 -0.084404 0.102720 -0.006882 -0.056104 -0.009892 0.008620 0.043231 0.130565 -0.001501 0.053089 -0.018280 -0.001059 0.030044 0.025309 0.076984 -0.005665 0.008111 -0.086817 -0.014522 -0.086194 0.077395 -0.007492
|
||||
-0.035585 -0.065862 0.127926 0.004959 -0.064546 0.025609 -0.005482 0.055732 0.100431 -0.030859 0.019929 -0.020724 -0.040591 -0.006993 0.009032 0.079738 0.034741 -0.024826 -0.032029 -0.047096 -0.011275 0.101608 0.038382
|
||||
0.031961 -0.037518 0.145679 0.021693 -0.059740 0.053520 0.003348 0.064036 0.047561 -0.068056 -0.005875 -0.005389 -0.102336 -0.039437 0.009419 0.074184 0.056117 -0.016141 0.032853 -0.087198 0.035348 0.086760 0.091032
|
||||
0.075895 -0.006400 0.167295 0.076600 -0.058269 0.060814 -0.002476 0.035721 -0.003644 -0.102351 -0.057967 0.017786 -0.183456 -0.082695 0.023161 0.088710 0.055063 0.014349 0.055233 -0.085402 0.127212 0.042032 0.148731
|
||||
0.079230 -0.024711 0.109135 0.037787 -0.038784 0.003330 0.034484 0.063863 -0.011348 -0.087797 -0.013535 0.006485 -0.113409 -0.017592 0.004977 0.013853 0.030234 0.036630 -0.002867 -0.038980 0.033412 -0.044698 0.105429
|
||||
0.051675 -0.054522 0.050520 -0.004887 -0.019062 -0.051016 0.053209 0.074677 -0.017411 -0.051624 0.035007 -0.016152 -0.048910 0.026899 0.017409 -0.029509 0.004375 0.029169 -0.048670 -0.005679 -0.026781 -0.153869 0.058451
|
||||
0.039556 -0.070671 0.008498 -0.031640 -0.003894 -0.095262 0.069079 0.062016 -0.000151 -0.000894 0.078499 -0.030044 -0.004237 0.064258 0.030266 -0.012247 -0.002919 0.006927 -0.083768 -0.018979 -0.078678 -0.219661 0.008161
|
||||
0.051833 -0.054765 0.049895 -0.005192 -0.018823 -0.051922 0.052469 0.075164 -0.014954 0.050192 0.036899 -0.016087 0.044046 0.031262 0.016613 -0.027766 -0.008071 -0.021535 -0.053924 -0.014113 -0.023488 -0.155497 -0.043035
|
||||
0.079383 -0.024547 0.108830 0.038247 -0.036867 0.001570 0.032310 0.066953 -0.007222 0.087229 -0.006709 0.006794 0.111574 -0.009036 0.002961 0.014293 -0.038599 -0.035991 -0.008504 0.037115 0.015596 -0.051643 -0.098056
|
||||
0.144108 0.023833 0.210733 0.031591 -0.059646 0.003043 -0.102283 -0.012721 -0.102885 0.175549 -0.057728 0.072258 0.225509 0.038803 -0.066549 -0.120286 0.195125 0.072363 0.108993 0.071842 -0.015195 0.056219 -0.097176
|
||||
0.022333 -0.048589 0.128472 -0.008328 -0.078016 -0.025266 -0.051956 0.029051 0.011046 0.079465 -0.038228 0.018401 0.098178 0.062052 -0.001465 -0.038823 0.090318 0.047318 -0.026470 0.040963 0.047517 0.053465 -0.041889
|
||||
-0.061457 -0.088535 0.070973 -0.012616 -0.068967 -0.073790 0.016160 0.050480 0.130572 -0.002697 -0.003664 -0.017939 -0.001248 0.098222 0.052866 0.062872 -0.011868 0.017901 -0.163166 -0.010316 0.032337 0.019060 -0.002854
|
||||
0.021979 -0.049490 0.127429 -0.009883 -0.080038 -0.024367 -0.046620 0.022104 0.010781 -0.083181 -0.047125 0.018999 -0.096739 0.062325 -0.000728 -0.054757 -0.086306 -0.040301 -0.034877 -0.027398 0.073444 0.059353 0.038798
|
||||
0.142694 0.022419 0.209582 0.029398 -0.063686 0.004604 -0.091487 -0.026014 -0.105037 -0.177208 -0.077247 0.073338 -0.222836 0.037657 -0.064264 -0.154528 -0.166751 -0.093826 0.089637 -0.055384 0.030980 0.065702 0.091014
|
||||
0.116813 -0.015290 0.098294 -0.027889 -0.037219 -0.024853 0.001723 0.038184 -0.031296 -0.079111 -0.018053 0.064650 -0.096347 0.069229 -0.022347 -0.072090 -0.072641 -0.038239 0.025412 -0.029043 -0.087848 -0.100824 0.039553
|
||||
0.089323 -0.051246 0.009126 -0.046362 -0.009383 -0.073680 0.099634 0.076495 0.056663 -0.001649 0.055586 0.041026 -0.003175 0.099148 0.026202 0.031114 -0.000590 0.005485 -0.070567 -0.026852 -0.193679 -0.213317 0.003024
|
||||
0.117592 -0.015042 0.098196 -0.027487 -0.036629 -0.025410 -0.002671 0.042636 -0.029774 0.076182 -0.010119 0.064261 0.095826 0.070074 -0.022651 -0.055786 0.090197 0.029593 0.033172 0.012973 -0.109351 -0.104770 -0.034005
|
||||
# The variances of the components (eigenvalues) of identity or combined identity and expression model
|
||||
1
|
||||
23
|
||||
6
|
||||
795.358907 526.466957 323.962380 149.332995 108.218528 86.462266 78.978172 71.817921 63.124413 56.631775 49.840502 37.133586 32.292271 27.991391 25.613033 20.062292 16.082399 14.009888 12.585536 4.127530 1.562736 1.104694 0.909219
|
||||
Binary file not shown.
@@ -0,0 +1,421 @@
|
||||
# The mean values of the components (in mm)
|
||||
204
|
||||
1
|
||||
6
|
||||
-73.393523
|
||||
-72.775014
|
||||
-70.533638
|
||||
-66.850058
|
||||
-59.790187
|
||||
-48.368973
|
||||
-34.121101
|
||||
-17.875411
|
||||
0.098749
|
||||
17.477031
|
||||
32.648966
|
||||
46.372358
|
||||
57.343480
|
||||
64.388482
|
||||
68.212038
|
||||
70.486405
|
||||
71.375822
|
||||
-61.119406
|
||||
-51.287588
|
||||
-37.804800
|
||||
-24.022754
|
||||
-11.635713
|
||||
12.056636
|
||||
25.106256
|
||||
38.338588
|
||||
51.191007
|
||||
60.053851
|
||||
0.653940
|
||||
0.804809
|
||||
0.992204
|
||||
1.226783
|
||||
-14.772472
|
||||
-7.180239
|
||||
0.555920
|
||||
8.272499
|
||||
15.214351
|
||||
-46.047290
|
||||
-37.674688
|
||||
-27.883856
|
||||
-19.648268
|
||||
-28.272965
|
||||
-38.082418
|
||||
19.265868
|
||||
27.894191
|
||||
37.437529
|
||||
45.170805
|
||||
38.196454
|
||||
28.764989
|
||||
-28.916267
|
||||
-17.533194
|
||||
-6.684590
|
||||
0.381001
|
||||
8.375443
|
||||
18.876618
|
||||
28.794412
|
||||
19.057574
|
||||
8.956375
|
||||
0.381549
|
||||
-7.428895
|
||||
-18.160634
|
||||
-24.377490
|
||||
-6.897633
|
||||
0.340663
|
||||
8.444722
|
||||
24.474473
|
||||
8.449166
|
||||
0.205322
|
||||
-7.198266
|
||||
-29.801432
|
||||
-10.949766
|
||||
7.929818
|
||||
26.074280
|
||||
42.564390
|
||||
56.481080
|
||||
67.246992
|
||||
75.056892
|
||||
77.061286
|
||||
74.758448
|
||||
66.929021
|
||||
56.311389
|
||||
42.419126
|
||||
25.455880
|
||||
6.990805
|
||||
-11.666193
|
||||
-30.365191
|
||||
-49.361602
|
||||
-58.769795
|
||||
-61.996155
|
||||
-61.033399
|
||||
-56.686759
|
||||
-57.391033
|
||||
-61.902186
|
||||
-62.777713
|
||||
-59.302347
|
||||
-50.190255
|
||||
-42.193790
|
||||
-30.993721
|
||||
-19.944596
|
||||
-8.414541
|
||||
2.598255
|
||||
4.751589
|
||||
6.562900
|
||||
4.661005
|
||||
2.643046
|
||||
-37.471411
|
||||
-42.730510
|
||||
-42.711517
|
||||
-36.754742
|
||||
-35.134493
|
||||
-34.919043
|
||||
-37.032306
|
||||
-43.342445
|
||||
-43.110822
|
||||
-38.086515
|
||||
-35.532024
|
||||
-35.484289
|
||||
28.612716
|
||||
22.172187
|
||||
19.029051
|
||||
20.721118
|
||||
19.035460
|
||||
22.394109
|
||||
28.079924
|
||||
36.298248
|
||||
39.634575
|
||||
40.395647
|
||||
39.836405
|
||||
36.677899
|
||||
28.677771
|
||||
25.475976
|
||||
26.014269
|
||||
25.326198
|
||||
28.323008
|
||||
30.596216
|
||||
31.408738
|
||||
30.844876
|
||||
47.667532
|
||||
45.909403
|
||||
44.842580
|
||||
43.141114
|
||||
38.635298
|
||||
30.750622
|
||||
18.456453
|
||||
3.609035
|
||||
-0.881698
|
||||
5.181201
|
||||
19.176563
|
||||
30.770570
|
||||
37.628629
|
||||
40.886309
|
||||
42.281449
|
||||
44.142567
|
||||
47.140426
|
||||
14.254422
|
||||
7.268147
|
||||
0.442051
|
||||
-6.606501
|
||||
-11.967398
|
||||
-12.051204
|
||||
-7.315098
|
||||
-1.022953
|
||||
5.349435
|
||||
11.615746
|
||||
-13.380835
|
||||
-21.150853
|
||||
-29.284036
|
||||
-36.948060
|
||||
-20.132003
|
||||
-23.536684
|
||||
-25.944448
|
||||
-23.695741
|
||||
-20.858157
|
||||
7.037989
|
||||
3.021217
|
||||
1.353629
|
||||
-0.111088
|
||||
-0.147273
|
||||
1.476612
|
||||
-0.665746
|
||||
0.247660
|
||||
1.696435
|
||||
4.894163
|
||||
0.282961
|
||||
-1.172675
|
||||
-2.240310
|
||||
-15.934335
|
||||
-22.611355
|
||||
-23.748437
|
||||
-22.721995
|
||||
-15.610679
|
||||
-3.217393
|
||||
-14.987997
|
||||
-22.554245
|
||||
-23.591626
|
||||
-22.406106
|
||||
-15.121907
|
||||
-4.785684
|
||||
-20.893742
|
||||
-22.220479
|
||||
-21.025520
|
||||
-5.712776
|
||||
-20.671489
|
||||
-21.903670
|
||||
-20.328022
|
||||
# The principal components (eigenvectors) of identity or combined identity and expression model
|
||||
204
|
||||
34
|
||||
6
|
||||
-0.007395 -0.093690 0.039362 0.204443 -0.104698 0.033568 -0.090173 0.010170 -0.042341 0.104375 0.032695 0.038750 0.064385 -0.037025 0.058377 0.032457 -0.100005 -0.082042 -0.053440 0.008782 -0.027164 -0.000368 -0.129614 0.035436 -0.062685 -0.075349 0.140764 -0.032290 -0.115829 -0.037865 0.068590 0.008886 -0.066442 0.259211
|
||||
-0.002553 -0.075344 0.037127 0.201967 -0.069124 0.041645 -0.100939 0.018352 0.006598 0.081569 0.004894 0.038886 0.050631 0.056656 0.055353 -0.028457 -0.022518 -0.089693 -0.079196 0.010851 -0.017583 0.015095 -0.077834 -0.000944 -0.104255 -0.060338 0.106169 -0.065799 -0.067068 -0.051588 0.080490 0.063152 -0.047531 0.178216
|
||||
-0.002097 -0.055385 0.025705 0.215785 -0.026274 0.053548 -0.086364 0.041926 0.035784 0.033485 -0.014602 0.049999 0.031950 0.125201 0.045372 -0.064200 0.070073 -0.074313 -0.083942 -0.007566 -0.003666 0.034226 -0.018354 -0.011639 -0.084633 -0.039431 0.064057 -0.056515 -0.046926 -0.074699 0.073477 0.074109 -0.054882 0.046675
|
||||
-0.005533 -0.035821 0.019787 0.226957 0.030415 0.059508 -0.051058 0.057386 0.023240 -0.025487 -0.013088 0.043330 0.025141 0.113119 0.017370 -0.071064 0.108140 -0.049138 -0.043417 -0.065375 0.012959 0.070483 0.075536 -0.035685 -0.005847 0.012618 0.040297 -0.049743 -0.061354 -0.087164 0.033762 0.048771 -0.096563 -0.045189
|
||||
-0.006914 0.011987 0.030022 0.205560 0.099633 0.072384 -0.008313 0.060244 -0.006584 -0.104943 -0.018036 0.032806 0.029879 0.068434 -0.043721 -0.052564 0.077505 -0.062192 0.026865 -0.122834 -0.001529 0.064443 0.160557 -0.036750 0.124476 0.072641 0.048609 -0.043443 -0.060729 -0.040443 -0.050540 0.050509 -0.118886 -0.146867
|
||||
-0.004182 0.064263 0.036886 0.149341 0.158261 0.075501 0.030568 0.067074 -0.040268 -0.167116 -0.020230 0.029360 0.046726 0.033410 -0.121685 -0.004528 -0.017505 -0.050390 0.063237 -0.133203 -0.070794 0.005133 0.178032 -0.002768 0.153446 0.105966 0.061693 0.011010 -0.027442 0.001944 -0.103967 0.045708 -0.083197 -0.172889
|
||||
0.016954 0.088125 0.034199 0.081242 0.170872 0.048964 0.063434 0.083842 -0.058188 -0.164769 -0.012135 0.002128 0.084787 -0.009691 -0.136231 0.068411 -0.091616 0.042046 0.053339 -0.068859 -0.141834 -0.040710 0.017020 0.034007 0.053187 0.096749 0.068416 0.075079 0.038728 0.063588 -0.109581 0.007737 0.033105 -0.152075
|
||||
0.021733 0.081042 0.015310 0.029492 0.112212 0.012959 0.065003 0.095565 -0.047228 -0.120559 -0.022904 -0.051461 0.036411 -0.036990 -0.101765 0.150918 -0.102123 0.163128 0.047199 0.037063 -0.223718 -0.065303 -0.149191 -0.017823 -0.134138 0.084419 0.010718 0.087970 0.043030 0.040099 -0.068487 -0.008773 0.077035 -0.082281
|
||||
0.024713 0.084952 0.002319 -0.002792 0.028194 -0.016856 0.036083 0.087381 -0.020743 -0.024386 -0.027268 -0.091654 -0.009025 -0.052124 -0.033407 0.168353 -0.061447 0.244847 0.024587 0.064221 -0.161138 0.020993 -0.164584 -0.068179 -0.181775 0.087509 -0.068202 0.059078 -0.004250 -0.001472 -0.031248 -0.049011 -0.019415 0.022163
|
||||
0.025404 0.095704 -0.013447 -0.036864 -0.064015 -0.035962 0.001144 0.050101 0.006172 0.084003 -0.015860 -0.102295 -0.028308 -0.053076 0.017520 0.110370 -0.009494 0.248830 -0.017769 0.064655 -0.062487 0.133872 -0.077193 -0.077102 -0.104610 0.084923 -0.116710 -0.000424 -0.001453 -0.001504 -0.004986 -0.072792 -0.151917 0.063339
|
||||
0.027234 0.088446 -0.037011 -0.090962 -0.124015 -0.052844 -0.020061 0.017974 0.031824 0.138013 -0.009523 -0.093892 -0.061812 -0.016350 0.043025 0.034106 0.036403 0.177560 -0.066137 0.039288 0.041972 0.145398 -0.004524 -0.021113 0.025045 0.065780 -0.102128 -0.061053 0.010043 -0.018688 0.018733 -0.002990 -0.240304 0.007274
|
||||
0.033301 0.051083 -0.050161 -0.137239 -0.130410 -0.078352 -0.030467 -0.016581 0.042916 0.153230 -0.008295 -0.048519 -0.056020 -0.017449 0.051644 -0.021078 0.049456 0.042549 -0.075780 0.051205 0.057200 0.117965 0.058462 0.078890 0.121853 0.027311 -0.037081 -0.082100 0.013948 0.019188 0.029703 0.076102 -0.243643 -0.067711
|
||||
0.034561 -0.024817 -0.037181 -0.171731 -0.091823 -0.080914 -0.018022 -0.019280 0.055534 0.112038 -0.006388 0.000380 -0.027767 -0.031689 0.027915 -0.012644 0.004351 -0.072270 -0.053990 0.028620 0.011428 0.077628 0.073278 0.159948 0.096141 0.006855 0.036568 -0.013290 -0.001587 0.033748 0.052795 0.164287 -0.166678 -0.098685
|
||||
0.031311 -0.094373 -0.015266 -0.181991 -0.032285 -0.067979 0.020822 -0.028457 0.050194 0.060652 0.006169 0.060618 0.005717 -0.047184 0.006512 0.012425 -0.059877 -0.141325 -0.029145 -0.010906 -0.069894 0.032082 0.054382 0.151384 0.041519 0.026929 0.076049 0.067107 -0.027885 0.040313 0.041582 0.194576 -0.086531 -0.080338
|
||||
0.030327 -0.127857 -0.008012 -0.166922 0.025066 -0.062660 0.063753 -0.029802 0.044933 0.028298 0.025152 0.109179 0.013585 -0.043385 0.003918 0.007538 -0.080941 -0.141969 0.011067 -0.055727 -0.099322 -0.018025 0.009874 0.065510 -0.019589 0.084273 0.059580 0.099232 -0.026102 0.043042 0.023322 0.151827 -0.031702 -0.023000
|
||||
0.030239 -0.141766 -0.020490 -0.154724 0.073176 -0.066098 0.076339 -0.045120 0.049403 -0.014474 0.024782 0.109864 0.005943 -0.008921 0.001482 -0.008304 -0.060453 -0.100507 0.030769 -0.093919 -0.042422 -0.045051 -0.014060 -0.020183 -0.093279 0.134797 0.006048 0.040717 -0.038709 0.039630 0.006137 0.076303 0.021244 0.014680
|
||||
0.030493 -0.158938 -0.031460 -0.156567 0.120023 -0.070626 0.084879 -0.065759 0.063746 -0.047728 -0.002344 0.094855 -0.013995 0.014159 0.011125 -0.034394 -0.064702 -0.055871 0.041269 -0.110361 0.045722 -0.064289 -0.013213 -0.104140 -0.133226 0.183607 -0.037284 0.002311 -0.041808 0.033510 -0.034315 0.012710 0.065609 0.046794
|
||||
-0.029307 -0.000612 0.006003 0.066897 -0.126329 0.008282 0.106455 -0.058070 -0.127455 0.112217 0.028721 -0.008227 0.023123 -0.184660 -0.000131 0.060814 -0.038192 0.061802 0.055924 -0.086767 -0.011372 0.116214 0.039681 -0.047083 0.046626 0.042705 0.011194 -0.002237 0.023832 0.021378 0.074731 -0.040608 -0.025003 0.203421
|
||||
-0.038458 0.020813 -0.004500 0.021759 -0.086203 0.017004 0.123118 -0.051398 -0.154096 0.048594 0.160783 0.035847 -0.105209 -0.131283 -0.034334 0.088202 -0.022053 0.065794 0.043514 -0.164773 0.038562 0.221823 -0.008980 0.076251 -0.067806 0.014541 0.027230 -0.014379 -0.016754 -0.010835 0.026126 -0.010414 0.029183 0.058614
|
||||
-0.021490 0.036216 -0.005865 0.020024 -0.060804 0.026512 0.126241 -0.083197 -0.120419 0.032472 0.187630 -0.015555 -0.159327 -0.011903 -0.087082 0.079345 -0.061540 0.015194 0.062573 -0.039469 0.032277 0.191416 0.026454 0.082398 -0.056523 -0.017131 0.027510 -0.008610 0.004494 -0.034043 -0.017450 0.006765 0.078634 -0.036122
|
||||
0.000867 0.042636 0.003104 0.029552 -0.036234 0.016402 0.123844 -0.126971 -0.075012 0.060293 0.148833 -0.081953 -0.173218 0.088994 -0.136465 0.063644 -0.092909 -0.034989 0.083554 0.107321 0.022452 0.121649 0.095422 0.064093 -0.044127 -0.041514 -0.001734 -0.007934 0.040275 -0.042178 -0.037676 0.021143 0.091871 -0.056272
|
||||
0.024120 0.058528 0.006018 0.028610 -0.012243 0.008813 0.097121 -0.159602 -0.017056 0.077811 0.087002 -0.120528 -0.150197 0.184860 -0.180434 0.040369 -0.097894 -0.042266 0.075094 0.203623 0.039492 0.033806 0.132455 0.059185 -0.102173 -0.071020 -0.051542 0.002257 0.073697 -0.021845 -0.035627 0.009661 0.123071 -0.065039
|
||||
-0.056420 0.059125 -0.030321 -0.057038 0.055493 -0.007116 -0.126529 0.019949 -0.058614 -0.078223 0.002145 0.050900 0.167834 -0.173333 0.181067 -0.004047 0.063488 0.151506 -0.125850 -0.136067 0.023547 0.034287 -0.056834 0.003824 0.134406 -0.055792 0.087938 0.068804 -0.033240 0.076407 -0.033551 -0.097730 0.084249 -0.079917
|
||||
-0.038591 0.041658 -0.021071 -0.054808 0.085131 -0.020672 -0.150923 -0.028119 -0.005051 -0.082123 -0.027470 0.004437 0.151800 -0.139134 0.205779 0.055682 0.024516 0.096154 -0.038417 -0.113849 0.045637 0.075165 -0.039525 0.011140 0.058496 -0.061165 0.070389 0.031381 -0.020956 0.065917 -0.033395 -0.096762 0.067056 0.005758
|
||||
-0.007940 0.026461 -0.003035 -0.037585 0.112114 -0.032320 -0.154598 -0.070183 0.034104 -0.066949 -0.048103 -0.076036 0.108505 -0.081056 0.189128 0.100712 0.001290 0.009722 0.046728 -0.023127 0.013390 0.076873 0.012671 0.031037 0.075639 -0.064473 0.061414 -0.019564 0.014597 0.046786 -0.011485 -0.084927 -0.000334 0.061175
|
||||
0.018946 -0.000145 0.011179 -0.029672 0.136914 -0.030086 -0.147824 -0.105721 0.066935 -0.079902 -0.036968 -0.110909 0.052283 0.004188 0.126896 0.134626 -0.006676 -0.052490 0.091685 0.063396 -0.013036 0.002970 0.053049 0.019284 0.038579 -0.025497 0.025340 -0.089926 0.050450 -0.006666 -0.013118 -0.030505 -0.058633 0.064143
|
||||
0.026629 -0.059165 -0.000823 -0.058599 0.151849 -0.022073 -0.130501 -0.084385 0.071751 -0.134872 0.039773 -0.057794 -0.044027 0.076494 0.035989 0.101529 0.005315 -0.029779 0.032498 0.028803 0.005618 -0.063529 -0.004924 -0.022183 -0.113427 0.055922 -0.008186 -0.140830 0.090960 -0.114112 -0.009417 0.083947 -0.041032 -0.006371
|
||||
-0.010951 0.075350 -0.001817 -0.012876 0.013096 0.004579 -0.016153 -0.047823 -0.029850 0.016150 0.033334 0.015682 0.035621 0.037191 -0.019504 -0.019256 0.044839 0.020295 -0.073131 0.039780 -0.036879 -0.040970 0.053655 -0.001482 -0.002821 -0.032902 -0.000066 0.005729 0.001116 0.056517 -0.017058 -0.021947 0.037761 -0.039276
|
||||
-0.012100 0.064207 -0.001096 -0.013941 0.006814 0.008710 -0.012277 -0.037790 -0.022203 0.014245 0.023934 0.012607 0.028185 0.041440 -0.015444 -0.022646 0.048805 0.020521 -0.080918 0.029123 -0.081415 -0.044517 0.073681 0.021481 -0.045782 -0.048161 0.003254 0.036460 -0.020011 0.065280 0.002563 -0.013150 0.045393 -0.015692
|
||||
-0.013403 0.059276 0.001032 -0.014545 0.001798 0.010646 -0.008624 -0.026081 -0.017773 0.015405 0.015492 0.014040 0.022709 0.044120 -0.010399 -0.025661 0.051172 0.017503 -0.087720 0.021120 -0.123991 -0.047505 0.087387 0.047337 -0.088646 -0.065851 0.004667 0.069448 -0.040053 0.076718 0.023178 -0.004565 0.059432 0.003138
|
||||
-0.013951 0.058265 0.004661 -0.015235 -0.000197 0.012932 -0.005151 -0.015313 -0.012719 0.014418 0.008297 0.018443 0.016678 0.051541 -0.004867 -0.028055 0.052224 0.011609 -0.091004 0.016980 -0.158439 -0.046922 0.104617 0.077207 -0.137148 -0.078657 0.005486 0.103939 -0.062683 0.082257 0.041975 0.000801 0.070429 0.027527
|
||||
-0.012210 0.028100 -0.049457 -0.000857 0.000872 -0.019030 0.038293 -0.002178 0.022197 0.008799 -0.017828 -0.005589 -0.010209 -0.026452 0.021247 -0.052723 0.074659 0.058170 -0.117953 -0.020708 -0.092993 -0.079196 0.037883 0.239302 -0.027228 -0.100648 0.058909 0.082147 0.014782 0.033906 0.058190 -0.035069 -0.021313 -0.027376
|
||||
-0.009373 0.029412 -0.026531 -0.009199 -0.003610 -0.013154 0.015847 0.006945 0.008617 0.011675 -0.022788 0.000421 -0.007697 0.005751 0.004594 -0.044864 0.063024 0.031416 -0.086743 -0.005786 -0.098907 -0.064158 0.049203 0.156108 -0.042964 -0.089257 0.038446 0.080608 -0.015415 0.071399 0.069731 -0.012170 0.005798 -0.005172
|
||||
-0.007108 0.026011 0.001392 -0.008785 -0.008676 0.005534 -0.002323 0.008151 -0.006538 0.012718 -0.016466 0.016828 0.006599 0.032792 -0.008449 -0.031395 0.045979 0.010267 -0.064263 0.010528 -0.087206 -0.035954 0.070434 0.037452 -0.075439 -0.048176 -0.000307 0.074329 -0.047401 0.093968 0.057921 0.003554 0.025206 0.029137
|
||||
-0.008616 0.022966 0.025314 -0.006647 -0.012574 0.026313 -0.017855 0.005573 -0.012147 0.015962 -0.009681 0.035391 0.015389 0.061577 -0.023327 -0.005465 0.025007 -0.014906 -0.045808 0.023055 -0.069940 -0.012007 0.101986 -0.066696 -0.085795 -0.002255 -0.051891 0.079767 -0.057766 0.078189 0.009062 0.022309 0.030125 0.051138
|
||||
-0.007559 0.013536 0.044396 -0.007128 -0.015567 0.038755 -0.032699 0.009439 -0.018290 0.012901 -0.008295 0.047013 0.018435 0.076580 -0.045586 0.016721 0.010805 -0.037831 -0.013755 0.026798 -0.057710 -0.005862 0.113804 -0.159457 -0.085242 0.031892 -0.090113 0.066240 -0.055402 0.053706 -0.034191 0.047815 0.018971 0.071248
|
||||
-0.009091 0.030428 0.013028 0.035270 -0.081955 0.036276 0.100983 -0.087388 -0.023476 0.093938 -0.074920 -0.042748 0.009283 -0.052713 0.069944 0.007487 0.044433 0.011768 -0.036858 -0.036562 0.024165 -0.141056 -0.039714 -0.075826 0.052239 0.062199 -0.048408 -0.033798 0.070343 0.124688 -0.003466 0.051026 0.026850 -0.026589
|
||||
-0.006597 0.030631 0.019664 0.021478 -0.061211 0.024677 0.092608 -0.095386 -0.041650 0.068021 -0.054620 -0.036136 0.003440 -0.021689 0.046307 0.007803 0.056620 0.018329 -0.048106 -0.037355 0.044779 -0.170111 -0.043462 -0.076020 0.064547 0.063396 -0.047873 -0.054226 0.076392 0.081326 0.000747 0.074683 0.030657 -0.067772
|
||||
-0.006641 0.024694 0.004169 0.027776 -0.027517 0.013511 0.064805 -0.082940 -0.047464 0.039102 -0.047983 -0.025260 -0.012175 0.006766 0.039254 0.004585 0.108825 0.031769 -0.009359 -0.008230 0.016421 -0.164640 -0.117072 -0.007971 0.069640 0.013253 -0.033817 -0.074767 0.071010 0.026436 0.003056 0.090554 0.005886 -0.126966
|
||||
0.003124 0.009371 0.014768 0.046412 -0.023874 0.007554 0.036147 -0.057698 -0.058069 0.021256 -0.033315 -0.028152 -0.018259 0.027895 0.014161 0.004788 0.111066 0.042408 -0.022688 -0.017329 0.008180 -0.162840 -0.121148 0.012000 0.040787 0.005472 -0.028935 -0.070284 0.051087 0.002654 0.026039 0.077896 -0.025666 -0.138535
|
||||
-0.000470 0.012891 0.009958 0.038234 -0.036776 0.012638 0.068663 -0.077589 -0.036998 0.050930 -0.057174 -0.042770 -0.006013 -0.005012 0.037131 0.011314 0.092853 0.040593 -0.014258 -0.022855 0.028109 -0.170083 -0.092356 -0.017012 0.053071 0.021873 -0.039264 -0.061002 0.057296 0.043219 0.021993 0.064114 -0.018287 -0.100373
|
||||
-0.004849 0.015938 0.022983 0.026902 -0.073622 0.023429 0.089584 -0.088285 -0.026052 0.080286 -0.059955 -0.060351 0.007903 -0.035545 0.046797 0.007563 0.038369 0.030247 -0.059021 -0.056175 0.056872 -0.166273 -0.011250 -0.093711 0.035468 0.071037 -0.053530 -0.042127 0.065314 0.098363 0.023179 0.056227 0.018585 -0.031417
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|
||||
0.012182 -0.107450 -0.027021 0.065245 0.008961 -0.027772 -0.074458 0.050282 0.025229 -0.041151 0.086397 -0.119923 -0.099702 -0.055513 -0.011844 -0.012761 -0.000561 0.025024 0.077500 0.042190 0.004065 0.022608 -0.020626 -0.014056 0.026667 -0.025100 0.039847 0.066569 -0.072695 0.106463 0.007401 -0.072767 0.005736 0.071139
|
||||
-0.009462 0.065949 -0.034941 0.008894 -0.064655 -0.020166 -0.060698 0.028627 0.066320 0.002801 0.040050 0.031191 -0.045838 0.048249 0.022311 -0.088733 0.012498 0.012592 -0.012528 -0.038889 0.028963 -0.007368 -0.006653 0.082948 -0.006713 0.005645 -0.025498 -0.054304 -0.022462 0.175263 -0.039024 -0.042552 -0.094353 -0.013449
|
||||
0.000399 0.075432 -0.010525 0.041532 -0.020281 -0.016042 -0.094246 0.065468 0.057754 -0.013075 0.035003 0.037001 -0.063322 0.051499 0.004328 -0.061380 -0.015256 0.001025 -0.051518 0.003395 -0.032991 0.024094 0.008757 0.054130 -0.053594 0.010905 -0.022832 -0.025114 -0.048340 0.149929 -0.021867 0.081009 -0.007931 -0.009067
|
||||
0.011378 0.085467 -0.017111 0.041300 -0.001692 -0.039680 -0.104984 0.079709 0.063221 -0.028397 0.048561 0.041353 -0.084814 0.040411 0.000268 -0.038789 -0.000559 -0.008586 -0.044596 0.040237 -0.063474 -0.003204 -0.031149 0.016331 -0.050858 0.018453 -0.008099 -0.080392 -0.015774 0.091864 -0.016377 0.134277 0.049921 -0.027301
|
||||
0.029766 0.102153 -0.038143 0.053924 0.038638 -0.061103 -0.101860 0.090831 0.056649 -0.017724 0.060045 0.040849 -0.108462 0.025297 0.013784 -0.048798 0.017389 -0.036169 -0.049864 0.021916 -0.066484 0.016243 -0.106255 -0.005066 -0.033200 -0.008221 0.050207 -0.137478 0.022810 0.034341 -0.021252 0.120671 0.042481 -0.025859
|
||||
0.006889 0.087347 -0.040353 0.029840 -0.010245 -0.040820 -0.091202 0.072685 0.079209 -0.016224 0.043485 -0.001910 -0.084857 0.044870 -0.001342 -0.071705 -0.002282 -0.026485 -0.039688 0.033741 -0.055799 -0.013397 -0.029281 0.000374 -0.037317 -0.004296 0.042230 -0.104897 0.024080 0.125291 0.011644 0.079126 -0.013272 0.018850
|
||||
-0.000936 0.077182 -0.035678 0.029087 -0.033747 -0.023682 -0.089809 0.060071 0.081219 -0.000659 0.033152 -0.007048 -0.054525 0.054060 -0.010472 -0.078847 -0.000530 -0.009111 -0.033111 0.004942 -0.009483 0.002476 0.026701 0.054112 -0.050766 -0.014615 0.013950 -0.054182 -0.017408 0.176648 0.019946 -0.001332 -0.069141 0.058993
|
||||
-0.053340 -0.049736 0.202485 -0.040699 0.016891 0.098603 -0.079165 0.012530 -0.068702 0.013827 -0.018413 0.064039 -0.096530 -0.107456 -0.034620 0.115038 0.176489 0.048911 0.043125 -0.004140 0.021027 -0.096280 0.063451 0.033838 -0.029605 0.024958 -0.044214 -0.018466 -0.082116 -0.029533 0.007344 -0.061482 0.038981 -0.084020
|
||||
-0.084313 -0.038019 0.077710 -0.058798 0.076335 0.124114 -0.036329 -0.056135 -0.011941 0.019801 -0.032605 0.049799 -0.014743 -0.022984 -0.023983 0.002739 0.115499 0.010250 -0.071667 0.052221 0.028701 -0.018035 0.046885 0.065758 -0.088996 0.058902 0.045509 0.021842 0.012293 -0.058012 -0.054652 -0.028210 -0.045572 0.005237
|
||||
-0.092694 -0.031386 -0.029516 -0.066011 0.056512 0.140318 0.017759 -0.055408 0.042409 -0.001841 -0.047881 0.006271 -0.044880 0.010562 -0.008572 -0.032142 0.031237 0.011784 -0.071950 -0.017154 0.021388 0.094393 -0.059446 -0.036018 -0.074495 0.032641 0.092606 0.062712 0.134488 -0.112228 -0.109084 0.090907 -0.032517 0.032689
|
||||
-0.086068 -0.007082 -0.045041 -0.060765 0.055270 0.132259 0.009008 -0.042025 0.050070 -0.002958 -0.051816 0.001503 -0.066612 -0.017554 -0.020320 -0.047269 0.007336 0.021029 -0.065278 0.045943 0.031788 0.044150 -0.060233 -0.015205 -0.047170 0.032557 0.110315 0.067668 0.142436 -0.112995 -0.095937 0.043696 -0.053263 0.018166
|
||||
-0.089411 0.023741 -0.038912 -0.067964 0.042282 0.140245 0.010622 -0.036806 0.040610 0.006060 -0.017474 0.000163 -0.063926 0.009072 -0.059385 -0.064253 -0.040611 0.016892 -0.098455 0.064721 0.042317 0.071934 -0.068174 -0.023171 -0.006137 0.021292 0.136552 0.086574 0.159669 -0.085905 -0.090037 0.025543 -0.060574 -0.002428
|
||||
-0.078575 0.034575 0.031263 -0.073552 0.040647 0.136747 -0.043737 -0.008796 0.032331 0.016926 -0.029196 0.043721 -0.033823 -0.069883 -0.054957 0.000382 0.001785 -0.066324 -0.031587 0.075610 0.002026 0.123617 -0.016946 -0.073108 0.082295 -0.003377 0.160760 0.045913 0.138259 -0.012841 -0.021037 0.019773 -0.081271 0.003220
|
||||
-0.033366 0.059208 0.160210 -0.064990 0.028624 0.104300 -0.099598 0.045261 -0.039277 0.065556 -0.102912 0.108074 -0.081503 -0.190293 -0.052187 0.075107 0.008671 -0.121671 0.069010 0.122685 -0.035632 -0.012154 0.063158 -0.139158 0.053250 0.013035 0.078006 -0.006941 0.005533 0.101138 0.135668 0.005174 -0.004429 -0.021124
|
||||
-0.092656 0.031357 0.103505 -0.059111 0.068764 0.010312 0.008929 0.034866 0.057992 0.068053 0.014425 0.007778 0.041020 -0.040683 -0.027837 -0.022634 -0.126523 -0.071192 0.073877 0.037044 -0.024998 0.031381 0.000446 -0.063882 0.075465 -0.089846 -0.003293 -0.014744 -0.039966 0.049482 0.125205 -0.021707 -0.015263 0.035730
|
||||
-0.111708 0.016302 0.021802 -0.017327 0.098757 -0.032632 0.102916 -0.004106 0.112659 0.043944 0.086722 -0.075135 0.053748 0.008377 0.026036 -0.051027 -0.181615 0.007593 -0.029718 -0.022786 -0.013286 0.004632 0.013051 -0.001664 0.043884 -0.080356 -0.074392 -0.041220 -0.096235 -0.001700 0.105291 -0.079759 -0.034690 -0.007809
|
||||
-0.106284 -0.022433 0.016803 -0.009022 0.113956 -0.059454 0.115911 -0.012451 0.125340 0.015307 0.082184 -0.057654 0.037795 0.019407 0.065630 -0.026223 -0.104086 0.015953 -0.052260 -0.022874 -0.001840 -0.000797 -0.004680 0.054162 0.031667 -0.086636 -0.106973 -0.052172 -0.115387 -0.039377 0.098135 -0.063370 -0.010368 -0.058260
|
||||
-0.105834 -0.044185 0.028207 -0.010833 0.109847 -0.041639 0.113964 -0.035423 0.117943 0.018785 0.073258 -0.043540 0.048715 0.037758 0.075421 -0.003877 -0.043429 0.013819 -0.039051 -0.084951 -0.018739 0.005618 -0.000400 0.028961 0.006799 -0.081430 -0.141147 -0.095855 -0.105823 -0.040548 0.071096 -0.022040 -0.010334 -0.072087
|
||||
-0.085770 -0.066339 0.119689 -0.034493 0.098418 0.002001 0.025266 -0.023246 0.059661 0.027629 0.052453 0.022351 0.015313 -0.007107 -0.005840 0.096765 0.062508 -0.012640 -0.032725 -0.080090 -0.027756 -0.041996 0.055252 0.063300 -0.038983 -0.076443 -0.130005 -0.083137 -0.110099 -0.085295 0.021676 -0.004858 0.062427 -0.049960
|
||||
-0.063490 -0.034197 0.223953 -0.071609 0.017273 0.072534 -0.070046 0.008472 -0.059151 0.024538 -0.057458 0.054908 -0.069500 -0.108298 -0.024305 0.086168 0.173404 0.023995 0.062833 0.058041 0.036625 -0.084243 -0.007661 0.049316 -0.069261 0.031241 -0.034048 -0.059035 -0.063512 -0.030367 -0.002864 -0.044970 0.061520 -0.067669
|
||||
-0.080995 -0.029362 -0.020969 -0.037152 0.055714 0.092056 0.009933 -0.025303 0.020523 -0.004640 -0.020295 -0.009164 -0.005931 0.018848 0.033915 -0.030364 0.045067 0.004015 0.011173 -0.058507 0.056901 -0.042073 -0.006012 0.046935 -0.107241 0.032777 0.116424 0.038938 0.083070 0.044785 -0.024341 -0.040868 -0.054497 0.021228
|
||||
-0.079570 -0.003619 -0.038468 -0.043009 0.061929 0.088254 0.002999 -0.017741 0.034379 -0.004900 -0.032478 -0.019353 -0.018212 -0.005055 0.014637 -0.048472 -0.001520 0.022877 0.006651 -0.017392 0.069312 -0.058844 -0.004646 0.065142 -0.096265 0.026598 0.135522 0.071861 0.091550 0.032257 -0.016765 -0.075337 -0.064651 0.050908
|
||||
-0.077037 0.036024 -0.029906 -0.041175 0.045056 0.108172 0.001799 -0.013867 0.031473 0.010155 -0.003491 -0.014995 -0.021891 0.005419 -0.006514 -0.067131 -0.050711 0.002908 -0.017700 0.003424 0.063512 -0.037825 -0.008255 0.061508 -0.030670 0.015575 0.161325 0.090053 0.117788 0.091435 -0.010989 -0.096824 -0.085735 0.003260
|
||||
-0.051962 0.043127 0.185753 -0.068488 0.030906 0.083935 -0.070252 0.031192 -0.032752 0.081860 -0.058415 0.100433 -0.075819 -0.159865 -0.059411 0.067034 0.026048 -0.117863 0.048451 0.078422 -0.022589 0.005932 0.109565 -0.086305 0.028208 0.027111 0.068306 -0.018619 -0.000395 0.065584 0.129299 -0.018649 -0.057046 -0.000423
|
||||
-0.110771 0.026821 0.039896 -0.026400 0.073464 0.011366 0.088839 0.010905 0.059433 0.027762 0.038964 -0.069547 0.034358 0.017245 0.035428 -0.063296 -0.129262 0.026781 -0.092055 0.071498 -0.050266 0.045878 -0.036457 -0.040249 0.060855 -0.044906 -0.090430 -0.018843 -0.111822 -0.025148 0.069191 -0.000310 -0.018828 -0.067576
|
||||
-0.109310 -0.015148 0.033856 -0.022173 0.084027 -0.011325 0.100709 0.004099 0.070556 0.012019 0.035921 -0.046262 0.047837 0.012906 0.059339 -0.023335 -0.082080 0.034241 -0.099980 0.038508 -0.057517 0.048531 -0.049704 -0.033707 0.035725 -0.049554 -0.119832 -0.033233 -0.116399 -0.076705 0.057450 0.017861 0.007758 -0.058416
|
||||
-0.105002 -0.041286 0.052806 -0.020899 0.081333 0.007181 0.095687 -0.011183 0.063719 0.009967 0.029662 -0.037522 0.062980 0.038468 0.065127 -0.003635 -0.032995 0.016733 -0.100860 -0.006462 -0.072928 0.073195 -0.048581 -0.059580 0.018777 -0.048728 -0.138328 -0.072245 -0.108275 -0.063238 0.030578 0.066053 0.024802 -0.084883
|
||||
# The variances of the components (eigenvalues) of identity or combined identity and expression model
|
||||
1
|
||||
34
|
||||
6
|
||||
826.213804 695.783596 380.584790 282.861398 209.814481 184.418561 113.076307 104.852653 81.857546 77.095662 71.081802 55.760367 49.883312 39.122009 37.668889 32.916377 31.165932 26.644275 24.233150 21.357573 17.029065 15.432317 13.812689 12.440567 10.213426 9.316734 5.327325 2.526152 1.659451 1.123615 1.015840 0.816193 0.718969 0.582660
|
||||
Binary file not shown.
@@ -0,0 +1,421 @@
|
||||
# The mean values of the components (in mm)
|
||||
204
|
||||
1
|
||||
6
|
||||
-73.373789
|
||||
-72.755424
|
||||
-70.514618
|
||||
-66.831997
|
||||
-59.773997
|
||||
-48.355832
|
||||
-34.111799
|
||||
-17.870498
|
||||
0.098877
|
||||
17.472593
|
||||
32.640591
|
||||
46.360399
|
||||
57.328628
|
||||
64.371747
|
||||
68.194256
|
||||
70.467988
|
||||
71.357150
|
||||
-61.103194
|
||||
-51.274051
|
||||
-37.794888
|
||||
-24.016540
|
||||
-11.632810
|
||||
12.053239
|
||||
25.099417
|
||||
38.328278
|
||||
51.177340
|
||||
60.037888
|
||||
0.653594
|
||||
0.804393
|
||||
0.991706
|
||||
1.226195
|
||||
-14.768687
|
||||
-7.178485
|
||||
0.555611
|
||||
8.270156
|
||||
15.210184
|
||||
-45.906975
|
||||
-37.784505
|
||||
-27.729718
|
||||
-19.666941
|
||||
-28.297429
|
||||
-38.171882
|
||||
19.406998
|
||||
27.723376
|
||||
37.535684
|
||||
45.150366
|
||||
38.199537
|
||||
28.661192
|
||||
-28.908562
|
||||
-17.528613
|
||||
-6.682934
|
||||
0.380782
|
||||
8.373112
|
||||
18.871554
|
||||
28.786809
|
||||
19.052496
|
||||
8.953933
|
||||
0.381372
|
||||
-7.426997
|
||||
-18.155851
|
||||
-24.371005
|
||||
-6.895899
|
||||
0.340472
|
||||
8.442393
|
||||
24.468001
|
||||
8.446857
|
||||
0.205188
|
||||
-7.196432
|
||||
-29.793333
|
||||
-10.946667
|
||||
7.927913
|
||||
26.067561
|
||||
42.553283
|
||||
56.466254
|
||||
67.229264
|
||||
75.037046
|
||||
77.040871
|
||||
74.738615
|
||||
66.911246
|
||||
56.296408
|
||||
42.407806
|
||||
25.449040
|
||||
6.988853
|
||||
-11.663198
|
||||
-30.357229
|
||||
-49.348360
|
||||
-58.754088
|
||||
-61.979633
|
||||
-61.017167
|
||||
-56.671714
|
||||
-57.375856
|
||||
-61.885829
|
||||
-62.761139
|
||||
-59.286709
|
||||
-50.177043
|
||||
-42.182614
|
||||
-30.985526
|
||||
-19.939343
|
||||
-8.412358
|
||||
2.597566
|
||||
4.750313
|
||||
6.561126
|
||||
4.659722
|
||||
2.642285
|
||||
-37.309194
|
||||
-42.654824
|
||||
-42.635820
|
||||
-36.652339
|
||||
-35.291876
|
||||
-35.116298
|
||||
-36.961936
|
||||
-43.195395
|
||||
-43.037316
|
||||
-37.933589
|
||||
-35.725267
|
||||
-35.673593
|
||||
28.605174
|
||||
22.166312
|
||||
19.023984
|
||||
20.715586
|
||||
19.030359
|
||||
22.388095
|
||||
28.072396
|
||||
36.288547
|
||||
39.624011
|
||||
40.384901
|
||||
39.825825
|
||||
36.668186
|
||||
28.670195
|
||||
25.469200
|
||||
26.007335
|
||||
25.319428
|
||||
28.315419
|
||||
30.588056
|
||||
31.400381
|
||||
30.836687
|
||||
47.655420
|
||||
45.897739
|
||||
44.831169
|
||||
43.130111
|
||||
38.625415
|
||||
30.742730
|
||||
18.451712
|
||||
3.608115
|
||||
-0.881548
|
||||
5.179627
|
||||
19.171178
|
||||
30.762024
|
||||
37.618202
|
||||
40.874987
|
||||
42.269747
|
||||
44.130378
|
||||
47.127458
|
||||
14.251094
|
||||
7.266613
|
||||
0.442241
|
||||
-6.604531
|
||||
-11.964088
|
||||
-12.048015
|
||||
-7.313252
|
||||
-1.022865
|
||||
5.347743
|
||||
11.612322
|
||||
-13.377250
|
||||
-21.145213
|
||||
-29.276244
|
||||
-36.938241
|
||||
-20.126559
|
||||
-23.530391
|
||||
-25.937570
|
||||
-23.689510
|
||||
-20.852724
|
||||
7.284119
|
||||
2.923373
|
||||
1.151365
|
||||
0.266493
|
||||
-0.381583
|
||||
1.385374
|
||||
-0.333662
|
||||
0.065813
|
||||
1.582963
|
||||
5.216842
|
||||
0.154685
|
||||
-1.406395
|
||||
-2.239548
|
||||
-15.930013
|
||||
-22.605331
|
||||
-23.742161
|
||||
-22.716042
|
||||
-15.606685
|
||||
-3.216756
|
||||
-14.984163
|
||||
-22.548336
|
||||
-23.585387
|
||||
-22.400130
|
||||
-15.117794
|
||||
-4.784273
|
||||
-20.888182
|
||||
-22.214615
|
||||
-21.020027
|
||||
-5.711445
|
||||
-20.666067
|
||||
-21.897867
|
||||
-20.322589
|
||||
# The principal components (eigenvectors) of identity or combined identity and expression model
|
||||
204
|
||||
40
|
||||
6
|
||||
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|
||||
-0.105846 -0.044192 0.028351 -0.010971 0.109839 -0.041667 0.113996 -0.035640 0.118299 0.019369 0.072622 -0.043148 0.048912 0.037821 0.075681 -0.002336 -0.042502 0.013842 -0.037719 -0.085127 -0.018249 0.004397 -0.001762 0.032164 0.024951 -0.073639 -0.031012 -0.139714 -0.024712 -0.093660 0.105859 -0.004051 -0.055358 0.059215 0.024371 -0.011832 -0.068208 0.034876 -0.000105 0.002078
|
||||
-0.085798 -0.066340 0.119873 -0.034725 0.098091 0.001938 0.025168 -0.023316 0.059782 0.027775 0.052292 0.022333 0.015326 -0.007160 -0.005906 0.094748 0.066845 -0.011505 -0.029463 -0.079473 -0.029799 -0.040752 0.056511 0.063384 -0.019562 -0.082531 -0.019004 -0.129260 -0.014240 -0.082470 0.112765 0.003543 -0.083892 0.001334 0.004039 0.061603 -0.044741 0.024378 0.025277 0.053960
|
||||
-0.063535 -0.034186 0.224097 -0.071885 0.016458 0.072452 -0.070314 0.008452 -0.059782 0.023955 -0.056748 0.054156 -0.069439 -0.108735 -0.024702 0.080023 0.174649 0.024722 0.065013 0.059578 0.033906 -0.084548 -0.000715 0.043127 -0.080794 0.016293 -0.006149 -0.033301 -0.018165 -0.056718 0.063332 0.004258 -0.028921 -0.011645 0.044894 0.060372 -0.057430 0.060711 0.032087 0.014914
|
||||
-0.080995 -0.029372 -0.020936 -0.037229 0.055793 0.092033 0.009902 -0.025321 0.020486 -0.004590 -0.020467 -0.009133 -0.005915 0.018745 0.034023 -0.031465 0.044439 0.004361 0.013800 -0.058051 0.056430 -0.044453 -0.000960 0.041938 -0.108613 -0.001029 0.041861 0.114037 0.006060 0.037582 -0.084442 -0.005612 0.045855 -0.015693 0.041334 -0.054024 0.014960 -0.031975 -0.037105 -0.060021
|
||||
-0.079566 -0.003629 -0.038445 -0.043082 0.062053 0.088229 0.003020 -0.017745 0.034363 -0.004754 -0.032766 -0.019325 -0.018234 -0.005061 0.014769 -0.048187 -0.002872 0.022872 0.007924 -0.017074 0.068502 -0.061796 0.001748 0.059751 -0.098735 -0.002292 0.035608 0.133567 0.010406 0.070390 -0.093039 -0.010619 0.028778 -0.015856 0.073491 -0.062689 0.038369 -0.028735 -0.058425 -0.036480
|
||||
-0.077036 0.036018 -0.029922 -0.041235 0.045187 0.108160 0.001796 -0.013844 0.031548 0.010327 -0.003792 -0.014940 -0.022032 0.005553 -0.006296 -0.065257 -0.052401 0.002676 -0.018271 0.003100 0.063487 -0.041284 -0.003496 0.058794 -0.034165 0.006084 0.024209 0.159948 0.005517 0.089435 -0.121754 -0.020812 0.082199 0.003058 0.096242 -0.084122 -0.010483 -0.009651 -0.070706 -0.062756
|
||||
-0.052003 0.043139 0.185843 -0.068728 0.030309 0.083874 -0.070488 0.031272 -0.033207 0.081536 -0.058105 0.100086 -0.076473 -0.159773 -0.059622 0.066329 0.028723 -0.117783 0.047918 0.080207 -0.025956 0.013106 0.104313 -0.085292 0.033005 0.023088 0.034794 0.066321 0.009281 -0.020213 -0.000276 -0.012863 0.033528 0.147404 0.029576 -0.060797 0.009791 0.078471 -0.024700 0.022279
|
||||
-0.110786 0.026822 0.039952 -0.026526 0.073416 0.011345 0.088964 0.010762 0.059680 0.028327 0.038491 -0.069111 0.034520 0.017497 0.035858 -0.059230 -0.130560 0.026149 -0.096236 0.069057 -0.047770 0.045632 -0.040172 -0.035966 0.067283 -0.023591 -0.032511 -0.088576 -0.006475 -0.017264 0.112017 0.000010 -0.038685 0.063336 0.002604 -0.019499 -0.062213 -0.062912 0.063804 -0.028722
|
||||
-0.109322 -0.015151 0.033951 -0.022305 0.083966 -0.011351 0.100828 0.003915 0.070816 0.012543 0.035456 -0.045839 0.048000 0.013029 0.059677 -0.020739 -0.081918 0.034125 -0.102676 0.036050 -0.054717 0.047892 -0.053124 -0.029803 0.043430 -0.033969 -0.034854 -0.117903 -0.009254 -0.031637 0.117845 0.007656 -0.085368 0.038397 -0.018079 0.007744 -0.053858 -0.077995 0.076237 0.002876
|
||||
-0.105018 -0.041290 0.052918 -0.021046 0.081223 0.007153 0.095745 -0.011381 0.063893 0.010411 0.029284 -0.037083 0.063172 0.038511 0.065429 -0.002500 -0.031949 0.017075 -0.102069 -0.008865 -0.069669 0.073388 -0.053990 -0.055034 0.029993 -0.040109 -0.027041 -0.136941 -0.009460 -0.071253 0.110548 0.014470 -0.061265 0.021618 -0.064074 0.023098 -0.072362 -0.084130 0.106998 0.013525
|
||||
# The variances of the components (eigenvalues) of identity or combined identity and expression model
|
||||
1
|
||||
40
|
||||
6
|
||||
825.653911 695.251764 379.949309 282.608425 209.372158 184.276210 112.929629 104.747486 81.754313 76.948819 70.997626 55.694115 49.831240 39.097028 37.608409 32.901692 31.071894 26.573259 24.065792 21.351787 16.963006 15.400988 13.770505 12.405087 10.380942 9.568418 6.233860 5.322387 2.812823 2.519250 1.647141 1.340653 1.086666 0.992569 0.812544 0.718175 0.591089 0.511102 0.480803 0.371234
|
||||
Binary file not shown.
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@@ -0,0 +1,41 @@
|
||||
function [ observations ] = prune_observations( observations, percentage_to_keep )
|
||||
%PRUNE_OBSERVATIONS Summary of this function goes here
|
||||
% Detailed explanation goes here
|
||||
|
||||
distances = pdist(observations, @euclid_dist);
|
||||
|
||||
distances = squareform(distances);
|
||||
|
||||
m = max(distances(:));
|
||||
|
||||
distances(logical(eye(size(distances)))) = m;
|
||||
|
||||
to_rem = false(size(observations,1),1);
|
||||
|
||||
% need to get rid of the smallest distances
|
||||
for i=size(observations,1):-1:round(percentage_to_keep * size(observations,1))
|
||||
|
||||
[~, ind] = min(distances(:));
|
||||
[row, col] = ind2sub(size(distances),ind);
|
||||
|
||||
% always remove the row?
|
||||
|
||||
to_rem(row) = true;
|
||||
|
||||
distances(row,:) = m;
|
||||
distances(:,row) = m;
|
||||
end
|
||||
|
||||
observations = observations(~to_rem,:);
|
||||
|
||||
end
|
||||
|
||||
function [dist] = euclid_dist(XI, XJ)
|
||||
|
||||
x_dist = bsxfun(@plus, XJ(:, 1:end/3), -XI(1:end/3)).^2;
|
||||
y_dist = bsxfun(@plus, XJ(:, end/3+1:2*end/3), -XI(end/3+1:2*end/3)).^2;
|
||||
z_dist = bsxfun(@plus, XJ(:, 2*end/3+1:end), - XI(2*end/3+1:end)).^2;
|
||||
|
||||
dist = mean(sqrt(x_dist + y_dist + z_dist),2);
|
||||
|
||||
end
|
||||
Binary file not shown.
@@ -0,0 +1,41 @@
|
||||
function writePDM( V, E, M, outputFile, Vmorph, Emorph )
|
||||
%WRITEPDM Summary of this function goes here
|
||||
% Detailed explanation goes here
|
||||
|
||||
fId = fopen(outputFile,'w');
|
||||
|
||||
% number of elements
|
||||
|
||||
% Comment
|
||||
fprintf(fId, '# The mean values of the components (in mm)\n');
|
||||
writeMatrix(fId, M, 6);
|
||||
|
||||
fprintf(fId, '# The principal components (eigenvectors) of identity or combined identity and expression model\n');
|
||||
writeMatrix(fId, V, 6);
|
||||
|
||||
fprintf(fId, '# The variances of the components (eigenvalues) of identity or combined identity and expression model\n');
|
||||
writeMatrix(fId, E', 6);
|
||||
|
||||
if(nargin > 4)
|
||||
fprintf(fId, '# The principal components (eigenvectors) of expression\n');
|
||||
writeMatrix(fId, Vmorph, 6);
|
||||
|
||||
fprintf(fId, '# The variances of the components (eigenvalues) of expression\n');
|
||||
writeMatrix(fId, Emorph', 6);
|
||||
end
|
||||
|
||||
fclose(fId);
|
||||
end
|
||||
|
||||
% for easier readibility write them row by row
|
||||
function writeMatrix(fileID, M, type)
|
||||
|
||||
fprintf(fileID, '%d\n', size(M,1));
|
||||
fprintf(fileID, '%d\n', size(M,2));
|
||||
fprintf(fileID, '%d\n', type);
|
||||
|
||||
for i=1:size(M,1)
|
||||
fprintf(fileID, '%f ', M(i,:));
|
||||
fprintf(fileID, '\n');
|
||||
end
|
||||
end
|
||||
@@ -0,0 +1,106 @@
|
||||
% collect the training data annotations (from the menpo challenge)
|
||||
clear
|
||||
train_data_loc = 'D:\Datasets\menpo/';
|
||||
|
||||
dataset_locs = {[train_data_loc, '/train/'];};
|
||||
|
||||
% Mapping all the points (profile and semi-frontal) to the same 68 point
|
||||
% annotation scheme
|
||||
left_to_frontal_map = [17,28; 18,29; 19,30; 20,31;
|
||||
21,34; 22,32; 23,39; 24,38; 25,37; 26,42; 27,41;
|
||||
28,52; 29,51; 30,50; 31,49; 32,60; 33,59; 34,58;
|
||||
35,63; 36,62; 37,61; 38,68; 39,67];
|
||||
|
||||
right_to_frontal_map = [17,28; 18,29; 19,30; 20,31;
|
||||
21,34; 22,36; 23,44; 24,45; 25,46; 26,47; 27,48;
|
||||
28,52; 29,53; 30,54; 31,55; 32,56; 33,57; 34,58;
|
||||
35,63; 36,64; 37,65; 38,66; 39,67];
|
||||
|
||||
all_pts = [];
|
||||
mirr_pts = [];
|
||||
|
||||
add_flip = true;
|
||||
|
||||
mirror_inds = [1,17;2,16;3,15;4,14;5,13;6,12;7,11;8,10;18,27;19,26;20,25;21,24;22,23;...
|
||||
32,36;33,35;37,46;38,45;39,44;40,43;41,48;42,47;49,55;50,54;51,53;60,56;59,57;...
|
||||
61,65;62,64;68,66];
|
||||
|
||||
for i=1:numel(dataset_locs)
|
||||
landmarkLabels = dir([dataset_locs{i} '\*.pts']);
|
||||
landmarkImgs = dir([dataset_locs{i} '\*.jpg']);
|
||||
|
||||
for p=1:numel(landmarkLabels)
|
||||
landmarks = importdata([dataset_locs{i}, landmarkLabels(p).name], ' ', 3);
|
||||
img = imread([dataset_locs{i}, landmarkImgs(p).name]);
|
||||
landmarks = landmarks.data;
|
||||
landmark_labels = -ones(68,2);
|
||||
|
||||
if(size(landmarks,1) == 39)
|
||||
% Determine if the points are clock-wise or counter clock-wise
|
||||
% Clock-wise points are facing left, counter-clock-wise right
|
||||
sum = 0;
|
||||
for k=1:11
|
||||
step = (landmarks(k+1,1) - landmarks(k,1)) * (landmarks(k+1,2) + landmarks(k,2));
|
||||
sum = sum + step;
|
||||
end
|
||||
|
||||
if(sum > 0)
|
||||
% First need to resample the face outline as there are 9
|
||||
% points in the near-frontal and 10 points in profile for
|
||||
% the outline of the face
|
||||
|
||||
outline = iterate_piece_wise(landmarks(1:10,:), 9);
|
||||
brow = iterate_piece_wise(landmarks(13:16,:), 5);
|
||||
landmark_labels(1:9,:) = outline;
|
||||
landmark_labels(18:22,:) = brow;
|
||||
landmark_labels(left_to_frontal_map(:,2),:) = landmarks(left_to_frontal_map(:,1),:);
|
||||
else
|
||||
outline = iterate_piece_wise(landmarks(10:-1:1,:), 9);
|
||||
brow = iterate_piece_wise(landmarks(16:-1:13,:), 5);
|
||||
|
||||
landmark_labels(9:17,:) = outline;
|
||||
landmark_labels(23:27,:) = brow;
|
||||
|
||||
landmark_labels(right_to_frontal_map(:,2),:) = landmarks(right_to_frontal_map(:,1),:);
|
||||
end
|
||||
else
|
||||
landmark_labels = landmarks;
|
||||
end
|
||||
|
||||
all_pts = cat(3, all_pts, landmark_labels);
|
||||
|
||||
if(add_flip)
|
||||
|
||||
mirror_lbls = landmark_labels;
|
||||
mirror_lbls(mirror_lbls ==-1) = nan;
|
||||
mirror_lbls(:,1) = -mirror_lbls(:,1);
|
||||
tmp1 = mirror_lbls(mirror_inds(:,1),:);
|
||||
tmp2 = mirror_lbls(mirror_inds(:,2),:);
|
||||
mirror_lbls(mirror_inds(:,2),:) = tmp1;
|
||||
mirror_lbls(mirror_inds(:,1),:) = tmp2;
|
||||
|
||||
mirror_lbls(isnan(mirror_lbls)) = -1;
|
||||
|
||||
mirr_pts = cat(3, mirr_pts, mirror_lbls);
|
||||
end
|
||||
|
||||
end
|
||||
end
|
||||
all_pts_old = all_pts;
|
||||
%%
|
||||
xs = squeeze(all_pts(:,1,:));
|
||||
ys = squeeze(all_pts(:,2,:));
|
||||
|
||||
all_pts = cat(2,xs,ys)';
|
||||
save('menpo_68_pts', 'all_pts');
|
||||
|
||||
%%
|
||||
all_pts = all_pts_old ;
|
||||
all_pts = cat(3, all_pts, mirr_pts);
|
||||
|
||||
xs = squeeze(all_pts(:,1,:));
|
||||
ys = squeeze(all_pts(:,2,:));
|
||||
|
||||
all_pts = cat(2,xs,ys)';
|
||||
|
||||
save('menpo_68_pts_flip', 'all_pts');
|
||||
@@ -0,0 +1,74 @@
|
||||
% collect the training data annotations (from the menpo challenge)
|
||||
clear
|
||||
train_data_loc = 'D:\Datasets\menpo/';
|
||||
|
||||
dataset_locs = {[train_data_loc, '/valid/'];};
|
||||
|
||||
|
||||
left_to_frontal_map = [17,28; 18,29; 19,30; 20,31;
|
||||
21,34; 22,32; 23,39; 24,38; 25,37; 26,42; 27,41;
|
||||
28,52; 29,51; 30,50; 31,49; 32,60; 33,59; 34,58;
|
||||
35,63; 36,62; 37,61; 38,68; 39,67];
|
||||
|
||||
right_to_frontal_map = [17,28; 18,29; 19,30; 20,31;
|
||||
21,34; 22,36; 23,44; 24,45; 25,46; 26,47; 27,48;
|
||||
28,52; 29,53; 30,54; 31,55; 32,56; 33,57; 34,58;
|
||||
35,63; 36,64; 37,65; 38,66; 39,67];
|
||||
|
||||
all_pts = [];
|
||||
|
||||
for i=1:numel(dataset_locs)
|
||||
landmarkLabels = dir([dataset_locs{i} '\*.pts']);
|
||||
landmarkImgs = dir([dataset_locs{i} '\*.jpg']);
|
||||
|
||||
for p=1:numel(landmarkLabels)
|
||||
|
||||
landmarks = importdata([dataset_locs{i}, landmarkLabels(p).name], ' ', 3);
|
||||
img = imread([dataset_locs{i}, landmarkImgs(p).name]);
|
||||
landmarks = landmarks.data;
|
||||
landmark_labels = -ones(68,2);
|
||||
|
||||
if(size(landmarks,1) == 39)
|
||||
% Determine if the points are clock-wise or counter clock-wise
|
||||
% Clock-wise points are facing left, counter-clock-wise right
|
||||
sum = 0;
|
||||
for k=1:11
|
||||
step = (landmarks(k+1,1) - landmarks(k,1)) * (landmarks(k+1,2) + landmarks(k,2));
|
||||
sum = sum + step;
|
||||
end
|
||||
|
||||
if(sum > 0)
|
||||
% First need to resample the face outline as there are 9
|
||||
% points in the near-frontal and 10 points in profile for
|
||||
% the outline of the face
|
||||
|
||||
outline = iterate_piece_wise(landmarks(1:10,:), 9);
|
||||
brow = iterate_piece_wise(landmarks(13:16,:), 5);
|
||||
landmark_labels(1:9,:) = outline;
|
||||
landmark_labels(18:22,:) = brow;
|
||||
landmark_labels(left_to_frontal_map(:,2),:) = landmarks(left_to_frontal_map(:,1),:);
|
||||
else
|
||||
outline = iterate_piece_wise(landmarks(10:-1:1,:), 9);
|
||||
brow = iterate_piece_wise(landmarks(16:-1:13,:), 5);
|
||||
|
||||
landmark_labels(9:17,:) = outline;
|
||||
landmark_labels(23:27,:) = brow;
|
||||
|
||||
landmark_labels(right_to_frontal_map(:,2),:) = landmarks(right_to_frontal_map(:,1),:);
|
||||
end
|
||||
else
|
||||
landmark_labels = landmarks;
|
||||
end
|
||||
|
||||
all_pts = cat(3, all_pts, landmark_labels);
|
||||
end
|
||||
end
|
||||
|
||||
%%
|
||||
|
||||
xs = squeeze(all_pts(:,1,:));
|
||||
ys = squeeze(all_pts(:,2,:));
|
||||
|
||||
all_pts = cat(2,xs,ys)';
|
||||
|
||||
save('menpo_68_pts_valid', 'all_pts');
|
||||
@@ -0,0 +1,101 @@
|
||||
clear;
|
||||
|
||||
addpath('../PDM_helpers/');
|
||||
|
||||
Reconstruct_Torresani;
|
||||
|
||||
%% Create the PDM using PCA, from the recovered 3D data
|
||||
clear
|
||||
load('Torr_menpo_wild.mat');
|
||||
|
||||
% need to still perform procrustes though
|
||||
|
||||
x = P3(1:end/3,:);
|
||||
y = P3(end/3+1:2*end/3,:);
|
||||
|
||||
% To make sure that PDM faces the right way (positive Z towards the screen)
|
||||
z = P3(2*end/3+1:end,:);
|
||||
|
||||
[ normX, normY, normZ, meanShape, Transform ] = ProcrustesAnalysis3D(x,y,z, true);
|
||||
observations = [normX normY normZ];
|
||||
|
||||
[princComp, score, eigenVals] = princomp(observations,'econ');
|
||||
% Keeping most variation
|
||||
totalSum = sum(eigenVals);
|
||||
count = numel(eigenVals);
|
||||
for i=1:numel(eigenVals)
|
||||
if ((sum(eigenVals(1:i)) / totalSum) >= 0.999)
|
||||
count = i;
|
||||
break;
|
||||
end
|
||||
end
|
||||
|
||||
V = princComp(:,1:count);
|
||||
E = eigenVals(1:count);
|
||||
M = meanShape(:);
|
||||
|
||||
% Now normalise it to have actual world scale
|
||||
lPupil = [(M(37) + M(40))/2; (M(37 + 68) + M(40 + 68))/2];
|
||||
rPupil = [(M(43) + M(46))/2; (M(43 + 68) + M(46 + 68))/2];
|
||||
|
||||
dist = norm(lPupil - rPupil,2);
|
||||
|
||||
% average human interocular distance is 65mm
|
||||
scaling = 65 / dist;
|
||||
|
||||
% normalise the mean values as well
|
||||
M(1:end/3) = M(1:end/3) - mean(M(1:end/3));
|
||||
M(end/3+1:2*end/3) = M(end/3+1:2*end/3) - mean(M(end/3+1:2*end/3));
|
||||
M(2*end/3+1:end) = M(2*end/3+1:end) - mean(M(2*end/3+1:end));
|
||||
|
||||
M = M * scaling;
|
||||
E = E * scaling .^ 2;
|
||||
|
||||
% orthonormalise V
|
||||
scalingV = sqrt(sum(V.^2));
|
||||
V = V ./ repmat(scalingV, numel(M),1);
|
||||
|
||||
E = E .* (scalingV') .^ 2;
|
||||
|
||||
%% Also align the model to a Multi-PIE one for accurate head orientation
|
||||
% also align the mean shape model (an aligned 68 point PDM from Multi-PIE dataset)
|
||||
M_wild = M;
|
||||
|
||||
load('pdm_68_multi_pie.mat', 'M');
|
||||
M_align = M;
|
||||
|
||||
n_points = numel(M)/3;
|
||||
|
||||
M_wild = reshape(M_wild, n_points, 3);
|
||||
|
||||
% work out the translation and rotation needed
|
||||
[ R, T ] = AlignShapesKabsch(M_wild, reshape(M_align, n_points,3));
|
||||
|
||||
% Transform the wild one to be in the same reference as the Multi-PIE one
|
||||
M_aligned = (R * M_wild')';
|
||||
|
||||
M_aligned(:,1) = M_aligned(:,1) + T(1);
|
||||
M_aligned(:,2) = M_aligned(:,2) + T(2);
|
||||
M_aligned(:,3) = M_aligned(:,3) + T(3);
|
||||
|
||||
M_aligned = M_aligned(:);
|
||||
V_aligned = V;
|
||||
|
||||
% need to align the principal components as well
|
||||
for i=1:size(V,2)
|
||||
|
||||
V_aligned_pie_curr = (R * reshape(V(:,i), n_points, 3)')';
|
||||
V_aligned(:,i) = V_aligned_pie_curr(:);
|
||||
|
||||
end
|
||||
|
||||
V = V_aligned;
|
||||
M = M_aligned;
|
||||
|
||||
save('pdm_68_aligned_menpo.mat', 'E', 'M', 'V');
|
||||
writePDM(V, E, M, 'pdm_68_aligned_menpo.txt');
|
||||
|
||||
% also save this to model location
|
||||
if(exist('../../models/pdm/', 'file'))
|
||||
save('../../models/pdm/pdm_68_aligned_menpo.mat', 'E', 'M', 'V');
|
||||
end
|
||||
@@ -0,0 +1,48 @@
|
||||
clear
|
||||
load('Noise_PDM/noise_0.2.mat');
|
||||
addpath('../PDM_helpers');
|
||||
|
||||
xs_orig = data_orig(:,1:end/2);
|
||||
ys_orig = data_orig(:,end/2+1:end);
|
||||
|
||||
xs_noise = data_noise(:,1:end/2);
|
||||
ys_noise = data_noise(:,end/2+1:end);
|
||||
|
||||
num_imgs = size(xs_noise, 1);
|
||||
|
||||
errs_orig = zeros(1,num_imgs);
|
||||
errs_noise = zeros(1,num_imgs);
|
||||
probs_orig = zeros(1,num_imgs);
|
||||
probs_noise = zeros(1,num_imgs);
|
||||
|
||||
pdmLoc = ['pdm_68_aligned_menpo_v5.mat'];
|
||||
|
||||
load(pdmLoc);
|
||||
|
||||
pdm = struct;
|
||||
pdm.M = double(M);
|
||||
pdm.E = double(E);
|
||||
pdm.V = double(V);
|
||||
|
||||
for i=1:num_imgs
|
||||
|
||||
labels_curr_orig = cat(2, xs_orig(i,:)', ys_orig(i,:)') * 100;
|
||||
labels_curr_orig(labels_curr_orig==-200) = 0;
|
||||
|
||||
[ a, R, T, ~, l_params, err, shapeOrtho] = fit_PDM_ortho_proj_to_2D(pdm.M, pdm.E, pdm.V, labels_curr_orig);
|
||||
errs_orig(i) = err/a;
|
||||
probs_orig(i) = sum(log(exp((-l_params.^2)./(pdm.E.^2))./(sqrt(2*pi.*pdm.E))));
|
||||
labels_curr_noise = cat(2, xs_noise(i,:)', ys_noise(i,:)') * 100;
|
||||
labels_curr_noise(labels_curr_orig==0) = 0;
|
||||
|
||||
[ a, R, T, ~, l_params, err, shapeOrtho] = fit_PDM_ortho_proj_to_2D(pdm.M, pdm.E, pdm.V, labels_curr_noise);
|
||||
errs_noise(i) = err/a;
|
||||
probs_noise(i) = sum(log(exp((-l_params.^2)./(pdm.E.^2))./(sqrt(2*pi.*pdm.E))));
|
||||
|
||||
end
|
||||
|
||||
% Current error is 2.1728 on the training data
|
||||
% After cleanup and smaller steps it is 1.5388
|
||||
% After training on it we have 1.1999
|
||||
% V2 - 1.1392
|
||||
% V3 - 1.1406
|
||||
@@ -0,0 +1,110 @@
|
||||
% This is the final model used for 3D PDM, it contains both Menpo and 300W
|
||||
% data
|
||||
clear
|
||||
|
||||
% Combining 300W and Menpo data for PDM
|
||||
load('menpo_68_pts_flip');
|
||||
num_pts = size(all_pts,1)/2;
|
||||
xs_m = all_pts(1:num_pts,:);
|
||||
ys_m = all_pts(num_pts+1:end,:);
|
||||
|
||||
load('wild_68_pts');
|
||||
num_pts = size(all_pts,1)/2;
|
||||
xs_w= all_pts(1:num_pts,:);
|
||||
ys_w = all_pts(num_pts+1:end,:);
|
||||
|
||||
all_pts = cat(1, xs_m, xs_w, ys_m, ys_w);
|
||||
|
||||
pdmLoc = ['../../models/pdm/pdm_68_aligned_wild.mat'];
|
||||
load(pdmLoc);
|
||||
% Before plugging into NRSFM, align the points in 2D
|
||||
num_pts = size(all_pts,1)/2;
|
||||
|
||||
num_lmks = numel(M) / 3;
|
||||
m = reshape(M, num_lmks, 3)';
|
||||
width_model = max(m(1,:)) - min(m(1,:));
|
||||
height_model = max(m(2,:)) - min(m(2,:));
|
||||
|
||||
for i=1:size(all_pts,1)/2
|
||||
|
||||
shape2D = cat(2, all_pts(i,:)', all_pts(i+num_pts,:)');
|
||||
|
||||
M_n = M;
|
||||
|
||||
if(sum(shape2D(:)==-1) > 0)
|
||||
|
||||
hidden = true;
|
||||
% which indices to remove
|
||||
inds_to_rem = shape2D(:,1) == -1 | shape2D(:,2) == -1;
|
||||
|
||||
shape2D = shape2D(~inds_to_rem,:);
|
||||
|
||||
inds_to_rem = repmat(inds_to_rem, 3, 1);
|
||||
|
||||
M_n = M(~inds_to_rem);
|
||||
|
||||
end
|
||||
|
||||
% To deal with really extreme cases of roll
|
||||
M2D = cat(2, M_n(1:end/3), M_n(end/3+1:2*end/3));
|
||||
[ A, t, error, alignedShape, s ] = AlignShapesWithScale(M2D, shape2D);
|
||||
R = A/s;
|
||||
|
||||
% Transform the shape
|
||||
shape2D(:,1) = shape2D(:,1) - t(1);
|
||||
shape2D(:,2) = shape2D(:,2) - t(2);
|
||||
|
||||
shape2D = (R' * shape2D')/s;
|
||||
shape2D = shape2D';
|
||||
|
||||
all_pts(i,all_pts(i,:)~=-1) = shape2D(:,1);
|
||||
all_pts(i+num_pts,all_pts(i+num_pts,:)~=-1) = shape2D(:,2);
|
||||
end
|
||||
|
||||
%%
|
||||
% to_rem = randperm(round(0.1*num_pts)); % Remove 10% to break some symmetry
|
||||
% all_pts([to_rem, to_rem+num_pts],:) = [];
|
||||
num_pts = size(all_pts,1)/2;
|
||||
|
||||
left_ids = all_pts(1:num_pts,10) == -1;
|
||||
right_ids = all_pts(1:num_pts,8) == -1;
|
||||
frontal = true(num_pts,1);
|
||||
frontal(left_ids | right_ids) = false;
|
||||
|
||||
%%
|
||||
xs = all_pts(1:num_pts,:);
|
||||
ys = all_pts(num_pts+1:end,:);
|
||||
|
||||
% Randperm the data, as a test
|
||||
|
||||
xs_f = xs(frontal,:);
|
||||
ys_f = ys(frontal,:);
|
||||
scatter(xs_f(:), -ys_f(:));
|
||||
|
||||
%% Perform NRSFM by Torresani
|
||||
addpath('../nrsfm-em');
|
||||
% (T is the number of frames, J is the number of points)
|
||||
|
||||
J = size(all_pts,2);
|
||||
T = size(all_pts,1)/2;
|
||||
|
||||
use_lds = 0; % not modeling a linear dynamic system here
|
||||
max_em_iter = 200;
|
||||
tol = 0.001;
|
||||
K = 30; % number of deformation shapes
|
||||
|
||||
MD = all_pts(1:end/2,:)==-1;
|
||||
|
||||
[P3, S_hat, V, RO, Tr, Z] = em_sfm(all_pts, MD, K, use_lds, tol, max_em_iter);
|
||||
|
||||
save('Torr_menpo_wild', 'P3', 'S_hat', 'V', 'RO', 'Tr', 'Z');
|
||||
|
||||
%%
|
||||
% xs = P3(1:num_pts,:);
|
||||
% ys = P3(num_pts+1:2*num_pts,:);
|
||||
% zs = P3(2*num_pts+1:end,:);
|
||||
% %
|
||||
% xs_f = xs(left_ids,:);
|
||||
% ys_f = ys(left_ids,:);
|
||||
% zs_f = zs(left_ids,:);
|
||||
% scatter3(xs_f(:), ys_f(:), zs_f(:));
|
||||
@@ -0,0 +1,97 @@
|
||||
clear
|
||||
|
||||
load('menpo_68_pts_flip');
|
||||
|
||||
pdmLoc = ['../../models/pdm/pdm_68_aligned_wild.mat'];
|
||||
load(pdmLoc);
|
||||
% Before plugging into NRSFM, align the points in 2D
|
||||
num_pts = size(all_pts,1)/2;
|
||||
|
||||
num_lmks = numel(M) / 3;
|
||||
m = reshape(M, num_lmks, 3)';
|
||||
width_model = max(m(1,:)) - min(m(1,:));
|
||||
height_model = max(m(2,:)) - min(m(2,:));
|
||||
|
||||
for i=1:size(all_pts,1)/2
|
||||
|
||||
shape2D = cat(2, all_pts(i,:)', all_pts(i+num_pts,:)');
|
||||
|
||||
M_n = M;
|
||||
|
||||
if(sum(shape2D(:)==-1) > 0)
|
||||
|
||||
hidden = true;
|
||||
% which indices to remove
|
||||
inds_to_rem = shape2D(:,1) == -1 | shape2D(:,2) == -1;
|
||||
|
||||
shape2D = shape2D(~inds_to_rem,:);
|
||||
|
||||
inds_to_rem = repmat(inds_to_rem, 3, 1);
|
||||
|
||||
M_n = M(~inds_to_rem);
|
||||
|
||||
end
|
||||
|
||||
% To deal with really extreme cases of roll
|
||||
M2D = cat(2, M_n(1:end/3), M_n(end/3+1:2*end/3));
|
||||
[ A, t, error, alignedShape, s ] = AlignShapesWithScale(M2D, shape2D);
|
||||
R = A/s;
|
||||
|
||||
% Transform the shape
|
||||
shape2D(:,1) = shape2D(:,1) - t(1);
|
||||
shape2D(:,2) = shape2D(:,2) - t(2);
|
||||
|
||||
shape2D = (R' * shape2D')/s;
|
||||
shape2D = shape2D';
|
||||
|
||||
all_pts(i,all_pts(i,:)~=-1) = shape2D(:,1);
|
||||
all_pts(i+num_pts,all_pts(i+num_pts,:)~=-1) = shape2D(:,2);
|
||||
end
|
||||
|
||||
%%
|
||||
% to_rem = randperm(round(0.1*num_pts)); % Remove 10% to break some symmetry
|
||||
% all_pts([to_rem, to_rem+num_pts],:) = [];
|
||||
num_pts = size(all_pts,1)/2;
|
||||
|
||||
left_ids = all_pts(1:num_pts,10) == -1;
|
||||
right_ids = all_pts(1:num_pts,8) == -1;
|
||||
frontal = true(num_pts,1);
|
||||
frontal(left_ids | right_ids) = false;
|
||||
|
||||
%%
|
||||
xs = all_pts(1:num_pts,:);
|
||||
ys = all_pts(num_pts+1:end,:);
|
||||
|
||||
% Randperm the data, as a test
|
||||
|
||||
% xs_f = xs(frontal,:);
|
||||
% ys_f = ys(frontal,:);
|
||||
% scatter(xs_f(:), -ys_f(:));
|
||||
|
||||
%% Perform NRSFM by Torresani
|
||||
addpath('../nrsfm-em');
|
||||
% (T is the number of frames, J is the number of points)
|
||||
|
||||
J = size(all_pts,2);
|
||||
T = size(all_pts,1)/2;
|
||||
|
||||
use_lds = 0; % not modeling a linear dynamic system here
|
||||
max_em_iter = 200;
|
||||
tol = 0.001;
|
||||
K = 30; % number of deformation shapes
|
||||
|
||||
MD = all_pts(1:end/2,:)==-1;
|
||||
|
||||
[P3, S_hat, V, RO, Tr, Z] = em_sfm(all_pts, MD, K, use_lds, tol, max_em_iter);
|
||||
|
||||
save('Torr_menpo', 'P3', 'S_hat', 'V', 'RO', 'Tr', 'Z');
|
||||
|
||||
%%
|
||||
% xs = P3(1:num_pts,:);
|
||||
% ys = P3(num_pts+1:2*num_pts,:);
|
||||
% zs = P3(2*num_pts+1:end,:);
|
||||
% %
|
||||
% xs_f = xs(left_ids,:);
|
||||
% ys_f = ys(left_ids,:);
|
||||
% zs_f = zs(left_ids,:);
|
||||
% scatter3(xs_f(:), ys_f(:), zs_f(:));
|
||||
163
pkg/OpenFace/model_training/pdm_generation/menpo_pdm/em_sfm.m
Normal file
163
pkg/OpenFace/model_training/pdm_generation/menpo_pdm/em_sfm.m
Normal file
@@ -0,0 +1,163 @@
|
||||
function [P3, S_bar, V, RO, Tr, Z, sigma_sq, phi, Q, mu0, sigma0] = em_sfm(P, MD, K, use_lds, tol, max_em_iter)
|
||||
|
||||
% Non-Rigid Structure From Motion with Gaussian/LDS Deformation Model
|
||||
% Copyright (c) by Lorenzo Torresani, Stanford University
|
||||
%
|
||||
% Based on the following paper:
|
||||
%
|
||||
% Lorenzo Torresani, Aaron Hertzmann and Christoph Bregler,
|
||||
% Learning Non-Rigid 3D Shape from 2D Motion, NIPS 16, 2003
|
||||
% http://cs.stanford.edu/~ltorresa/projects/learning-nr-shape/
|
||||
%
|
||||
% Please refer to this publication if you use this program for
|
||||
% research or for technical applications.
|
||||
%
|
||||
%
|
||||
% INPUT:
|
||||
%
|
||||
% P - (2*T) x J tracking matrix: P([t t+T],:) contains the 2D projections of the J points at time t
|
||||
% MD - T x J missing data binary matrix: MD(t, j)=1 if no valid data is available for point j at time t, 0 otherwise
|
||||
% K - number of deformation basis
|
||||
% use_lds - set to 1 to model deformations using a linear dynamical system; set to 0 otherwise
|
||||
% tol - termination tolerance (proportional change in likelihood)
|
||||
% max_em_iter - maximum number of EM iterations
|
||||
%
|
||||
%
|
||||
% OUTPUT:
|
||||
%
|
||||
% P3 - (3*T) x J 3D-motion matrix: ( P3([t t+T t+2*T],:) contains the 3D coordinates of the J points at time t )
|
||||
% S_bar - shape average: 3 x J matrix
|
||||
% V - deformation shapes: (3*K) x J matrix ( V((n-1)*3+[1:3],:) contains the n-th deformation basis )
|
||||
% RO - rotation: cell array ( RO{t} gives the rotation matrix at time t )
|
||||
% Tr - translation: T x 2 matrix
|
||||
% Z - deformation weights: T x K matrix
|
||||
% sigma_sq - variance of the noise in feature position
|
||||
% phi - LDS transition matrix
|
||||
% Q - LDS state noise matrix
|
||||
% mu0 - initial state mean
|
||||
% sigma0 - initial state variance
|
||||
|
||||
if mod(size(P,1), 1) ~= 0,
|
||||
fprintf('Error: size(P) must be (2*T)xJ\n');
|
||||
return;
|
||||
end
|
||||
if (size(P,1)/2 ~= size(MD,1)) | (size(P,2) ~= size(MD,2))
|
||||
fprintf('Error: Size incompatibility between P and MD\n');
|
||||
return;
|
||||
end
|
||||
if mod(K, 1) ~= 0,
|
||||
fprintf('Error: K must be an integer value\n');
|
||||
return;
|
||||
end
|
||||
|
||||
[T, J] = size(MD);
|
||||
r = 3*(K + 1); % motion rank
|
||||
|
||||
P_hat = P; % if any of the points are missing, P_hat will be updated during the M-step
|
||||
|
||||
% uses rank 3 factorization to get a first initialization for rotation and S_bar
|
||||
[R_init, Trvect, S_bar] = rigidfac(P_hat, MD);
|
||||
|
||||
Tr(:,1) = Trvect(1:T);
|
||||
Tr(:,2) = Trvect(T+1:2*T);
|
||||
|
||||
R = zeros(2*T, 3);
|
||||
% enforces rotation constraints
|
||||
for t = 1:T,
|
||||
Ru = R_init(t,:);
|
||||
Rv = R_init(T+t,:);
|
||||
Rz = cross(Ru,Rv); if det([Ru;Rv;Rz])<0, Rz = -Rz; end;
|
||||
RO_approx = apprRot([Ru;Rv;Rz]);
|
||||
RO{t} = RO_approx;
|
||||
R(t,:) = RO_approx(1,:);
|
||||
R(t+T,:) = RO_approx(2,:);
|
||||
end;
|
||||
|
||||
% given the initial estimates of rotation, translation and shape average, it initializes
|
||||
% deformation shapes and weights through LSQ minimization of the reprojection error
|
||||
[V, Z] = init_SB(P_hat, Tr, R, S_bar, K);
|
||||
|
||||
% initializes sigma_sq
|
||||
E_zz_init = cov(Z);
|
||||
E_zz_init = repmat(E_zz_init, T, 1);
|
||||
sigma_sq = mstep_update_noisevar(P_hat, S_bar, V, Z', E_zz_init, RO, Tr);
|
||||
|
||||
if use_lds,
|
||||
[phi, mu0, sigma0, Q] = init_lds(P_hat, S_bar, V, R, Tr, sigma_sq);
|
||||
else
|
||||
phi = [];
|
||||
mu0 = [];
|
||||
sigma0 = [];
|
||||
Q = [];
|
||||
end
|
||||
|
||||
loglik = 0;
|
||||
% annealing_const = 60;
|
||||
annealing_const = 100;
|
||||
|
||||
max_anneal_iter = round(max_em_iter/2);
|
||||
|
||||
for em_iter=1:max_em_iter,
|
||||
if use_lds,
|
||||
[E_z, E_zz, y, M, xt_n, Pt_n, Ptt1_n, xt_t1, Pt_t1] = estep_lds_compute_Z_distr(P_hat, S_bar, V, R, Tr, phi, mu0, sigma0, Q, sigma_sq);
|
||||
|
||||
[phi, Q, sigma_sq, mu0, sigma0] = mstep_lds_update(y, M, xt_n, Pt_n, Ptt1_n);
|
||||
else
|
||||
% computes the hidden variables distributions
|
||||
[E_z, E_zz] = estep_compute_Z_distr(P_hat, S_bar, V, R, Tr, sigma_sq); % (Eq 17-18)
|
||||
end
|
||||
Z = E_z';
|
||||
|
||||
% updates shape basis
|
||||
[S_bar, V] = mstep_update_shapebasis(P_hat, E_z, E_zz, R, Tr, S_bar, V); % (Eq 21)
|
||||
|
||||
% fills in missing points
|
||||
if sum(MD(:))>0,
|
||||
P_hat = mstep_update_missingdata(P_hat, MD, S_bar, V, E_z, RO, Tr); % (Eq 25)
|
||||
end
|
||||
|
||||
% updates rotation
|
||||
[RO, R] = mstep_update_rotation(P_hat, S_bar, V, E_z, E_zz, RO, Tr); % (Eq 24)
|
||||
|
||||
% updates translation
|
||||
Tr = mstep_update_transl(P_hat, S_bar, V, E_z, RO); % (Eq 23)
|
||||
|
||||
if ~use_lds,
|
||||
% updates noise variance
|
||||
sigma_sq = mstep_update_noisevar(P_hat, S_bar, V, E_z, E_zz, RO, Tr); % (Eq 22)
|
||||
if em_iter < max_anneal_iter,
|
||||
sigma_sq = sigma_sq * (1 + annealing_const*(1 - em_iter/max_anneal_iter));
|
||||
end
|
||||
|
||||
oldloglik = loglik;
|
||||
% computes log likelihood
|
||||
loglik = compute_log_lik(P_hat, S_bar, V, E_z, E_zz, RO, Tr, sigma_sq);
|
||||
|
||||
fprintf('LogLik(%d): %f\n', em_iter, loglik);
|
||||
|
||||
if (em_iter <= 2),
|
||||
loglikbase = loglik;
|
||||
elseif (loglik < oldloglik)
|
||||
fprintf('Violation');
|
||||
% keyboard;
|
||||
elseif 0 & ((loglik-loglikbase)<(1 + tol)*(oldloglik-loglikbase)),
|
||||
fprintf('\n');
|
||||
break;
|
||||
end
|
||||
else
|
||||
fprintf('Iteration %d/%d\n', em_iter, max_em_iter);
|
||||
end
|
||||
end
|
||||
|
||||
P3 = zeros(3*T, J);
|
||||
for t = 1:T,
|
||||
z_t = Z(t,:);
|
||||
Rf = [R(t,:); R(t+T,:)];
|
||||
S = S_bar;
|
||||
for kk = 1:K,
|
||||
S = S+z_t(kk)*V((kk-1)*3+[1:3],:);
|
||||
end;
|
||||
S = RO{t}*S;
|
||||
|
||||
P3([t t+T t+2*T], :) = S + [Tr(t, [1 2]) -mean(S(3,:))]'*ones(1,J);
|
||||
end
|
||||
@@ -0,0 +1,373 @@
|
||||
function [ a, R, T, T3D, params, error, shapeOrtho ] = fit_PDM_ortho_proj_to_2D( M, E, V, shape2D, f, cx, cy)
|
||||
%FITPDMTO2DSHAPE Summary of this function goes here
|
||||
% Detailed explanation goes here
|
||||
|
||||
params = zeros(size(E));
|
||||
|
||||
hidden = false;
|
||||
|
||||
% if some of the points are unavailable modify M, V, and shape2D (can
|
||||
% later infer the actual shape from this)
|
||||
if(sum(shape2D(:)==0) > 0)
|
||||
|
||||
hidden = true;
|
||||
% which indices to remove
|
||||
inds_to_rem = shape2D(:,1) == 0 | shape2D(:,2) == 0;
|
||||
|
||||
shape2D = shape2D(~inds_to_rem,:);
|
||||
|
||||
inds_to_rem = repmat(inds_to_rem, 3, 1);
|
||||
|
||||
M_old = M;
|
||||
V_old = V;
|
||||
|
||||
M = M(~inds_to_rem);
|
||||
V = V(~inds_to_rem,:);
|
||||
|
||||
end
|
||||
|
||||
num_points = numel(M) / 3;
|
||||
|
||||
m = reshape(M, num_points, 3)';
|
||||
width_model = max(m(1,:)) - min(m(1,:));
|
||||
height_model = max(m(2,:)) - min(m(2,:));
|
||||
|
||||
bounding_box = [min(shape2D(:,1)), min(shape2D(:,2)),...
|
||||
max(shape2D(:,1)), max(shape2D(:,2))];
|
||||
|
||||
a = (((bounding_box(3) - bounding_box(1)) / width_model) + ((bounding_box(4) - bounding_box(2))/ height_model)) / 2;
|
||||
|
||||
tx = (bounding_box(3) + bounding_box(1))/2;
|
||||
ty = (bounding_box(4) + bounding_box(2))/2;
|
||||
|
||||
% correct it so that the bounding box is just around the minimum
|
||||
% and maximum point in the initialised face
|
||||
tx = tx - a*(min(m(1,:)) + max(m(1,:)))/2;
|
||||
ty = ty - a*(min(m(2,:)) + max(m(2,:)))/2;
|
||||
|
||||
% To deal with really extreme cases of roll
|
||||
M3D = cat(2, M(1:end/3), M(end/3+1:2*end/3), zeros(numel(M(1:end/3)),1));
|
||||
shape3D = cat(2, shape2D, zeros(numel(M(1:end/3)),1));
|
||||
[ A, T, error, alignedShape, s ] = AlignShapesWithScale(M3D, shape3D);
|
||||
R = A/s;
|
||||
% R = eye(3);
|
||||
|
||||
T = [tx; ty];
|
||||
|
||||
currShape = getShapeOrtho(M, V, params, R, T, a);
|
||||
|
||||
currError = getRMSerror(currShape, shape2D);
|
||||
|
||||
reg_rigid = zeros(6,1);
|
||||
regFactor = 20;
|
||||
regularisations = [reg_rigid; regFactor ./ E]; % the above version, however, does not perform as well
|
||||
regularisations = diag(regularisations)*diag(regularisations);
|
||||
|
||||
red_in_a_row = 0;
|
||||
|
||||
for i=1:0
|
||||
|
||||
shape3D = M + V * params;
|
||||
shape3D = reshape(shape3D, numel(shape3D) / 3, 3);
|
||||
|
||||
% Now find the current residual error
|
||||
currShape = a * R(1:2,:)*shape3D' + repmat(T, 1, numel(M)/3);
|
||||
currShape = currShape';
|
||||
|
||||
error_res = shape2D - currShape;
|
||||
|
||||
eul = Rot2Euler(R);
|
||||
|
||||
p_global = [a; eul'; T];
|
||||
|
||||
% get the Jacobians
|
||||
J = CalcJacobian(M, V, params, p_global);
|
||||
|
||||
% RLMS style update
|
||||
p_delta = (J'*J + regularisations) \ (J'*error_res(:) - regularisations*[p_global;params]);
|
||||
|
||||
% Take smaller steps
|
||||
p_delta = 0.25 * p_delta;
|
||||
|
||||
[params, p_global] = CalcReferenceUpdate(p_delta, params, p_global);
|
||||
|
||||
% Make sure the params do not get out of hand
|
||||
params = ClampPDM(params, E);
|
||||
|
||||
a = p_global(1);
|
||||
R = Euler2Rot(p_global(2:4));
|
||||
T = p_global(5:6);
|
||||
|
||||
shape3D = M + V * params;
|
||||
shape3D = reshape(shape3D, numel(shape3D) / 3, 3);
|
||||
currShape = a * R(1:2,:)*shape3D' + repmat(T, 1, numel(M)/3);
|
||||
currShape = currShape';
|
||||
|
||||
error = getRMSerror(currShape, shape2D);
|
||||
|
||||
if(0.999 * currError < error)
|
||||
red_in_a_row = red_in_a_row + 1;
|
||||
if(red_in_a_row == 5)
|
||||
break;
|
||||
end
|
||||
end
|
||||
|
||||
currError = error;
|
||||
|
||||
end
|
||||
|
||||
if(hidden)
|
||||
shapeOrtho = getShapeOrtho(M_old, V_old, params, R, T, a);
|
||||
else
|
||||
shapeOrtho = currShape;
|
||||
end
|
||||
if(nargin == 7)
|
||||
|
||||
Zavg = f / a;
|
||||
Xavg = (T(1) - cx) / a;
|
||||
Yavg = (T(2) - cy) / a;
|
||||
|
||||
T3D = [Xavg;Yavg;Zavg];
|
||||
else
|
||||
T3D = [0;0;0];
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
function [shape2D] = getShapeOrtho(M, V, p, R, T, a)
|
||||
|
||||
% M - mean shape vector
|
||||
% V - eigenvectors
|
||||
% p - parameters of non-rigid shape
|
||||
% R - rotation matrix
|
||||
% T - translation vector (tx, ty)
|
||||
shape3D = getShape3D(M, V, p);
|
||||
shape2D = a * R(1:2,:)*shape3D' + repmat(T, 1, numel(M)/3);
|
||||
shape2D = shape2D';
|
||||
end
|
||||
|
||||
function [shape2D] = getShapeOrthoFull(M, V, p, R, T, a)
|
||||
|
||||
% M - mean shape vector
|
||||
% V - eigenvectors
|
||||
% p - parameters of non-rigid shape
|
||||
% R - rotation matrix
|
||||
% T - translation vector (tx, ty)
|
||||
T = [T; 0];
|
||||
shape3D = getShape3D(M, V, p);
|
||||
shape2D = a * R*shape3D' + repmat(T, 1, numel(M)/3);
|
||||
shape2D = shape2D';
|
||||
end
|
||||
|
||||
function [shape3D] = getShape3D(M, V, params)
|
||||
|
||||
shape3D = M + V * params;
|
||||
shape3D = reshape(shape3D, numel(shape3D) / 3, 3);
|
||||
|
||||
end
|
||||
|
||||
function [error] = getRMSerror(shape2Dv1, shape2Dv2)
|
||||
|
||||
error = sqrt(mean(reshape(shape2Dv1 - shape2Dv2, numel(shape2Dv1), 1).^2));
|
||||
|
||||
end
|
||||
|
||||
% This calculates the combined rigid with non-rigid Jacobian
|
||||
function J = CalcJacobian(M, V, p, p_global)
|
||||
|
||||
n = size(M, 1)/3;
|
||||
|
||||
non_rigid_modes = size(V,2);
|
||||
|
||||
J = zeros(n*2, 6 + non_rigid_modes);
|
||||
|
||||
|
||||
% now the layour is
|
||||
% ---------- Rigid part -------------------|----Non rigid part--------|
|
||||
% dx_1/ds, dx_1/dr1, ... dx_1/dtx, dx_1/dty dx_1/dp_1 ... dx_1/dp_m
|
||||
% dx_2/ds, dx_2/dr1, ... dx_2/dtx, dx_2/dty dx_2/dp_1 ... dx_2/dp_m
|
||||
% ...
|
||||
% dx_n/ds, dx_n/dr1, ... dx_n/dtx, dx_n/dty dx_n/dp_1 ... dx_n/dp_m
|
||||
% dy_1/ds, dy_1/dr1, ... dy_1/dtx, dy_1/dty dy_1/dp_1 ... dy_1/dp_m
|
||||
% ...
|
||||
% dy_n/ds, dy_n/dr1, ... dy_n/dtx, dy_n/dty dy_n/dp_1 ... dy_n/dp_m
|
||||
|
||||
% getting the rigid part
|
||||
J(:,1:6) = CalcRigidJacobian(M, V, p, p_global);
|
||||
|
||||
% constructing the non-rigid part
|
||||
R = Euler2Rot(p_global(2:4));
|
||||
s = p_global(1);
|
||||
|
||||
% 'rotate' and 'scale' the principal components
|
||||
|
||||
% First reshape to 3D
|
||||
V_X = V(1:n,:);
|
||||
V_Y = V(n+1:2*n,:);
|
||||
V_Z = V(2*n+1:end,:);
|
||||
|
||||
J_x_non_rigid = s*(R(1,1)*V_X + R(1,2)*V_Y + R(1,3)*V_Z);
|
||||
J_y_non_rigid = s*(R(2,1)*V_X + R(2,2)*V_Y + R(2,3)*V_Z);
|
||||
|
||||
J(1:n, 7:end) = J_x_non_rigid;
|
||||
J(n+1:end, 7:end) = J_y_non_rigid;
|
||||
|
||||
end
|
||||
|
||||
function J = CalcRigidJacobian(M, V, p, p_global)
|
||||
|
||||
n = size(M, 1)/3;
|
||||
|
||||
% Get the current 3D shape (not affected by global transform, as this
|
||||
% is how the Jacobian was derived (for derivation please see
|
||||
% ../derivations/orthoJacobian
|
||||
shape3D = GetShape3D(M, V, p);
|
||||
|
||||
% Get the rotation matrix corresponding to current global orientation
|
||||
R = Euler2Rot(p_global(2:4));
|
||||
s = p_global(1);
|
||||
|
||||
% Rigid Jacobian is laid out as follows
|
||||
% dx_1/ds, dx_1/dr1, dx_1/dr2, dx_1/dr3, dx_1/dtx, dx_1/dty
|
||||
% dx_2/ds, dx_2/dr1, dx_2/dr2, dx_2/dr3, dx_2/dtx, dx_2/dty
|
||||
% ...
|
||||
% dx_n/ds, dx_n/dr1, dx_n/dr2, dx_n/dr3, dx_n/dtx, dx_n/dty
|
||||
% dy_1/ds, dy_1/dr1, dy_1/dr2, dy_1/dr3, dy_1/dtx, dy_1/dty
|
||||
% ...
|
||||
% dy_n/ds, dy_n/dr1, dy_n/dr2, dy_n/dr3, dy_n/dtx, dy_n/dty
|
||||
|
||||
J = zeros(n*2, 6);
|
||||
|
||||
% dx/ds = X * r11 + Y * r12 + Z * r13
|
||||
% dx/dr1 = s*(r13 * Y - r12 * Z)
|
||||
% dx/dr2 = -s*(r13 * X - r11 * Z)
|
||||
% dx/dr3 = s*(r12 * X - r11 * Y)
|
||||
% dx/dtx = 1
|
||||
% dx/dty = 0
|
||||
|
||||
% dy/ds = X * r21 + Y * r22 + Z * r23
|
||||
% dy/dr1 = s * (r23 * Y - r22 * Z)
|
||||
% dy/dr2 = -s * (r23 * X - r21 * Z)
|
||||
% dy/dr3 = s * (r22 * X - r21 * Y)
|
||||
% dy/dtx = 0
|
||||
% dy/dty = 1
|
||||
|
||||
% set the Jacobian for x's
|
||||
|
||||
% with respect to scaling factor
|
||||
J(1:n,1) = shape3D * R(1,:)';
|
||||
|
||||
% with respect to angular rotation around x, y, and z axes
|
||||
|
||||
% Change of x with respect to change in axis angle rotation
|
||||
dxdR = [ 0, R(1,3), -R(1,2);
|
||||
-R(1,3), 0, R(1,1);
|
||||
R(1,2), -R(1,1), 0];
|
||||
|
||||
J(1:n,2:4) = s*(dxdR * shape3D')';
|
||||
|
||||
% with respect to translation
|
||||
J(1:n,5) = 1;
|
||||
J(1:n,6) = 0;
|
||||
|
||||
% set the Jacobian for y's
|
||||
|
||||
% with respect to scaling factor
|
||||
J(n+1:end,1) = shape3D * R(2,:)';
|
||||
|
||||
% with respect to angular rotation around x, y, and z axes
|
||||
|
||||
% Change of y with respect to change in axis angle rotation
|
||||
dydR = [ 0, R(2,3), -R(2,2);
|
||||
-R(2,3), 0, R(2,1);
|
||||
R(2,2), -R(2,1), 0];
|
||||
|
||||
J(n+1:end,2:4) = s*(dydR * shape3D')';
|
||||
|
||||
% with respect to translation
|
||||
J(n+1:end,5) = 0;
|
||||
J(n+1:end,6) = 1;
|
||||
|
||||
end
|
||||
|
||||
% This updates the parameters based on the updates from the RLMS
|
||||
function [non_rigid, rigid] = CalcReferenceUpdate(params_delta, current_non_rigid, current_global)
|
||||
|
||||
|
||||
rigid = zeros(6, 1);
|
||||
% Same goes for scaling and translation parameters
|
||||
rigid(1) = current_global(1) + params_delta(1);
|
||||
rigid(5) = current_global(5) + params_delta(5);
|
||||
rigid(6) = current_global(6) + params_delta(6);
|
||||
|
||||
% for rotation however, we want to make sure that the rotation matrix
|
||||
% approximation we have
|
||||
% R' = [1, -wz, wy
|
||||
% wz, 1, -wx
|
||||
% -wy, wx, 1]
|
||||
% is a legal rotation matrix, and then we combine it with current
|
||||
% rotation (through matrix multiplication) to acquire the new rotation
|
||||
|
||||
R = Euler2Rot(current_global(2:4));
|
||||
|
||||
wx = params_delta(2);
|
||||
wy = params_delta(3);
|
||||
wz = params_delta(4);
|
||||
|
||||
R_delta = [1, -wz, wy;
|
||||
wz, 1, -wx;
|
||||
-wy, wx, 1];
|
||||
|
||||
% Make sure R_delta is orthonormal
|
||||
R_delta = double(OrthonormaliseRotation(R_delta));
|
||||
|
||||
% Combine rotations
|
||||
R_final = R * R_delta;
|
||||
|
||||
% Extract euler angle
|
||||
euler = real(Rot2Euler(R_final));
|
||||
|
||||
rigid(2:4) = euler;
|
||||
|
||||
if(length(params_delta) > 6)
|
||||
% non-rigid parameters can just be added together
|
||||
non_rigid = params_delta(7:end) + current_non_rigid;
|
||||
else
|
||||
non_rigid = current_non_rigid;
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
function R_ortho = OrthonormaliseRotation(R)
|
||||
|
||||
% U * V' is basically what we want, as it's guaranteed to be
|
||||
% orthonormal
|
||||
[U, ~, V] = svd(R);
|
||||
|
||||
% We also want to make sure no reflection happened
|
||||
|
||||
% get the orthogonal matrix from the initial rotation matrix
|
||||
X = U*V';
|
||||
|
||||
% This makes sure that the handedness is preserved and no reflection happened
|
||||
% by making sure the determinant is 1 and not -1
|
||||
W = eye(3);
|
||||
W(3,3) = det(X);
|
||||
R_ortho = U*W*V';
|
||||
end
|
||||
|
||||
% This clamps the non-rigid parameters to stay within +- 3 standard
|
||||
% deviations
|
||||
function [non_rigid_params] = ClampPDM(non_rigid, E)
|
||||
|
||||
stds = sqrt(E);
|
||||
|
||||
non_rigid_params = non_rigid;
|
||||
|
||||
lower = non_rigid_params < -3 * stds;
|
||||
non_rigid_params(lower) = -3*stds(lower);
|
||||
|
||||
higher = non_rigid_params > 3 * stds;
|
||||
non_rigid_params(higher) = 3*stds(higher);
|
||||
|
||||
end
|
||||
@@ -0,0 +1,34 @@
|
||||
% A script for visualizing the orientations in the menpo data, allows to
|
||||
% see the distributions of the data
|
||||
clear
|
||||
load('../menpo_68_pts.mat');
|
||||
addpath('../../PDM_helpers');
|
||||
|
||||
xs = all_pts(1:end/2,:);
|
||||
ys = all_pts(end/2+1:end,:);
|
||||
num_imgs = size(xs, 1);
|
||||
|
||||
rots = zeros(3, num_imgs);
|
||||
errs = zeros(1,num_imgs);
|
||||
|
||||
pdmLoc = ['../pdm_68_aligned_menpo.mat'];
|
||||
|
||||
load(pdmLoc);
|
||||
|
||||
pdm = struct;
|
||||
pdm.M = double(M);
|
||||
pdm.E = double(E);
|
||||
pdm.V = double(V);
|
||||
errs_poss = [];
|
||||
for i=1:num_imgs
|
||||
|
||||
labels_curr = cat(2, xs(i,:)', ys(i,:)');
|
||||
labels_curr(labels_curr==-1) = 0;
|
||||
|
||||
[ a, R, T, ~, l_params, err, shapeOrtho] = fit_PDM_ortho_proj_to_2D(pdm.M, pdm.E, pdm.V, labels_curr);
|
||||
errs(i) = err/a;
|
||||
rots(:,i) = Rot2Euler(R);
|
||||
|
||||
end
|
||||
|
||||
hist(rots', 100);
|
||||
@@ -0,0 +1,121 @@
|
||||
function [images, detections, labels] = Collect_wild_imgs_train(root_test_data)
|
||||
|
||||
use_lfpw = true;
|
||||
use_helen = true;
|
||||
|
||||
use_68 = true;
|
||||
|
||||
images = [];
|
||||
labels = [];
|
||||
detections = [];
|
||||
|
||||
if(use_lfpw)
|
||||
[img, det, lbl] = Collect_LFPW(root_test_data, use_68);
|
||||
images = cat(1, images, img');
|
||||
detections = cat(1, detections, det);
|
||||
labels = cat(1, labels, lbl);
|
||||
end
|
||||
|
||||
if(use_helen)
|
||||
[img, det, lbl] = Collect_helen(root_test_data, use_68);
|
||||
images = cat(1, images, img');
|
||||
detections = cat(1, detections, det);
|
||||
labels = cat(1, labels, lbl);
|
||||
end
|
||||
|
||||
% convert to format expected by the Fitting method
|
||||
detections(:,3) = detections(:,1) + detections(:,3);
|
||||
detections(:,4) = detections(:,2) + detections(:,4);
|
||||
|
||||
|
||||
end
|
||||
|
||||
function [images, detections, labels] = Collect_LFPW(root_test_data, use_68)
|
||||
|
||||
dataset_loc = [root_test_data, '/lfpw/trainset/'];
|
||||
|
||||
landmarkLabels = dir([dataset_loc '\*.pts']);
|
||||
|
||||
num_imgs = size(landmarkLabels,1);
|
||||
|
||||
images = struct;
|
||||
if(use_68)
|
||||
labels = zeros(num_imgs, 68, 2);
|
||||
else
|
||||
labels = zeros(num_imgs, 66, 2);
|
||||
end
|
||||
|
||||
detections = zeros(num_imgs, 4);
|
||||
|
||||
load([root_test_data, '/Bounding Boxes/bounding_boxes_lfpw_trainset.mat']);
|
||||
|
||||
num_landmarks = 68;
|
||||
|
||||
for imgs = 1:num_imgs
|
||||
|
||||
[~,name,~] = fileparts(landmarkLabels(imgs).name);
|
||||
|
||||
landmarks = dlmread([dataset_loc, landmarkLabels(imgs).name], ' ', [3,0,num_landmarks+2,1]);
|
||||
|
||||
if(~use_68)
|
||||
inds_frontal = [1:60,62:64,66:68];
|
||||
landmarks = landmarks(inds_frontal,:);
|
||||
end
|
||||
|
||||
images(imgs).img = [dataset_loc, name '.png'];
|
||||
|
||||
labels(imgs,:,:) = landmarks;
|
||||
|
||||
detections(imgs,:) = bounding_boxes{imgs}.bb_detector;
|
||||
|
||||
end
|
||||
|
||||
detections(:,3) = detections(:,3) - detections(:,1);
|
||||
detections(:,4) = detections(:,4) - detections(:,2);
|
||||
|
||||
|
||||
end
|
||||
|
||||
function [images, detections, labels] = Collect_helen(root_test_data, use_68)
|
||||
|
||||
dataset_loc = [root_test_data, '/helen/trainset/'];
|
||||
|
||||
landmarkLabels = dir([dataset_loc '\*.pts']);
|
||||
|
||||
num_imgs = size(landmarkLabels,1);
|
||||
|
||||
images = struct;
|
||||
|
||||
if(use_68)
|
||||
labels = zeros(num_imgs, 68, 2);
|
||||
else
|
||||
labels = zeros(num_imgs, 66, 2);
|
||||
end
|
||||
|
||||
detections = zeros(num_imgs, 4);
|
||||
|
||||
load([root_test_data, '/Bounding Boxes/bounding_boxes_helen_trainset.mat']);
|
||||
num_landmarks = 68;
|
||||
for imgs = 1:num_imgs
|
||||
|
||||
[~,name,~] = fileparts(landmarkLabels(imgs).name);
|
||||
|
||||
landmarks = dlmread([dataset_loc, landmarkLabels(imgs).name], ' ', [3,0,num_landmarks+2,1]);
|
||||
|
||||
if(~use_68)
|
||||
inds_frontal = [1:60,62:64,66:68];
|
||||
landmarks = landmarks(inds_frontal,:);
|
||||
end
|
||||
|
||||
images(imgs).img = [dataset_loc, name '.jpg'];
|
||||
|
||||
labels(imgs,:,:) = landmarks;
|
||||
|
||||
detections(imgs,:) = bounding_boxes{imgs}.bb_detector;
|
||||
|
||||
end
|
||||
|
||||
detections(:,3) = detections(:,3) - detections(:,1);
|
||||
detections(:,4) = detections(:,4) - detections(:,2);
|
||||
|
||||
end
|
||||
@@ -0,0 +1,54 @@
|
||||
clear
|
||||
load('../menpo_68_pts_valid.mat');
|
||||
addpath('../../PDM_helpers');
|
||||
|
||||
xs = all_pts(1:end/2,:);
|
||||
ys = all_pts(end/2+1:end,:);
|
||||
num_imgs = size(xs, 1);
|
||||
|
||||
rots_menpo = zeros(3, num_imgs);
|
||||
errs_menpo = zeros(1,num_imgs);
|
||||
|
||||
pdmLoc = ['../pdm_68_aligned_menpo.mat'];
|
||||
|
||||
load(pdmLoc);
|
||||
|
||||
pdm = struct;
|
||||
pdm.M = double(M);
|
||||
pdm.E = double(E);
|
||||
pdm.V = double(V);
|
||||
errs_poss = [];
|
||||
for i=1:num_imgs
|
||||
|
||||
labels_curr = cat(2, xs(i,:)', ys(i,:)');
|
||||
labels_curr(labels_curr==-1) = 0;
|
||||
|
||||
[ a, R, T, ~, l_params, err, shapeOrtho] = fit_PDM_ortho_proj_to_2D(pdm.M, pdm.E, pdm.V, labels_curr);
|
||||
errs_menpo(i) = err/a;
|
||||
rots_menpo(:,i) = Rot2Euler(R);
|
||||
|
||||
if(errs_menpo(i) < 0 || errs_menpo(i) > 4)
|
||||
fprintf('i - %d, err - %.3f\n', i, errs_menpo(i));
|
||||
errs_poss = cat(1, errs_poss, i);
|
||||
end
|
||||
end
|
||||
|
||||
[~, ~, labels] = Collect_wild_imgs_train('D:/Dropbox/Dropbox/AAM/test data/');
|
||||
num_imgs = size(labels,1);
|
||||
rots_wild = zeros(3, num_imgs);
|
||||
errs_wild = zeros(1,num_imgs);
|
||||
|
||||
for i=1:num_imgs
|
||||
|
||||
labels_curr = squeeze(labels(i,:,:));
|
||||
labels_curr(labels_curr==-1) = 0;
|
||||
|
||||
[ a, R, T, ~, l_params, err, shapeOrtho] = fit_PDM_ortho_proj_to_2D(pdm.M, pdm.E, pdm.V, labels_curr);
|
||||
errs_wild(i) = err/a;
|
||||
rots_wild(:,i) = Rot2Euler(R);
|
||||
|
||||
end
|
||||
errs = cat(2, errs_wild, errs_menpo);
|
||||
fprintf('%.3f, %.3f, %.3f\n', mean(errs_menpo), mean(errs_wild), mean(errs));
|
||||
% 300W PDM error is 1.537, 1.017, 1.285
|
||||
% Menpo+300W PDM error is 1.130, 0.985, 1.060
|
||||
@@ -0,0 +1,157 @@
|
||||
% If a different type of PDM is to be trained, prepare training data here
|
||||
|
||||
clear
|
||||
load('menpo_68_pts_flip.mat');
|
||||
addpath('../PDM_helpers');
|
||||
|
||||
xs = all_pts(1:end/2,:);
|
||||
ys = all_pts(end/2+1:end,:);
|
||||
num_imgs = size(xs, 1);
|
||||
|
||||
pdmLoc = ['../../models/pdm/pdm_68_aligned_wild.mat'];
|
||||
% pdmLoc = ['pdm_68_aligned_menpo_v1.mat'];
|
||||
|
||||
load(pdmLoc);
|
||||
|
||||
pdm = struct;
|
||||
pdm.M = double(M);
|
||||
pdm.E = double(E);
|
||||
pdm.V = double(V);
|
||||
errs_poss = [];
|
||||
|
||||
all_shapes = -200 * ones(num_imgs, 68 * 2);
|
||||
min_x = 0;
|
||||
max_x = 0;
|
||||
min_y = 0;
|
||||
max_y = 0;
|
||||
|
||||
for i=1:num_imgs
|
||||
|
||||
shape2D = cat(2, all_pts(i,:)', all_pts(i+num_imgs,:)');
|
||||
|
||||
M_n = M;
|
||||
ind_rem = find(shape2D(:,1) == -1);
|
||||
to_keep = setdiff(1:68, ind_rem);
|
||||
|
||||
if(sum(shape2D(:)==-1) > 0)
|
||||
|
||||
hidden = true;
|
||||
% which indices to remove
|
||||
inds_to_rem = shape2D(:,1) == -1 | shape2D(:,2) == -1;
|
||||
|
||||
shape2D = shape2D(~inds_to_rem,:);
|
||||
|
||||
inds_to_rem = repmat(inds_to_rem, 3, 1);
|
||||
|
||||
M_n = M(~inds_to_rem);
|
||||
|
||||
end
|
||||
|
||||
% To deal with really extreme cases of roll
|
||||
M2D = cat(2, M_n(1:end/3), M_n(end/3+1:2*end/3));
|
||||
[ A, t, error, alignedShape, s ] = AlignShapesWithScale(M2D, shape2D);
|
||||
R = A/s;
|
||||
|
||||
% Transform the shape
|
||||
shape2D(:,1) = shape2D(:,1) - t(1);
|
||||
shape2D(:,2) = shape2D(:,2) - t(2);
|
||||
|
||||
shape2D = (R' * shape2D')/s;
|
||||
shape2D = shape2D';
|
||||
|
||||
% all_pts(i,all_pts(i,:)~=-1) = shape2D(:,1);
|
||||
% all_pts(i+num_pts,all_pts(i+num_pts,:)~=-1) = shape2D(:,2);
|
||||
%
|
||||
all_shapes(i,[to_keep,to_keep+68]) = shape2D(:);
|
||||
|
||||
if(min(shape2D(:,1)) < min_x)
|
||||
min_x = min(shape2D(:,1));
|
||||
end
|
||||
if(min(shape2D(:,2)) < min_y)
|
||||
min_y = min(shape2D(:,2));
|
||||
end
|
||||
if(max(shape2D(:,1)) > max_x)
|
||||
max_x = max(shape2D(:,1));
|
||||
end
|
||||
if(max(shape2D(:,2)) > max_y)
|
||||
max_y = max(shape2D(:,2));
|
||||
end
|
||||
end
|
||||
|
||||
% Scaling and shifting the model so that all points are from -1 to 1
|
||||
MD = all_shapes == -200;
|
||||
|
||||
xs = 2 * (all_shapes(:,1:68) - min_x)/(max_x-min_x) - 1;
|
||||
ys = 2 * (all_shapes(:,69:end) - min_y)/(max_y - min_y) - 1;
|
||||
|
||||
all_shapes = cat(2, xs, ys);
|
||||
all_shapes(MD) = -2;
|
||||
|
||||
xs = all_shapes(:,1:68);
|
||||
ys = all_shapes(:,69:end);
|
||||
|
||||
save('menpo_train.mat', 'all_shapes');
|
||||
|
||||
%%
|
||||
load('menpo_68_pts_valid.mat');
|
||||
|
||||
xs = all_pts(1:end/2,:);
|
||||
ys = all_pts(end/2+1:end,:);
|
||||
num_imgs = size(xs, 1);
|
||||
|
||||
all_shapes = -200 * ones(num_imgs, 68 * 2);
|
||||
|
||||
for i=1:num_imgs
|
||||
|
||||
shape2D = cat(2, all_pts(i,:)', all_pts(i+num_imgs,:)');
|
||||
|
||||
M_n = M;
|
||||
ind_rem = find(shape2D(:,1) == -1);
|
||||
to_keep = setdiff(1:68, ind_rem);
|
||||
|
||||
if(sum(shape2D(:)==-1) > 0)
|
||||
|
||||
hidden = true;
|
||||
% which indices to remove
|
||||
inds_to_rem = shape2D(:,1) == -1 | shape2D(:,2) == -1;
|
||||
|
||||
shape2D = shape2D(~inds_to_rem,:);
|
||||
|
||||
inds_to_rem = repmat(inds_to_rem, 3, 1);
|
||||
|
||||
M_n = M(~inds_to_rem);
|
||||
|
||||
end
|
||||
|
||||
% To deal with really extreme cases of roll
|
||||
M2D = cat(2, M_n(1:end/3), M_n(end/3+1:2*end/3));
|
||||
[ A, t, error, alignedShape, s ] = AlignShapesWithScale(M2D, shape2D);
|
||||
R = A/s;
|
||||
|
||||
% Transform the shape
|
||||
shape2D(:,1) = shape2D(:,1) - t(1);
|
||||
shape2D(:,2) = shape2D(:,2) - t(2);
|
||||
|
||||
shape2D = (R' * shape2D')/s;
|
||||
shape2D = shape2D';
|
||||
|
||||
% all_pts(i,all_pts(i,:)~=-1) = shape2D(:,1);
|
||||
% all_pts(i+num_pts,all_pts(i+num_pts,:)~=-1) = shape2D(:,2);
|
||||
%
|
||||
all_shapes(i,[to_keep,to_keep+68]) = shape2D(:);
|
||||
|
||||
end
|
||||
|
||||
% Scaling and shifting the model so that all points are from -1 to 1
|
||||
MD = all_shapes == -200;
|
||||
|
||||
xs = 2 * (all_shapes(:,1:68) - min_x)/(max_x-min_x) - 1;
|
||||
ys = 2 * (all_shapes(:,69:end) - min_y)/(max_y - min_y) - 1;
|
||||
|
||||
all_shapes = cat(2, xs, ys);
|
||||
all_shapes(MD) = -2;
|
||||
|
||||
xs = all_shapes(:,1:68);
|
||||
ys = all_shapes(:,69:end);
|
||||
|
||||
save('menpo_valid.mat', 'all_shapes');
|
||||
@@ -0,0 +1,32 @@
|
||||
function [ pts_new ] = iterate_piece_wise( pts_orig, new_num_points )
|
||||
%ITERATE_PIECE_WISE Summary of this function goes here
|
||||
% Detailed explanation goes here
|
||||
|
||||
% Reinterpolate the new points, but make sure they are still on the
|
||||
% same lines
|
||||
num_orig = size(pts_orig,1);
|
||||
|
||||
% Divide the number of original segments by number of new segments
|
||||
step_size = (num_orig - 1) / (new_num_points-1);
|
||||
|
||||
pts_new = zeros(new_num_points,2);
|
||||
|
||||
% Clamp the beginning and end, as they will be the same
|
||||
pts_new(1,:) = pts_orig(1,:);
|
||||
pts_new(end,:) = pts_orig(end,:);
|
||||
|
||||
for i=1:new_num_points-2
|
||||
|
||||
low_point = floor(1 + i * step_size);
|
||||
high_point = ceil(1 + i * step_size);
|
||||
|
||||
coeff_1 = floor(1 + i * step_size) - i * step_size;
|
||||
coeff_2 = 1 - coeff_1;
|
||||
|
||||
new_pt = coeff_1 * pts_orig(low_point,:) + coeff_2 * pts_orig(high_point,:);
|
||||
pts_new(i+1,:) = new_pt;
|
||||
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
Binary file not shown.
Binary file not shown.
Binary file not shown.
@@ -0,0 +1,77 @@
|
||||
% collect the training data annotations (from the menpo challenge)
|
||||
clear
|
||||
train_data_loc = 'C:\Users\tbaltrus\Documents\menpo_data_orig/';
|
||||
|
||||
dataset_locs = {[train_data_loc, '/train/'];};
|
||||
|
||||
|
||||
left_to_frontal_map = [17,28; 18,29; 19,30; 20,31;
|
||||
21,34; 22,32; 23,39; 24,38; 25,37; 26,42; 27,41;
|
||||
28,52; 29,51; 30,50; 31,49; 32,60; 33,59; 34,58;
|
||||
35,63; 36,62; 37,61; 38,68; 39,67];
|
||||
|
||||
right_to_frontal_map = [17,28; 18,29; 19,30; 20,31;
|
||||
21,34; 22,36; 23,44; 24,45; 25,46; 26,47; 27,48;
|
||||
28,52; 29,53; 30,54; 31,55; 32,56; 33,57; 34,58;
|
||||
35,63; 36,64; 37,65; 38,66; 39,67];
|
||||
|
||||
all_pts_left = [];
|
||||
all_pts_right = [];
|
||||
all_pts_orig_left = [];
|
||||
all_pts_orig_right = [];
|
||||
|
||||
for i=1:numel(dataset_locs)
|
||||
landmarkLabels = dir([dataset_locs{i} '\*.pts']);
|
||||
landmarkImgs = dir([dataset_locs{i} '\*.jpg']);
|
||||
|
||||
for p=1:numel(landmarkLabels)
|
||||
landmarks = importdata([dataset_locs{i}, landmarkLabels(p).name], ' ', 3);
|
||||
img = imread([dataset_locs{i}, landmarkImgs(p).name]);
|
||||
landmarks = landmarks.data;
|
||||
landmark_labels = -ones(68,2);
|
||||
|
||||
if(size(landmarks,1) == 39)
|
||||
% Determine if the points are clock-wise or counter clock-wise
|
||||
% Clock-wise points are facing left, counter-clock-wise right
|
||||
sum = 0;
|
||||
for k=1:11
|
||||
step = (landmarks(k+1,1) - landmarks(k,1)) * (landmarks(k+1,2) + landmarks(k,2));
|
||||
sum = sum + step;
|
||||
end
|
||||
|
||||
if(sum > 0)
|
||||
% First need to resample the face outline as there are 9
|
||||
% points in the near-frontal and 10 points in profile for
|
||||
% the outline of the face
|
||||
|
||||
outline = iterate_piece_wise(landmarks(1:10,:), 9);
|
||||
brow = iterate_piece_wise(landmarks(13:16,:), 5);
|
||||
landmark_labels(1:9,:) = outline;
|
||||
landmark_labels(18:22,:) = brow;
|
||||
landmark_labels(left_to_frontal_map(:,2),:) = landmarks(left_to_frontal_map(:,1),:);
|
||||
|
||||
all_pts_orig_right = cat(3, all_pts_orig_right, landmarks);
|
||||
all_pts_right = cat(3, all_pts_right, landmark_labels);
|
||||
else
|
||||
outline = iterate_piece_wise(landmarks(10:-1:1,:), 9);
|
||||
brow = iterate_piece_wise(landmarks(16:-1:13,:), 5);
|
||||
|
||||
landmark_labels(9:17,:) = outline;
|
||||
landmark_labels(23:27,:) = brow;
|
||||
|
||||
landmark_labels(right_to_frontal_map(:,2),:) = landmarks(right_to_frontal_map(:,1),:);
|
||||
|
||||
all_pts_orig_left = cat(3, all_pts_orig_left, landmarks);
|
||||
all_pts_left = cat(3, all_pts_left, landmark_labels);
|
||||
end
|
||||
end
|
||||
|
||||
if(mod(p,50) == 0)
|
||||
fprintf('%d/%d\n', p, numel(landmarkLabels))
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
%%
|
||||
|
||||
save('menpo_68_pts_train_profile', 'all_pts_orig_right', 'all_pts_right', 'all_pts_orig_left', 'all_pts_left');
|
||||
@@ -0,0 +1,77 @@
|
||||
% collect the training data annotations (from the menpo challenge)
|
||||
clear
|
||||
train_data_loc = 'C:\Users\tbaltrus\Documents\menpo_data_orig/';
|
||||
|
||||
dataset_locs = {[train_data_loc, '/valid/'];};
|
||||
|
||||
|
||||
left_to_frontal_map = [17,28; 18,29; 19,30; 20,31;
|
||||
21,34; 22,32; 23,39; 24,38; 25,37; 26,42; 27,41;
|
||||
28,52; 29,51; 30,50; 31,49; 32,60; 33,59; 34,58;
|
||||
35,63; 36,62; 37,61; 38,68; 39,67];
|
||||
|
||||
right_to_frontal_map = [17,28; 18,29; 19,30; 20,31;
|
||||
21,34; 22,36; 23,44; 24,45; 25,46; 26,47; 27,48;
|
||||
28,52; 29,53; 30,54; 31,55; 32,56; 33,57; 34,58;
|
||||
35,63; 36,64; 37,65; 38,66; 39,67];
|
||||
|
||||
all_pts_left = [];
|
||||
all_pts_right = [];
|
||||
all_pts_orig_left = [];
|
||||
all_pts_orig_right = [];
|
||||
|
||||
for i=1:numel(dataset_locs)
|
||||
landmarkLabels = dir([dataset_locs{i} '\*.pts']);
|
||||
landmarkImgs = dir([dataset_locs{i} '\*.jpg']);
|
||||
|
||||
for p=1:numel(landmarkLabels)
|
||||
landmarks = importdata([dataset_locs{i}, landmarkLabels(p).name], ' ', 3);
|
||||
img = imread([dataset_locs{i}, landmarkImgs(p).name]);
|
||||
landmarks = landmarks.data;
|
||||
landmark_labels = -ones(68,2);
|
||||
|
||||
if(size(landmarks,1) == 39)
|
||||
% Determine if the points are clock-wise or counter clock-wise
|
||||
% Clock-wise points are facing left, counter-clock-wise right
|
||||
sum = 0;
|
||||
for k=1:11
|
||||
step = (landmarks(k+1,1) - landmarks(k,1)) * (landmarks(k+1,2) + landmarks(k,2));
|
||||
sum = sum + step;
|
||||
end
|
||||
|
||||
if(sum > 0)
|
||||
% First need to resample the face outline as there are 9
|
||||
% points in the near-frontal and 10 points in profile for
|
||||
% the outline of the face
|
||||
|
||||
outline = iterate_piece_wise(landmarks(1:10,:), 9);
|
||||
brow = iterate_piece_wise(landmarks(13:16,:), 5);
|
||||
landmark_labels(1:9,:) = outline;
|
||||
landmark_labels(18:22,:) = brow;
|
||||
landmark_labels(left_to_frontal_map(:,2),:) = landmarks(left_to_frontal_map(:,1),:);
|
||||
|
||||
all_pts_orig_right = cat(3, all_pts_orig_right, landmarks);
|
||||
all_pts_right = cat(3, all_pts_right, landmark_labels);
|
||||
else
|
||||
outline = iterate_piece_wise(landmarks(10:-1:1,:), 9);
|
||||
brow = iterate_piece_wise(landmarks(16:-1:13,:), 5);
|
||||
|
||||
landmark_labels(9:17,:) = outline;
|
||||
landmark_labels(23:27,:) = brow;
|
||||
|
||||
landmark_labels(right_to_frontal_map(:,2),:) = landmarks(right_to_frontal_map(:,1),:);
|
||||
|
||||
all_pts_orig_left = cat(3, all_pts_orig_left, landmarks);
|
||||
all_pts_left = cat(3, all_pts_left, landmark_labels);
|
||||
end
|
||||
end
|
||||
|
||||
if(mod(p,50) == 0)
|
||||
fprintf('%d/%d\n', p, numel(landmarkLabels))
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
%%
|
||||
|
||||
save('menpo_68_pts_valid_profile', 'all_pts_orig_right', 'all_pts_right', 'all_pts_orig_left', 'all_pts_left');
|
||||
@@ -0,0 +1,34 @@
|
||||
function [ error_per_image, frontal_ids ] = compute_error_menpo_prof( ground_truth_all, detected_points_all )
|
||||
%compute_error
|
||||
% compute the average point-to-point Euclidean error normalized by the
|
||||
% inter-ocular distance (measured as the Euclidean distance between the
|
||||
% outer corners of the eyes)
|
||||
%
|
||||
% Inputs:
|
||||
% grounth_truth_all, size: num_of_points x 2 x num_of_images
|
||||
% detected_points_all, size: num_of_points x 2 x num_of_images
|
||||
% Output:
|
||||
% error_per_image, size: num_of_images x 1
|
||||
|
||||
|
||||
num_of_images = numel(ground_truth_all);
|
||||
error_per_image = zeros(num_of_images,1);
|
||||
frontal_ids = true(num_of_images,1);
|
||||
|
||||
for i =1:num_of_images
|
||||
detected_points = detected_points_all{i};
|
||||
ground_truth_points = ground_truth_all{i};
|
||||
num_of_points = size(ground_truth_points,1);
|
||||
|
||||
normalization = (max(ground_truth_points(:,1))-min(ground_truth_points(:,1)))+...
|
||||
(max(ground_truth_points(:,2))-min(ground_truth_points(:,2)));
|
||||
normalization = normalization / 2;
|
||||
|
||||
sum=0;
|
||||
for j=1:num_of_points
|
||||
sum = sum+norm(detected_points(j,:)-ground_truth_points(j,:));
|
||||
end
|
||||
error_per_image(i) = sum/(num_of_points*normalization);
|
||||
end
|
||||
|
||||
end
|
||||
Binary file not shown.
@@ -0,0 +1,75 @@
|
||||
clear
|
||||
load('menpo_68_pts_train_profile');
|
||||
|
||||
vis_pts_left = all_pts_left(:,1,1) ~= -1;
|
||||
xs = all_pts_left(vis_pts_left,:,:);
|
||||
xs = squeeze(cat(1, xs(:,1,:), xs(:,2,:)));
|
||||
|
||||
ys = squeeze(cat(1, all_pts_orig_left(:,1,:), all_pts_orig_left(:,2,:)));
|
||||
|
||||
a_left = ys /xs;
|
||||
a_left(abs(a_left)<0.001) = 0;
|
||||
transformed_left = a_left * xs;
|
||||
xs_pred_left = transformed_left(1:end/2,:);
|
||||
ys_pred_left = transformed_left(end/2+1:end,:);
|
||||
|
||||
vis_pts_right = all_pts_right(:,1,1) ~= -1;
|
||||
xs = all_pts_right(vis_pts_right,:,:);
|
||||
xs = squeeze(cat(1, xs(:,1,:), xs(:,2,:)));
|
||||
|
||||
ys = squeeze(cat(1, all_pts_orig_right(:,1,:), all_pts_orig_right(:,2,:)));
|
||||
|
||||
a_right = ys /xs;
|
||||
a_right(abs(a_right)<0.001) = 0;
|
||||
transformed_right = a_right * xs;
|
||||
xs_pred_right = transformed_right(1:end/2,:);
|
||||
ys_pred_right = transformed_right(end/2+1:end,:);
|
||||
% pred_left = cat(2,transformed_left
|
||||
|
||||
%%
|
||||
num = 110;
|
||||
plot(all_pts_orig_right(:,1,num), -all_pts_orig_right(:,2,num), '.r');
|
||||
hold on;
|
||||
plot(xs_pred_right(:,num), -ys_pred_right(:,num), '.b');
|
||||
hold off;
|
||||
|
||||
%% Evaluate on the validation data (see how much error is added)
|
||||
|
||||
load('menpo_68_pts_valid_profile');
|
||||
|
||||
xs = all_pts_left(vis_pts_left,:,:);
|
||||
xs = squeeze(cat(1, xs(:,1,:), xs(:,2,:)));
|
||||
|
||||
transformed_left = a_left * xs;
|
||||
xs_pred_left = transformed_left(1:end/2,:);
|
||||
ys_pred_left = transformed_left(end/2+1:end,:);
|
||||
|
||||
shapes = cell(size(ys_pred_left,1),1);
|
||||
labels = cell(size(ys_pred_left,1),1);
|
||||
|
||||
for i=1:numel(shapes)
|
||||
shapes{i} = cat(2, xs_pred_left(:,i), ys_pred_left(:,i));
|
||||
labels{i} = all_pts_orig_left(:,:,i);
|
||||
end
|
||||
|
||||
errors_left = compute_error_menpo_prof(labels, shapes);
|
||||
|
||||
|
||||
xs = all_pts_right(vis_pts_right,:,:);
|
||||
xs = squeeze(cat(1, xs(:,1,:), xs(:,2,:)));
|
||||
|
||||
transformed_right = a_right * xs;
|
||||
xs_pred_right = transformed_right(1:end/2,:);
|
||||
ys_pred_right = transformed_right(end/2+1:end,:);
|
||||
|
||||
shapes = cell(size(ys_pred_right,1),1);
|
||||
labels = cell(size(ys_pred_right,1),1);
|
||||
|
||||
for i=1:numel(shapes)
|
||||
shapes{i} = cat(2, xs_pred_right(:,i), ys_pred_right(:,i));
|
||||
labels{i} = all_pts_orig_right(:,:,i);
|
||||
end
|
||||
|
||||
errors_right = compute_error_menpo_prof(labels, shapes);
|
||||
save('conversion', 'a_left', 'a_right', 'vis_pts_left', 'vis_pts_right');
|
||||
% Try with scaling
|
||||
Binary file not shown.
Binary file not shown.
@@ -0,0 +1 @@
|
||||
This includes scripts necessary to learn the mapping from the detected points using our PDM to the points expected in menpo (the different face outline and chin points in profile).
|
||||
Binary file not shown.
@@ -0,0 +1,421 @@
|
||||
# The mean values of the components (in mm)
|
||||
204
|
||||
1
|
||||
6
|
||||
-74.409969
|
||||
-74.137773
|
||||
-72.056496
|
||||
-67.915820
|
||||
-60.492143
|
||||
-48.932581
|
||||
-34.280137
|
||||
-17.760628
|
||||
0.514393
|
||||
18.358848
|
||||
34.248759
|
||||
48.283175
|
||||
59.483187
|
||||
66.851931
|
||||
71.085235
|
||||
73.234417
|
||||
73.635334
|
||||
-57.908717
|
||||
-49.068078
|
||||
-37.656400
|
||||
-25.729901
|
||||
-14.795319
|
||||
14.837927
|
||||
25.725682
|
||||
37.468905
|
||||
48.751250
|
||||
57.344747
|
||||
0.388587
|
||||
0.295350
|
||||
0.206926
|
||||
0.135388
|
||||
-15.498362
|
||||
-8.047687
|
||||
0.076176
|
||||
8.251717
|
||||
15.588112
|
||||
-45.515042
|
||||
-37.079098
|
||||
-27.956753
|
||||
-19.734098
|
||||
-28.329816
|
||||
-37.307204
|
||||
19.581417
|
||||
27.839109
|
||||
36.880288
|
||||
45.145696
|
||||
37.224189
|
||||
28.382643
|
||||
-27.977066
|
||||
-17.476087
|
||||
-6.663955
|
||||
0.244789
|
||||
7.291085
|
||||
17.947928
|
||||
28.125385
|
||||
18.687933
|
||||
8.539212
|
||||
0.242857
|
||||
-7.847825
|
||||
-18.237373
|
||||
-24.528857
|
||||
-7.104831
|
||||
0.273636
|
||||
7.739429
|
||||
24.736241
|
||||
7.968382
|
||||
0.229350
|
||||
-7.397604
|
||||
-30.248138
|
||||
-11.542661
|
||||
7.567939
|
||||
26.259376
|
||||
42.866270
|
||||
56.586917
|
||||
67.359002
|
||||
75.143546
|
||||
77.529037
|
||||
75.071547
|
||||
67.393621
|
||||
56.803934
|
||||
43.251437
|
||||
26.710196
|
||||
8.051821
|
||||
-10.968992
|
||||
-29.588592
|
||||
-52.172718
|
||||
-59.222312
|
||||
-61.949207
|
||||
-61.037213
|
||||
-57.532329
|
||||
-57.980133
|
||||
-61.715278
|
||||
-62.824686
|
||||
-60.232398
|
||||
-53.273185
|
||||
-40.542060
|
||||
-30.162960
|
||||
-20.232369
|
||||
-9.953997
|
||||
3.145708
|
||||
4.856711
|
||||
5.687939
|
||||
4.792678
|
||||
2.997034
|
||||
-37.288250
|
||||
-42.119954
|
||||
-42.362645
|
||||
-36.532986
|
||||
-34.532435
|
||||
-34.563887
|
||||
-36.758354
|
||||
-42.734934
|
||||
-42.649721
|
||||
-37.900147
|
||||
-35.115277
|
||||
-34.873489
|
||||
27.684553
|
||||
22.191257
|
||||
18.679379
|
||||
20.310742
|
||||
18.619478
|
||||
22.094260
|
||||
27.477987
|
||||
35.483072
|
||||
39.911465
|
||||
40.897777
|
||||
40.075424
|
||||
35.645402
|
||||
27.883771
|
||||
25.627237
|
||||
26.352545
|
||||
25.545734
|
||||
27.760907
|
||||
31.094250
|
||||
32.006269
|
||||
31.195088
|
||||
55.141955
|
||||
51.629462
|
||||
48.507238
|
||||
44.913190
|
||||
38.574081
|
||||
29.347878
|
||||
17.493884
|
||||
5.304010
|
||||
-1.371218
|
||||
5.342776
|
||||
17.851699
|
||||
30.323049
|
||||
40.570487
|
||||
47.890182
|
||||
52.297654
|
||||
55.916658
|
||||
60.074025
|
||||
13.228242
|
||||
6.263352
|
||||
-0.547326
|
||||
-6.314237
|
||||
-10.909358
|
||||
-13.043499
|
||||
-9.974582
|
||||
-5.801725
|
||||
-0.545529
|
||||
5.625345
|
||||
-13.691691
|
||||
-22.845392
|
||||
-32.311712
|
||||
-41.584645
|
||||
-21.080547
|
||||
-26.294217
|
||||
-29.003103
|
||||
-26.743598
|
||||
-22.061192
|
||||
9.230938
|
||||
3.879971
|
||||
1.219552
|
||||
1.017579
|
||||
0.985420
|
||||
3.658622
|
||||
-0.023947
|
||||
-0.773850
|
||||
0.704347
|
||||
5.283591
|
||||
0.421741
|
||||
-1.190907
|
||||
-7.844583
|
||||
-17.491041
|
||||
-24.300421
|
||||
-25.186808
|
||||
-24.409816
|
||||
-17.587587
|
||||
-7.690400
|
||||
-15.385836
|
||||
-21.456027
|
||||
-22.469566
|
||||
-21.062494
|
||||
-15.340380
|
||||
-9.728696
|
||||
-21.188579
|
||||
-22.512963
|
||||
-21.275175
|
||||
-9.282340
|
||||
-20.462720
|
||||
-21.609047
|
||||
-20.300170
|
||||
# The principal components (eigenvectors) of identity or combined identity and expression model
|
||||
204
|
||||
30
|
||||
6
|
||||
-0.190469 -0.071184 -0.054685 0.088181 -0.005885 0.117801 -0.017233 -0.027212 -0.081376 -0.065794 0.104253 -0.043337 0.060539 0.027374 -0.030921 0.019905 -0.032263 0.073285 -0.027532 0.067513 -0.106417 -0.052799 0.090934 0.071815 -0.103673 -0.018281 -0.142612 -0.136544 0.104777 -0.059287
|
||||
-0.181987 -0.077301 -0.040768 0.081699 -0.010115 0.074060 -0.030833 -0.002966 -0.045981 -0.047412 0.056452 -0.056207 0.046458 0.008748 -0.018044 0.054030 -0.035939 0.107036 0.006886 0.061526 -0.048319 -0.066964 0.074145 0.045579 -0.068658 0.034547 -0.074267 -0.093346 -0.011087 -0.057005
|
||||
-0.173515 -0.088597 -0.030820 0.084278 -0.018017 0.017465 -0.045721 0.022537 -0.010900 -0.021144 0.014483 -0.051229 0.043695 0.007049 0.008784 0.079550 -0.021801 0.121824 0.044955 0.054364 0.003371 -0.068850 0.062924 0.019579 -0.006031 0.059153 0.004337 -0.040960 -0.127230 -0.069391
|
||||
-0.161922 -0.097905 -0.029552 0.085923 -0.024253 -0.051497 -0.041131 0.032695 0.013614 0.006737 -0.022233 -0.015979 0.044671 0.016456 0.042545 0.100738 0.010838 0.104136 0.059488 0.030909 0.041065 -0.005391 0.037132 0.000199 0.070025 0.027990 0.075888 0.013117 -0.161032 -0.045139
|
||||
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|
||||
-0.028657 0.029431 -0.068325 0.054601 0.012282 0.062780 -0.002133 0.013389 -0.025454 -0.056386 -0.011356 0.002951 0.106448 -0.028775 -0.003876 0.024019 0.108897 -0.074610 0.073446 -0.011707 -0.021342 -0.103981 -0.127299 -0.041136 0.015961 -0.150684 -0.060020 -0.007779 0.011458 0.104385
|
||||
0.063578 -0.013445 -0.036971 0.039821 0.001675 0.036406 0.008455 0.014806 0.012789 -0.060290 0.005833 -0.017255 0.148953 -0.054571 -0.045515 -0.054626 0.052297 -0.089326 0.045593 -0.031234 -0.065034 -0.020746 -0.060929 -0.009637 0.100149 0.091730 0.043765 -0.056615 0.079685 0.025615
|
||||
0.071794 -0.035989 -0.017350 0.036990 -0.003460 0.016260 0.031031 0.060910 0.012329 -0.084441 0.041786 0.005125 0.109961 -0.055672 -0.038732 -0.010692 0.032560 -0.064027 0.032960 -0.029972 -0.036901 0.013067 -0.042376 0.010142 0.063392 0.038346 0.015748 -0.029226 0.050392 0.010939
|
||||
0.063759 -0.072482 0.011329 0.033642 -0.003268 -0.003311 0.050037 0.092532 0.026586 -0.086094 0.079641 0.022486 0.031071 -0.042563 -0.036040 0.024477 0.005832 -0.040663 0.028644 -0.032777 0.009618 0.022358 -0.035611 0.038247 0.053143 -0.007266 0.004593 -0.017910 0.040641 -0.012859
|
||||
0.051630 -0.117181 0.047808 0.024724 -0.004592 -0.020789 0.064649 0.102103 0.068610 -0.083927 0.110570 0.027264 -0.082106 -0.026394 -0.033806 0.052063 -0.018428 -0.022571 0.027617 -0.038539 0.051436 0.017891 -0.037344 0.066231 0.062368 -0.049007 -0.004398 0.002072 0.022906 -0.043357
|
||||
0.037553 -0.159331 0.094129 0.007582 -0.004139 -0.035834 0.050274 0.093946 0.144177 -0.068344 0.140700 0.034470 -0.232073 -0.011532 -0.037598 0.072213 -0.029598 0.003506 0.025876 -0.030173 0.107089 -0.017808 -0.016450 0.105897 0.059851 -0.155405 -0.048537 0.057366 0.015719 -0.052152
|
||||
0.087870 0.132848 -0.106554 0.114050 0.038210 0.044132 0.032271 -0.094621 0.019907 -0.012629 -0.009526 -0.097707 -0.099677 -0.074690 -0.098412 -0.073850 0.139562 -0.146851 0.008558 -0.023334 -0.026050 -0.004419 -0.012296 0.065288 0.086510 -0.052834 0.013366 0.022267 -0.018565 0.068817
|
||||
0.086836 0.145955 -0.069460 0.111975 0.043983 0.032422 0.100857 -0.081404 0.025667 0.022035 0.046275 -0.079727 -0.054927 -0.019261 -0.090570 -0.059888 0.109093 -0.094090 0.031810 0.034953 -0.041590 0.057182 0.024488 0.110023 -0.000851 -0.006638 0.052093 0.039009 -0.033395 0.022106
|
||||
0.084080 0.154417 -0.034041 0.105690 0.045131 0.023930 0.166083 -0.067288 0.030660 0.053197 0.097038 -0.065522 -0.001021 0.037451 -0.071101 -0.036729 0.070828 -0.034174 0.046568 0.083892 -0.054168 0.115358 0.046615 0.142656 -0.079375 0.029401 0.098207 0.048457 -0.065300 -0.025684
|
||||
0.081261 0.160882 -0.003245 0.092231 0.029959 0.015570 0.223819 -0.046800 0.037761 0.072737 0.155678 -0.060748 0.055695 0.089959 -0.052061 -0.015172 0.043441 0.057430 0.065570 0.130258 -0.061637 0.173404 0.050991 0.193601 -0.155228 0.070612 0.129626 0.047902 -0.127429 -0.069416
|
||||
0.036615 0.112465 -0.011870 0.050560 -0.023586 0.056578 0.075251 -0.036631 -0.016501 0.076340 0.043630 -0.054487 0.133027 0.086040 0.092223 0.053764 -0.056705 0.064417 -0.056585 -0.137660 0.031413 -0.033211 0.145916 -0.050020 0.094662 0.028183 -0.158190 0.014984 -0.105505 0.057209
|
||||
0.034375 0.077035 -0.000712 0.093236 0.006978 0.053717 0.099504 -0.040084 -0.015700 0.079458 0.061602 -0.060225 0.054172 0.136687 0.090498 0.097151 -0.051423 0.032246 -0.057680 -0.057839 0.069192 -0.083088 0.077574 -0.067482 0.030677 -0.009552 -0.072160 0.006569 0.043961 0.017029
|
||||
0.040684 0.068853 0.009671 0.113473 0.027127 0.051794 0.115783 -0.030462 -0.025635 0.092955 0.099086 -0.070271 0.013242 0.179470 0.140747 0.141755 -0.029324 0.017410 -0.028728 -0.024224 0.109705 -0.144193 0.024627 -0.046970 -0.026776 -0.014468 -0.040679 -0.023585 0.102728 -0.026368
|
||||
0.046633 0.057103 0.003683 0.104693 0.012417 0.057466 0.110430 -0.019549 -0.020361 0.050433 0.074178 -0.043027 0.016022 0.142928 0.125023 0.156119 -0.034944 0.003438 -0.062517 -0.058566 0.054831 -0.067995 0.003152 -0.089270 -0.000192 -0.033824 -0.040037 -0.070553 0.048853 -0.033546
|
||||
0.061039 0.064860 -0.005290 0.078749 -0.007805 0.061597 0.110715 0.013244 -0.030184 0.003642 0.055152 -0.030634 0.049493 0.116908 0.140058 0.174449 -0.053516 0.000190 -0.112349 -0.132149 0.000793 -0.040724 -0.061891 -0.068736 0.005926 -0.105995 -0.060387 -0.170157 -0.047231 -0.040790
|
||||
-0.175799 -0.045261 0.024858 0.038370 0.010499 -0.010330 0.018772 -0.031099 -0.053961 0.038583 -0.102321 0.087246 -0.049020 -0.044092 0.069199 0.011624 -0.010185 -0.018390 -0.149062 0.027037 0.007544 -0.016282 0.047502 -0.012530 -0.120693 -0.109381 0.017728 0.021220 -0.018403 0.033139
|
||||
-0.150738 -0.038016 -0.005976 0.025580 -0.000282 0.015390 -0.026600 -0.045379 -0.036542 0.013962 -0.087331 0.069087 -0.008413 -0.078009 -0.005205 -0.033280 0.049669 0.006012 -0.091357 0.053438 0.023519 0.013651 0.033399 -0.008797 -0.063309 0.003493 -0.051421 0.038373 -0.008723 -0.024371
|
||||
-0.136547 -0.040596 -0.023608 0.032877 -0.009103 0.034969 -0.039678 -0.056986 -0.024972 -0.003964 -0.084974 0.047129 -0.022096 -0.085478 -0.024092 -0.032102 0.079757 -0.016028 -0.065426 0.071981 0.047015 0.004380 0.016638 -0.024282 -0.037161 0.028609 -0.064721 0.047046 -0.011783 -0.024815
|
||||
-0.090047 -0.016193 -0.016122 0.026928 -0.022206 0.045202 -0.035464 -0.047036 0.002742 0.014525 -0.052179 0.016313 -0.012168 -0.076621 0.002176 -0.051683 0.077661 -0.049370 -0.001598 0.072597 0.042840 -0.010636 0.001025 -0.024299 -0.036344 -0.050376 -0.047760 0.035163 -0.038610 -0.003729
|
||||
-0.131264 -0.034580 -0.013268 0.034774 -0.006934 0.049566 -0.031704 -0.047514 -0.010250 0.009128 -0.078666 0.042389 -0.039003 -0.101736 0.018542 -0.024093 0.062698 -0.027135 -0.071540 0.073475 0.058385 -0.017673 0.017361 -0.002414 -0.023931 -0.011269 -0.073172 0.043355 -0.015340 -0.000193
|
||||
-0.154356 -0.033249 0.000233 0.028814 0.002312 0.031366 -0.019125 -0.041617 -0.027003 0.020765 -0.078860 0.065972 -0.018866 -0.090342 0.032012 -0.028281 0.033862 -0.002061 -0.102580 0.057186 0.038928 -0.004872 0.035828 0.019269 -0.055821 -0.033986 -0.059101 0.037779 -0.010706 -0.014104
|
||||
0.033417 -0.072532 0.012568 0.008946 -0.019681 0.027342 -0.018422 -0.021703 -0.005752 0.030767 -0.102117 -0.038138 0.007722 -0.038441 -0.028165 -0.047029 0.045147 -0.041711 -0.000110 0.026793 -0.045698 0.000772 0.024380 0.000760 0.004080 0.014080 0.027246 -0.013313 -0.023959 0.002622
|
||||
0.039215 -0.137846 0.026101 0.007934 -0.015806 0.010599 -0.027141 -0.026963 -0.019964 0.048780 -0.132766 -0.032062 0.004032 -0.028996 -0.063142 -0.040783 0.045465 0.014486 -0.001545 -0.018229 -0.030509 0.038953 0.014241 -0.004312 -0.039158 0.053120 0.021326 -0.045180 0.027409 0.009402
|
||||
0.043521 -0.145592 0.040519 0.010506 -0.013667 -0.006286 -0.010463 -0.020166 -0.031415 0.042002 -0.135580 0.015098 0.024166 -0.036230 -0.025575 -0.040553 0.024242 0.005260 0.004310 -0.036449 -0.001093 0.037421 0.040208 -0.003964 -0.056208 0.059177 -0.009590 -0.033246 0.021174 -0.013008
|
||||
0.046801 -0.169637 0.077587 0.023551 0.002886 -0.035031 0.018323 -0.056422 -0.055888 0.036378 -0.131809 0.063178 0.042467 0.002594 0.074243 -0.025358 -0.016624 -0.042451 0.017027 -0.058671 0.046846 0.011740 0.094474 -0.078083 -0.084720 0.033242 -0.013165 -0.023825 -0.006214 -0.047684
|
||||
0.047127 -0.148675 0.043016 0.015841 -0.008682 0.009800 -0.012490 -0.031526 -0.026918 0.043809 -0.147540 0.010436 0.022248 -0.041771 0.015715 -0.044134 0.019909 0.003267 0.012343 -0.043093 0.007270 0.028899 0.042830 0.005583 -0.024609 0.043346 -0.020205 -0.020537 0.014459 -0.010947
|
||||
0.037862 -0.132432 0.028533 0.015229 -0.009476 0.027310 -0.028606 -0.036439 -0.009620 0.058203 -0.140411 -0.033794 0.004687 -0.041138 -0.009726 -0.051973 0.027422 -0.006463 0.000827 -0.017258 -0.011153 0.018941 0.007685 0.000585 -0.000785 0.036124 0.010801 -0.031023 0.025637 0.006657
|
||||
-0.072053 -0.074598 -0.100711 -0.160392 -0.056590 -0.046253 0.022243 -0.033939 -0.070682 0.062764 0.074060 -0.097748 0.012162 0.038627 0.038864 0.066326 -0.035816 -0.139004 0.083591 0.117267 0.134277 0.020804 0.001839 0.085517 0.010905 0.060183 -0.029659 0.033860 0.004833 0.047905
|
||||
0.008856 0.022312 -0.093092 -0.096187 -0.110312 -0.030930 -0.023096 -0.007133 -0.029338 0.005534 0.021892 -0.041877 0.024922 -0.025176 0.009405 0.027628 -0.064749 0.029258 0.045688 0.051081 0.010396 -0.039200 -0.007260 -0.072501 0.003076 0.004612 0.027440 -0.007110 -0.028578 -0.055429
|
||||
0.042419 0.075052 -0.081836 -0.028702 -0.141576 -0.019808 -0.044103 0.022094 0.023906 -0.041791 0.007334 0.020262 0.009451 -0.052770 -0.013873 -0.032374 -0.045137 0.114123 0.003529 0.025807 -0.060978 -0.045002 -0.069777 -0.072668 -0.059290 -0.013371 0.048115 0.047343 -0.008194 -0.095606
|
||||
0.056245 0.073217 -0.085604 -0.014481 -0.139289 -0.012952 -0.065166 0.021197 0.040232 -0.054156 -0.003544 0.024890 -0.013008 -0.038209 0.002685 -0.040139 -0.023651 0.089468 0.003185 0.028247 -0.061535 -0.064831 -0.076752 -0.083293 -0.081248 0.035841 -0.022897 0.061927 0.006909 -0.072040
|
||||
0.056430 0.054020 -0.075907 -0.028402 -0.150533 -0.007712 -0.061734 0.021080 0.030544 -0.035952 0.013622 0.019362 0.007588 -0.014823 0.006822 -0.068151 -0.027590 0.106978 0.012945 0.046588 -0.080258 -0.070291 -0.051863 -0.083578 -0.101646 0.031158 -0.023454 0.089560 -0.024262 -0.077726
|
||||
0.024479 -0.009246 -0.089056 -0.082610 -0.118332 -0.003018 -0.047311 0.022264 -0.024587 -0.005407 0.027436 -0.026817 -0.000381 0.000645 0.030356 -0.021404 -0.042803 -0.008602 0.024542 0.091667 -0.051169 -0.082852 -0.054013 -0.049463 -0.075523 0.039438 -0.024571 -0.002215 -0.035084 -0.052036
|
||||
-0.012027 -0.136883 -0.081754 -0.149149 -0.055287 -0.009700 0.008094 -0.006322 -0.083587 0.062632 0.030406 -0.119596 -0.044029 0.034376 0.058444 0.083058 0.008314 -0.131333 0.060136 0.135252 0.037775 0.014841 -0.105155 0.067016 -0.042349 0.057074 0.020755 -0.044335 0.016350 0.028098
|
||||
0.012816 -0.053653 -0.100099 -0.097988 0.007326 -0.063234 -0.044976 0.019100 0.000113 0.020415 0.014232 -0.015097 -0.037545 0.018025 0.050639 -0.026776 0.001709 -0.055574 0.006984 0.107057 -0.015655 -0.009003 0.051013 0.002343 0.006298 -0.027962 0.015854 -0.091353 -0.016346 0.039465
|
||||
0.035534 0.010285 -0.097093 -0.025993 0.043429 -0.098898 -0.077835 0.037713 0.075033 -0.019078 -0.028117 0.072858 -0.038120 -0.010628 0.052424 -0.079396 0.009461 0.000612 -0.023804 0.043805 -0.006746 -0.000033 0.127073 -0.008097 0.050749 -0.034756 0.026520 -0.083538 -0.050395 0.020636
|
||||
0.030421 0.040185 -0.107600 -0.020036 0.045443 -0.101940 -0.073577 0.039398 0.089641 -0.036760 -0.037780 0.091039 -0.036830 -0.033786 0.025635 -0.067609 -0.020951 -0.002102 -0.021006 0.006076 0.043247 0.015986 0.090187 0.005710 0.062335 -0.028713 0.040719 -0.131139 -0.025086 0.002108
|
||||
0.011036 0.047297 -0.102586 -0.035860 0.046121 -0.110718 -0.049199 0.029296 0.077701 -0.015091 -0.022442 0.073219 -0.003970 -0.046326 0.008115 -0.052553 -0.037889 0.005420 -0.025423 -0.027524 0.058565 0.027155 0.082429 0.016126 0.080709 -0.088126 0.109562 -0.159245 -0.006448 -0.016464
|
||||
-0.023863 -0.001767 -0.112029 -0.110537 0.012159 -0.090593 -0.009916 0.004722 0.005667 0.023478 0.015308 -0.012738 0.005787 -0.017643 0.017190 0.018514 -0.050562 -0.056536 0.012880 0.004994 0.085020 0.028885 0.071570 0.002042 0.074510 -0.049359 0.066226 -0.121898 -0.005946 0.006471
|
||||
-0.050886 -0.055706 -0.121851 -0.167249 -0.044477 -0.046575 0.028548 -0.042874 -0.061687 0.059400 0.060959 -0.100667 0.005081 0.035377 0.021717 0.060243 -0.030080 -0.150824 0.080442 0.090665 0.113206 0.029119 0.010088 0.105332 -0.006041 0.123141 -0.083657 0.047525 0.028597 0.091883
|
||||
0.030708 0.078089 -0.080455 -0.012260 -0.109552 -0.041103 -0.041066 0.009557 0.026507 -0.046242 -0.026526 0.046953 0.028301 -0.060457 0.018475 -0.053304 -0.043608 0.094731 0.031432 -0.117133 -0.076221 -0.030731 0.016484 0.046091 -0.039803 -0.002365 0.051830 0.126565 0.100037 -0.043647
|
||||
0.055139 0.076245 -0.081522 0.004314 -0.107992 -0.039650 -0.063847 0.014757 0.044175 -0.065309 -0.027112 0.053595 -0.026360 -0.046824 0.012100 -0.022947 -0.031940 0.048766 0.001973 -0.055875 -0.071290 -0.061669 -0.018830 -0.025187 -0.043714 0.001550 0.010165 0.155243 0.019864 -0.063997
|
||||
0.060624 0.046756 -0.072069 -0.012080 -0.112141 -0.035260 -0.050129 0.028093 0.012172 -0.057691 -0.002134 0.044817 -0.014066 -0.049732 0.013478 0.000195 -0.048403 0.116300 -0.003782 -0.070723 -0.092908 -0.053813 0.005494 -0.043911 -0.042773 -0.024812 0.028047 0.200589 0.002444 0.028023
|
||||
-0.002693 -0.109254 -0.103698 -0.155319 -0.040843 -0.008397 0.025152 -0.004684 -0.075416 0.044165 0.036425 -0.106068 -0.063753 0.008950 0.032720 0.107046 0.006529 -0.150703 0.049184 0.114889 0.065819 0.022378 -0.105813 0.077860 -0.041574 0.066244 0.002608 -0.063551 0.013985 0.008026
|
||||
0.056392 0.032564 -0.123103 -0.042145 0.014634 -0.085346 -0.045427 0.044037 0.054277 -0.044440 -0.015580 0.091353 -0.020715 -0.046674 0.024152 -0.008198 -0.036096 0.105219 -0.027204 -0.058790 0.022864 0.002164 0.063033 -0.012096 0.021425 -0.015333 0.011114 -0.013654 0.020932 0.125969
|
||||
0.050734 0.066831 -0.133624 -0.025020 0.025214 -0.086764 -0.052195 0.036576 0.090356 -0.053293 -0.040101 0.097309 -0.028327 -0.042717 0.020156 -0.038668 -0.031980 0.037324 -0.028638 -0.046635 0.037633 0.003905 0.057016 0.012124 0.023034 0.010380 0.012591 -0.047595 0.045870 0.056652
|
||||
0.024006 0.067660 -0.131503 -0.044887 0.014372 -0.089393 -0.029303 0.029039 0.070116 -0.027935 -0.042161 0.091030 0.024491 -0.049115 0.023052 -0.069348 -0.035778 0.081727 -0.007838 -0.092164 0.033586 0.027022 0.084316 0.076691 0.038307 0.018769 0.032070 -0.086649 0.139818 0.057912
|
||||
# The variances of the components (eigenvalues) of identity or combined identity and expression model
|
||||
1
|
||||
30
|
||||
6
|
||||
1260.970668 622.171792 514.701969 368.231621 178.288803 141.373501 123.600203 108.077802 95.536656 70.169455 60.351993 56.235863 49.519216 44.933492 42.272445 39.564849 34.747298 28.830661 26.147964 25.285930 21.833110 18.995127 18.134667 16.329230 13.965430 12.933174 11.705294 11.301406 9.624030 8.423463
|
||||
Binary file not shown.
@@ -0,0 +1,29 @@
|
||||
% Script for internal menpo data split, convert the original training data
|
||||
% to 2/3rds training and 1/3rd validation
|
||||
|
||||
menpo_root = 'D:\Datasets\menpo/';
|
||||
|
||||
pts_files = dir([menpo_root, '/*.jpg']);
|
||||
jpg_files = dir([menpo_root, '/*.pts']);
|
||||
|
||||
% Do the actual copying to respective folders
|
||||
out_train = [menpo_root, '/train/'];
|
||||
out_valid = [menpo_root, '/valid/'];
|
||||
mkdir(out_train);
|
||||
mkdir(out_valid);
|
||||
|
||||
load('train_valid_split');
|
||||
|
||||
for i=1:numel(train_imgs)
|
||||
|
||||
copyfile([menpo_root, train_pts(i).name], [out_train, train_pts(i).name]);
|
||||
copyfile([menpo_root, train_imgs(i).name], [out_train, train_imgs(i).name]);
|
||||
|
||||
end
|
||||
|
||||
for i=1:numel(valid_imgs)
|
||||
|
||||
copyfile([menpo_root, valid_pts(i).name], [out_valid, valid_pts(i).name]);
|
||||
copyfile([menpo_root, valid_imgs(i).name], [out_valid, valid_imgs(i).name]);
|
||||
|
||||
end
|
||||
Binary file not shown.
Binary file not shown.
@@ -0,0 +1,41 @@
|
||||
function writePDM( V, E, M, outputFile, Vmorph, Emorph )
|
||||
%WRITEPDM Summary of this function goes here
|
||||
% Detailed explanation goes here
|
||||
|
||||
fId = fopen(outputFile,'w');
|
||||
|
||||
% number of elements
|
||||
|
||||
% Comment
|
||||
fprintf(fId, '# The mean values of the components (in mm)\n');
|
||||
writeMatrix(fId, M, 6);
|
||||
|
||||
fprintf(fId, '# The principal components (eigenvectors) of identity or combined identity and expression model\n');
|
||||
writeMatrix(fId, V, 6);
|
||||
|
||||
fprintf(fId, '# The variances of the components (eigenvalues) of identity or combined identity and expression model\n');
|
||||
writeMatrix(fId, E', 6);
|
||||
|
||||
if(nargin > 4)
|
||||
fprintf(fId, '# The principal components (eigenvectors) of expression\n');
|
||||
writeMatrix(fId, Vmorph, 6);
|
||||
|
||||
fprintf(fId, '# The variances of the components (eigenvalues) of expression\n');
|
||||
writeMatrix(fId, Emorph', 6);
|
||||
end
|
||||
|
||||
fclose(fId);
|
||||
end
|
||||
|
||||
% for easier readibility write them row by row
|
||||
function writeMatrix(fileID, M, type)
|
||||
|
||||
fprintf(fileID, '%d\n', size(M,1));
|
||||
fprintf(fileID, '%d\n', size(M,2));
|
||||
fprintf(fileID, '%d\n', type);
|
||||
|
||||
for i=1:size(M,1)
|
||||
fprintf(fileID, '%f ', M(i,:));
|
||||
fprintf(fileID, '\n');
|
||||
end
|
||||
end
|
||||
@@ -0,0 +1,26 @@
|
||||
function R = apprRot(Ra)
|
||||
%R = apprRot(Ra)
|
||||
|
||||
i1 = 0.5; i2 = 0.5;
|
||||
U = Ra(1,:);
|
||||
V = Ra(2,:);
|
||||
un = norm(U);
|
||||
vn = norm(V);
|
||||
Un = U/un;
|
||||
Vn = V/vn;
|
||||
|
||||
vp = Un*Vn';
|
||||
up = Vn*Un';
|
||||
|
||||
Vc = Vn-vp*Un; Vc = Vc/norm(Vc);
|
||||
Uc = Un-up*Vn; Uc = Uc/norm(Uc);
|
||||
|
||||
Ua = i1*Un+i2*Uc; Ua = Ua/norm(Ua);
|
||||
Va = i1*Vn+i2*Vc; Va = Va/norm(Va);
|
||||
|
||||
|
||||
|
||||
R = [Ua;Va;cross(Ua,Va)];
|
||||
if det(R)<0, R(3,:) = -R(3,:); end;
|
||||
|
||||
|
||||
710
pkg/OpenFace/model_training/pdm_generation/nrsfm-em/computeH.c
Normal file
710
pkg/OpenFace/model_training/pdm_generation/nrsfm-em/computeH.c
Normal file
@@ -0,0 +1,710 @@
|
||||
/* Code written by Lorenzo Torresani and Shoumen Saha */
|
||||
|
||||
#include <stdio.h>
|
||||
#include <math.h>
|
||||
#include <string.h>
|
||||
#include "mat.h"
|
||||
#include "mex.h"
|
||||
|
||||
|
||||
#define IN
|
||||
#define OUT
|
||||
#define MYDEBUG 0
|
||||
|
||||
|
||||
static mxArray * McomputeH(int nargout_,
|
||||
const mxArray * Uc,
|
||||
const mxArray * Vc,
|
||||
const mxArray * E_z,
|
||||
const mxArray * E_zz,
|
||||
const mxArray * RR);
|
||||
|
||||
|
||||
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
|
||||
{
|
||||
if (nlhs > 1) {
|
||||
mexErrMsgTxt(
|
||||
"Run-time Error: File: computeh Line: 1 Column:"
|
||||
" 1 The function \"computeh\" was called with"
|
||||
" more than the declared number of outputs (1).");
|
||||
}
|
||||
if (nrhs > 5) {
|
||||
mexErrMsgTxt(
|
||||
"Run-time Error: File: computeh Line: 1 Column:"
|
||||
" 1 The function \"computeh\" was called with"
|
||||
" more than the declared number of inputs (5).");
|
||||
}
|
||||
plhs[0] = McomputeH(nlhs, prhs[0], prhs[1], prhs[2], prhs[3], prhs[4]);
|
||||
}
|
||||
|
||||
|
||||
|
||||
double ** getMxArray(IN const mxArray *mxArr,
|
||||
OUT int *rows,
|
||||
OUT int *cols)
|
||||
{
|
||||
int i, j, numDim;
|
||||
double *arrDataPt, **matrix;
|
||||
|
||||
if((numDim = mxGetNumberOfDimensions(mxArr)) != 2)
|
||||
{
|
||||
printf("Input matrix has %d dimensions, not 2!\n", numDim);
|
||||
return NULL;
|
||||
}
|
||||
|
||||
*rows = mxGetM(mxArr);
|
||||
*cols = mxGetN(mxArr);
|
||||
|
||||
if(((matrix = (double **) malloc(sizeof(double *)*(*rows))) == NULL) ||
|
||||
((matrix[0] = (double *) malloc(sizeof(double)*(*rows)*(*cols))) == NULL))
|
||||
return NULL;
|
||||
|
||||
for(i=1; i<(*rows); i++)
|
||||
matrix[i] = matrix[0] + i*(*cols);
|
||||
|
||||
arrDataPt = mxGetPr(mxArr);
|
||||
for(j=0; j<(*cols); j++)
|
||||
for(i=0; i<(*rows); i++)
|
||||
matrix[i][j] = *(arrDataPt ++);
|
||||
|
||||
return matrix;
|
||||
}
|
||||
|
||||
|
||||
mxArray * putMxArray(double *img, int rows, int cols/*, char *nameImg*/)
|
||||
{
|
||||
int i, j;
|
||||
double *ptr;
|
||||
mxArray *mxArr;
|
||||
|
||||
mxArr = mxCreateDoubleMatrix(rows, cols, mxREAL);
|
||||
|
||||
ptr = mxGetPr(mxArr);
|
||||
|
||||
for(j=0; j<cols; j++)
|
||||
for(i=0; i<rows; i++)
|
||||
*(ptr ++) = img[i*cols + j];
|
||||
|
||||
/*mxSetPr(mxArr, data);*/
|
||||
/*mxSetName(mxArr, nameImg);*/
|
||||
|
||||
return mxArr;
|
||||
}
|
||||
|
||||
|
||||
|
||||
double ** createMatrix(IN int rows,
|
||||
IN int cols)
|
||||
{
|
||||
int i;
|
||||
double **matrix;
|
||||
|
||||
if(((matrix = (double **) malloc(sizeof(double *)*rows)) == NULL) ||
|
||||
((matrix[0] = (double *) malloc(sizeof(double)*rows*cols)) == NULL))
|
||||
return NULL;
|
||||
|
||||
for(i=1; i<rows; i++)
|
||||
matrix[i] = matrix[0] + i*cols;
|
||||
|
||||
|
||||
memset(matrix[0], 0, sizeof(double)*rows*cols);
|
||||
|
||||
return matrix;
|
||||
}
|
||||
|
||||
|
||||
int ** createIntMatrix(IN int rows,
|
||||
IN int cols)
|
||||
{
|
||||
int i;
|
||||
int **matrix;
|
||||
|
||||
if(((matrix = (int **) malloc(sizeof(int *)*rows)) == NULL) ||
|
||||
((matrix[0] = (int *) malloc(sizeof(int)*rows*cols)) == NULL))
|
||||
return NULL;
|
||||
|
||||
for(i=1; i<rows; i++)
|
||||
matrix[i] = matrix[0] + i*cols;
|
||||
|
||||
|
||||
memset(matrix[0], 0, sizeof(int)*rows*cols);
|
||||
|
||||
return matrix;
|
||||
}
|
||||
|
||||
|
||||
void freeMatrix(IN double **matrix)
|
||||
{
|
||||
free(*matrix);
|
||||
free(matrix);
|
||||
}
|
||||
|
||||
void freeIntMatrix(IN int **matrix)
|
||||
{
|
||||
free(*matrix);
|
||||
free(matrix);
|
||||
}
|
||||
|
||||
|
||||
void IO_MLabCreateFile(char *fileName)
|
||||
{
|
||||
MATFile *fp;
|
||||
|
||||
fp = matOpen(fileName, "w");
|
||||
|
||||
matClose(fp);
|
||||
}
|
||||
|
||||
|
||||
void IO_MLabWriteDoubleImg(char *fileName, char *nameImg, double *img, int rows, int cols)
|
||||
{
|
||||
MATFile *fp;
|
||||
int i, j, dims[2];
|
||||
double *ptr;
|
||||
mxArray *mxArr;
|
||||
|
||||
dims[0] = rows;
|
||||
dims[1] = cols;
|
||||
fp = matOpen(fileName, "u");
|
||||
|
||||
mxArr = mxCreateNumericArray(2, dims, mxDOUBLE_CLASS, mxREAL);
|
||||
|
||||
ptr = mxGetPr(mxArr);
|
||||
for(j=0; j<cols; j++)
|
||||
for(i=0; i<rows; i++)
|
||||
*(ptr ++) = img[i*cols + j];
|
||||
|
||||
/*mxSetName(mxArr, nameImg);
|
||||
matPutArray(fp, mxArr);*/
|
||||
matPutVariable(fp, nameImg, mxArr);
|
||||
|
||||
matClose(fp);
|
||||
|
||||
mxDestroyArray(mxArr);
|
||||
}
|
||||
|
||||
|
||||
void kron(IN int rowsA,
|
||||
IN int colsA,
|
||||
IN double **A,
|
||||
IN int rowsB,
|
||||
IN int colsB,
|
||||
IN double **B,
|
||||
IN int rowsC,
|
||||
IN int colsC,
|
||||
OUT double **C)
|
||||
{
|
||||
int i, j, k, l;
|
||||
|
||||
if ((rowsC != (rowsA*rowsB)) || (colsC != (colsA*colsB)))
|
||||
{
|
||||
printf("kron: incompatible matrix size\n");
|
||||
return;
|
||||
}
|
||||
|
||||
for(i=0; i<rowsA; i++)
|
||||
for(k=0; k<rowsB; k++)
|
||||
for(j=0; j<colsA; j++)
|
||||
for(l=0; l<colsB; l++)
|
||||
C[rowsB*i+k][colsB*j+l] = A[i][j]*B[k][l];
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
||||
double conjgradient(IN int n,
|
||||
IN double **A,
|
||||
IN double **b,
|
||||
IN int i_max, /* max # iterations */
|
||||
IN double epsilon, /* error tolerance */
|
||||
IN OUT double **x)
|
||||
{
|
||||
//my conjugate gradient solver for .5*x'*A*x -b'*x, based on the
|
||||
// tutorial by Jonathan Shewchuk
|
||||
//FILE * fd;
|
||||
int i=0, numrecompute, row, col;
|
||||
double Ax, delta_old, delta_new, delta_0, **r, **d, **q, alpha, alpha_denom, beta;
|
||||
|
||||
r = createMatrix(1, n);
|
||||
d = createMatrix(1, n);
|
||||
q = createMatrix(1, n);
|
||||
|
||||
/* r = b - A*x */
|
||||
/* delta_new = r'*r */
|
||||
delta_new = 0;
|
||||
for (row=0; row<n; row++)
|
||||
{
|
||||
Ax = 0;
|
||||
for (col=0; col<n; col++)
|
||||
Ax += A[row][col]*x[0][col];
|
||||
|
||||
d[0][row] = r[0][row] = b[0][row] - Ax;
|
||||
|
||||
delta_new += r[0][row]*r[0][row];
|
||||
}
|
||||
|
||||
delta_0 = delta_new;
|
||||
|
||||
numrecompute = (int) sqrt((double) n);
|
||||
// printf("numrecompute = %d\n",numrecompute);
|
||||
|
||||
|
||||
//fd = fopen("err.txt", "w");
|
||||
while ((i < i_max) && (delta_new > epsilon*epsilon*delta_0))
|
||||
{
|
||||
//printf("Step %d, delta_new = %f \r",i,delta_new);
|
||||
//fprintf(fd, "%d %f\n", i, (float)delta_new);
|
||||
|
||||
/* q = A*d */
|
||||
alpha_denom = 0;
|
||||
for (row=0; row<n; row++)
|
||||
{
|
||||
q[0][row] = 0;
|
||||
for (col=0; col<n; col++)
|
||||
q[0][row] += A[row][col]*d[0][col];
|
||||
|
||||
alpha_denom += d[0][row]*q[0][row];
|
||||
}
|
||||
|
||||
alpha = delta_new / alpha_denom;
|
||||
|
||||
/* x += d*alpha */
|
||||
for (row=0; row<n; row++)
|
||||
x[0][row] += alpha*d[0][row];
|
||||
|
||||
if (i % numrecompute == 0)
|
||||
{
|
||||
/* r = b - A*x */
|
||||
for (row=0; row<n; row++)
|
||||
{
|
||||
Ax = 0;
|
||||
for (col=0; col<n; col++)
|
||||
Ax += A[row][col]*x[0][col];
|
||||
|
||||
r[0][row] = b[0][row] - Ax;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
/* r = r-q*alpha; */
|
||||
for (row=0; row<n; row++)
|
||||
r[0][row] -= alpha*q[0][row];
|
||||
}
|
||||
|
||||
delta_old = delta_new;
|
||||
|
||||
/* delta_new = r'*r */
|
||||
delta_new = 0;
|
||||
for (row=0; row<n; row++)
|
||||
delta_new += r[0][row]*r[0][row];
|
||||
|
||||
beta = delta_new/delta_old;
|
||||
|
||||
/* d = r + beta*d */
|
||||
for (row=0; row<n; row++)
|
||||
d[0][row] = r[0][row] + beta*d[0][row];
|
||||
|
||||
i++;
|
||||
}
|
||||
//fclose(fd);
|
||||
|
||||
freeMatrix(r);
|
||||
freeMatrix(d);
|
||||
freeMatrix(q);
|
||||
|
||||
return delta_new;
|
||||
}
|
||||
|
||||
|
||||
|
||||
double conjgradient2(IN int n,
|
||||
IN double **A,
|
||||
IN double **b,
|
||||
IN int i_max, /* max # iterations */
|
||||
IN double epsilon, /* error tolerance */
|
||||
IN int k,
|
||||
IN OUT double **x)
|
||||
{
|
||||
//my conjugate gradient solver for .5*x'*A*x -b'*x, based on the
|
||||
// tutorial by Jonathan Shewchuk (or is it +b'*x?)
|
||||
//FILE * fd;
|
||||
int i=0, numrecompute, row, sparsity_offset, j, ind, col_offset;
|
||||
double Ax, delta_old, delta_new, delta_0, **r, **d, **q, alpha, alpha_denom, beta;
|
||||
|
||||
r = createMatrix(1, n);
|
||||
d = createMatrix(1, n);
|
||||
q = createMatrix(1, n);
|
||||
|
||||
sparsity_offset = n / (k+1);
|
||||
|
||||
/* r = b - A*x */
|
||||
/* delta_new = r'*r */
|
||||
delta_new = 0;
|
||||
for (row=0; row<n; row++)
|
||||
{
|
||||
Ax = 0;
|
||||
|
||||
col_offset = ((row%sparsity_offset)/3) * 3;
|
||||
for (j=0; j<(k+1); j++)
|
||||
{
|
||||
ind = col_offset + j*sparsity_offset;
|
||||
Ax += A[row][ind]*x[0][ind] + A[row][ind+1]*x[0][ind+1] + A[row][ind+2]*x[0][ind+2];
|
||||
}
|
||||
|
||||
d[0][row] = r[0][row] = b[0][row] - Ax;
|
||||
|
||||
delta_new += r[0][row]*r[0][row];
|
||||
}
|
||||
|
||||
delta_0 = delta_new;
|
||||
|
||||
numrecompute = (int) sqrt((double) n);
|
||||
// printf("numrecompute = %d\n",numrecompute);
|
||||
|
||||
|
||||
//fd = fopen("err.txt", "w");
|
||||
while ((i < i_max) && (delta_new > epsilon*epsilon*delta_0))
|
||||
{
|
||||
//printf("Step %d, delta_new = %f \r",i,delta_new);
|
||||
//fprintf(fd, "%d %f\n", i, (float)delta_new);
|
||||
|
||||
/* q = A*d */
|
||||
alpha_denom = 0;
|
||||
for (row=0; row<n; row++)
|
||||
{
|
||||
q[0][row] = 0;
|
||||
|
||||
col_offset = ((row%sparsity_offset)/3) * 3;
|
||||
for (j=0; j<(k+1); j++)
|
||||
{
|
||||
ind = col_offset + j*sparsity_offset;
|
||||
q[0][row] += A[row][ind]*d[0][ind] + A[row][ind+1]*d[0][ind+1] + A[row][ind+2]*d[0][ind+2];
|
||||
}
|
||||
|
||||
alpha_denom += d[0][row]*q[0][row];
|
||||
}
|
||||
|
||||
alpha = delta_new / alpha_denom;
|
||||
|
||||
/* x += d*alpha */
|
||||
for (row=0; row<n; row++)
|
||||
x[0][row] += alpha*d[0][row];
|
||||
|
||||
if (i % numrecompute == 0)
|
||||
{
|
||||
/* r = b - A*x */
|
||||
for (row=0; row<n; row++)
|
||||
{
|
||||
Ax = 0;
|
||||
|
||||
col_offset = ((row%sparsity_offset)/3) * 3;
|
||||
for (j=0; j<(k+1); j++)
|
||||
{
|
||||
ind = col_offset + j*sparsity_offset;
|
||||
Ax += A[row][ind]*x[0][ind] + A[row][ind+1]*x[0][ind+1] + A[row][ind+2]*x[0][ind+2];
|
||||
}
|
||||
|
||||
r[0][row] = b[0][row] - Ax;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
/* r = r-q*alpha; */
|
||||
for (row=0; row<n; row++)
|
||||
r[0][row] -= alpha*q[0][row];
|
||||
}
|
||||
|
||||
delta_old = delta_new;
|
||||
|
||||
/* delta_new = r'*r */
|
||||
delta_new = 0;
|
||||
for (row=0; row<n; row++)
|
||||
delta_new += r[0][row]*r[0][row];
|
||||
|
||||
beta = delta_new/delta_old;
|
||||
|
||||
/* d = r + beta*d */
|
||||
for (row=0; row<n; row++)
|
||||
d[0][row] = r[0][row] + beta*d[0][row];
|
||||
|
||||
i++;
|
||||
}
|
||||
//fclose(fd);
|
||||
|
||||
freeMatrix(r);
|
||||
freeMatrix(d);
|
||||
freeMatrix(q);
|
||||
|
||||
return delta_new;
|
||||
}
|
||||
|
||||
|
||||
|
||||
static mxArray * McomputeH(int nargout_,
|
||||
const mxArray * Uc,
|
||||
const mxArray * Vc,
|
||||
const mxArray * E_z,
|
||||
const mxArray * E_zz,
|
||||
const mxArray * RR) {
|
||||
double **Ucc, **Vcc, **E_zc, **E_zzc, **RRc, **KK1c, **KK2c, **kk3c, **P_tc, **R_tc, **zz_hat_tc, **Tmp1c, **Tmp2c, **vecH_hatc=NULL,
|
||||
delta_err, epsilon;
|
||||
int tc, Fc, Nc, junk1, junk2, kc, ic, jc, ii, jj, kk, ll, i_max, **sparsityMap;
|
||||
|
||||
mxArray * vecH_hat = NULL;
|
||||
|
||||
mxArray * KK1 = NULL;
|
||||
mxArray * R_t = NULL;
|
||||
mxArray * P_t = NULL;
|
||||
mxArray * t = NULL;
|
||||
mxArray * KK2 = NULL;
|
||||
mxArray * F = NULL;
|
||||
mxArray * N = NULL;
|
||||
mxArray * k = NULL;
|
||||
|
||||
|
||||
#if MYDEBUG
|
||||
#define DEBUGFILENAME ".\\debug.mat"
|
||||
IO_MLabCreateFile(DEBUGFILENAME);
|
||||
#endif
|
||||
|
||||
Ucc = getMxArray(Uc, &Fc, &Nc);
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "Ucc", Ucc[0], Fc, Nc);
|
||||
#endif
|
||||
|
||||
Vcc = getMxArray(Vc, &junk1, &junk2);
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "Vcc", Vcc[0], Fc, Nc);
|
||||
#endif
|
||||
|
||||
E_zc = getMxArray(E_z, &kc, &junk1);
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "E_zc", E_zc[0], kc, Fc);
|
||||
#endif
|
||||
|
||||
E_zzc = getMxArray(E_zz, &junk1, &junk2);
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "E_zzc", E_zzc[0], kc*Fc, kc);
|
||||
#endif
|
||||
|
||||
|
||||
RRc = getMxArray(RR, &junk1, &junk2);
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "RRc", RRc[0], 2*Fc, 3);
|
||||
#endif
|
||||
|
||||
/*
|
||||
* KK2 = zeros(3*N*(k+1), 3*N*(k+1));
|
||||
*/
|
||||
KK2c = createMatrix(3*Nc*(kc+1), 3*Nc*(kc+1));
|
||||
|
||||
/*
|
||||
* KK3 = zeros(3*N, k+1);
|
||||
*/
|
||||
kk3c = createMatrix(1,3*Nc*(kc+1));
|
||||
|
||||
P_tc = createMatrix(1, 2*Nc);
|
||||
zz_hat_tc = createMatrix(kc+1, kc+1);
|
||||
R_tc = createMatrix(2, 3);
|
||||
KK1c = createMatrix(2*Nc, 3*Nc);
|
||||
Tmp1c = createMatrix(3*Nc, 3*Nc);
|
||||
Tmp2c = createMatrix(1, 3*Nc);
|
||||
for(tc=0; tc<Fc; tc++)
|
||||
{
|
||||
|
||||
/*
|
||||
* P_t = [Uc(t,:); Vc(t,:)];
|
||||
*/
|
||||
memset(P_tc[0], 0, sizeof(double)*2*Nc);
|
||||
for(jc=0; jc<Nc; jc++)
|
||||
{
|
||||
P_tc[0][2*jc] = Ucc[tc][jc];
|
||||
P_tc[0][2*jc+1] = Vcc[tc][jc];
|
||||
}
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "P_tc", P_tc[0], 1, 2*Nc);
|
||||
#endif
|
||||
|
||||
/*
|
||||
* zz_hat_t = [1 E_z(:,t)'; E_z(:,t) E_zz((t-1)*k+1:t*k,:)];
|
||||
*/
|
||||
memset(zz_hat_tc[0], 0, sizeof(double)*(kc+1)*(kc+1));
|
||||
zz_hat_tc[0][0] = 1;
|
||||
for(jc=1; jc<kc+1; jc++)
|
||||
{
|
||||
zz_hat_tc[jc][0] = E_zc[jc-1][tc];
|
||||
zz_hat_tc[0][jc] = E_zc[jc-1][tc];
|
||||
}
|
||||
for(ic=1; ic<kc+1; ic++)
|
||||
{
|
||||
for(jc=1; jc<kc+1; jc++)
|
||||
{
|
||||
zz_hat_tc[ic][jc] = E_zzc[tc*kc + (ic-1)][jc-1];
|
||||
}
|
||||
}
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "zz_hat_tc", zz_hat_tc[0], kc+1, kc+1);
|
||||
#endif
|
||||
|
||||
/*
|
||||
* R_t = [RR(t, :); RR(t+F, :)];
|
||||
*/
|
||||
for(jc=0; jc<3; jc++)
|
||||
{
|
||||
R_tc[0][jc] = RRc[tc][jc];
|
||||
R_tc[1][jc] = RRc[tc+Fc][jc];
|
||||
}
|
||||
|
||||
/*
|
||||
* KK1 = kron(speye(N), R_t);
|
||||
*/
|
||||
memset(KK1c[0], 0, sizeof(double)*2*Nc*3*Nc);
|
||||
for(ic=0; ic<Nc; ic++)
|
||||
{
|
||||
KK1c[ic*2][ic*3] = R_tc[0][0];
|
||||
KK1c[ic*2][ic*3+1] = R_tc[0][1];
|
||||
KK1c[ic*2][ic*3+2] = R_tc[0][2];
|
||||
KK1c[ic*2+1][ic*3] = R_tc[1][0];
|
||||
KK1c[ic*2+1][ic*3+1] = R_tc[1][1];
|
||||
KK1c[ic*2+1][ic*3+2] = R_tc[1][2];
|
||||
}
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "KK1c", KK1c[0], 2*Nc, 3*Nc);
|
||||
#endif
|
||||
|
||||
/* computes KK1'*KK1 */
|
||||
memset(Tmp1c[0], 0, sizeof(double)*3*Nc*3*Nc);
|
||||
Tmp1c[0][0] = KK1c[0][0]*KK1c[0][0] + KK1c[1][0]*KK1c[1][0];
|
||||
Tmp1c[0][1] = KK1c[0][0]*KK1c[0][1] + KK1c[1][0]*KK1c[1][1];
|
||||
Tmp1c[0][2] = KK1c[0][0]*KK1c[0][2] + KK1c[1][0]*KK1c[1][2];
|
||||
|
||||
|
||||
Tmp1c[1][0] = KK1c[0][1]*KK1c[0][0] + KK1c[1][1]*KK1c[1][0];
|
||||
Tmp1c[1][1] = KK1c[0][1]*KK1c[0][1] + KK1c[1][1]*KK1c[1][1];
|
||||
Tmp1c[1][2] = KK1c[0][1]*KK1c[0][2] + KK1c[1][1]*KK1c[1][2];
|
||||
|
||||
Tmp1c[2][0] = KK1c[0][2]*KK1c[0][0] + KK1c[1][2]*KK1c[1][0];
|
||||
Tmp1c[2][1] = KK1c[0][2]*KK1c[0][1] + KK1c[1][2]*KK1c[1][1];
|
||||
Tmp1c[2][2] = KK1c[0][2]*KK1c[0][2] + KK1c[1][2]*KK1c[1][2];
|
||||
for(ic=1; ic<Nc; ic++)
|
||||
{
|
||||
Tmp1c[ic*3][ic*3] = Tmp1c[0][0];
|
||||
Tmp1c[ic*3][ic*3+1] = Tmp1c[0][1];
|
||||
Tmp1c[ic*3][ic*3+2] = Tmp1c[0][2];
|
||||
|
||||
|
||||
Tmp1c[ic*3+1][ic*3] = Tmp1c[1][0];
|
||||
Tmp1c[ic*3+1][ic*3+1] = Tmp1c[1][1];
|
||||
Tmp1c[ic*3+1][ic*3+2] = Tmp1c[1][2];
|
||||
|
||||
Tmp1c[ic*3+2][ic*3] = Tmp1c[2][0];
|
||||
Tmp1c[ic*3+2][ic*3+1] = Tmp1c[2][1];
|
||||
Tmp1c[ic*3+2][ic*3+2] = Tmp1c[2][2];
|
||||
}
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "Tmp1c", Tmp1c[0], 3*Nc, 3*Nc);
|
||||
#endif
|
||||
|
||||
/*
|
||||
* KK2 = KK2 + kron(zz_hat_t', KK1'*KK1);
|
||||
*/
|
||||
|
||||
/*for(ii=0; ii<(kc+1); ii++)
|
||||
for(kk=0; kk<(3*Nc); kk++)
|
||||
for(jj=0; jj<(kc+1); jj++)
|
||||
for(ll=0; ll<(3*Nc); ll++)
|
||||
KK2c[(3*Nc)*ii+kk][(3*Nc)*jj+ll] += zz_hat_tc[ii][jj]*Tmp1c[kk][ll];*/
|
||||
for(ii=0; ii<(kc+1); ii++)
|
||||
for(kk=0; kk<Nc; kk++)
|
||||
for(jj=0; jj<(kc+1); jj++)
|
||||
{
|
||||
KK2c[(3*Nc)*ii+kk*3][(3*Nc)*jj+kk*3] += zz_hat_tc[ii][jj]*Tmp1c[kk*3][kk*3];
|
||||
KK2c[(3*Nc)*ii+kk*3][(3*Nc)*jj+kk*3+1] += zz_hat_tc[ii][jj]*Tmp1c[kk*3][kk*3+1];
|
||||
KK2c[(3*Nc)*ii+kk*3][(3*Nc)*jj+kk*3+2] += zz_hat_tc[ii][jj]*Tmp1c[kk*3][kk*3+2];
|
||||
|
||||
KK2c[(3*Nc)*ii+kk*3+1][(3*Nc)*jj+kk*3] += zz_hat_tc[ii][jj]*Tmp1c[kk*3+1][kk*3];
|
||||
KK2c[(3*Nc)*ii+kk*3+1][(3*Nc)*jj+kk*3+1] += zz_hat_tc[ii][jj]*Tmp1c[kk*3+1][kk*3+1];
|
||||
KK2c[(3*Nc)*ii+kk*3+1][(3*Nc)*jj+kk*3+2] += zz_hat_tc[ii][jj]*Tmp1c[kk*3+1][kk*3+2];
|
||||
|
||||
KK2c[(3*Nc)*ii+kk*3+2][(3*Nc)*jj+kk*3] += zz_hat_tc[ii][jj]*Tmp1c[kk*3+2][kk*3];
|
||||
KK2c[(3*Nc)*ii+kk*3+2][(3*Nc)*jj+kk*3+1] += zz_hat_tc[ii][jj]*Tmp1c[kk*3+2][kk*3+1];
|
||||
KK2c[(3*Nc)*ii+kk*3+2][(3*Nc)*jj+kk*3+2] += zz_hat_tc[ii][jj]*Tmp1c[kk*3+2][kk*3+2];
|
||||
}
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "KK2c", KK2c[0], 3*Nc*(kc+1), 3*Nc*(kc+1));
|
||||
#endif
|
||||
|
||||
|
||||
/*
|
||||
* KK3 = KK3 + KK1'* P_t(:) * [1 E_z(:,t)'];
|
||||
*/
|
||||
|
||||
/* computes KK1'*P_t(:) */
|
||||
memset(Tmp2c[0], 0, sizeof(double)*3*Nc);
|
||||
for(ic=0; ic<Nc; ic++)
|
||||
{
|
||||
Tmp2c[0][3*ic] = KK1c[2*ic][3*ic]*P_tc[0][2*ic] + KK1c[2*ic+1][3*ic]*P_tc[0][2*ic+1];
|
||||
Tmp2c[0][3*ic+1] = KK1c[2*ic][3*ic+1]*P_tc[0][2*ic] + KK1c[2*ic+1][3*ic+1]*P_tc[0][2*ic+1];
|
||||
Tmp2c[0][3*ic+2] = KK1c[2*ic][3*ic+2]*P_tc[0][2*ic] + KK1c[2*ic+1][3*ic+2]*P_tc[0][2*ic+1];
|
||||
}
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "Tmp2c", Tmp2c[0], 1, 3*Nc);
|
||||
#endif
|
||||
|
||||
for(ic=0; ic<3*Nc; ic++)
|
||||
{
|
||||
/*KK3c[ic][0] = KK3c[ic][0] + Tmp2c[0][ic];*/
|
||||
kk3c[0][ic] = kk3c[0][ic] + Tmp2c[0][ic];
|
||||
|
||||
for(jc=1; jc<(kc+1); jc++)
|
||||
/*KK3c[ic][jc] = KK3c[ic][jc] + Tmp2c[0][ic]*E_zc[jc-1][tc];*/
|
||||
kk3c[0][ic + jc*(3*Nc)] = kk3c[0][ic + jc*(3*Nc)] + Tmp2c[0][ic]*E_zc[jc-1][tc];
|
||||
}
|
||||
#if MYDEBUG
|
||||
IO_MLabWriteDoubleImg(DEBUGFILENAME, "kk3c", kk3c[0], 1, 3*Nc*(kc+1));
|
||||
#endif
|
||||
|
||||
|
||||
//printf("debug\n");
|
||||
|
||||
}
|
||||
|
||||
|
||||
freeMatrix(Ucc);
|
||||
freeMatrix(Vcc);
|
||||
freeMatrix(E_zc);
|
||||
freeMatrix(E_zzc);
|
||||
freeMatrix(RRc);
|
||||
freeMatrix(KK1c);
|
||||
freeMatrix(P_tc);
|
||||
freeMatrix(R_tc);
|
||||
freeMatrix(zz_hat_tc);
|
||||
freeMatrix(Tmp1c);
|
||||
freeMatrix(Tmp2c);
|
||||
|
||||
|
||||
vecH_hatc = createMatrix(1, 3*Nc*(kc+1));
|
||||
for(ic=0; ic<3*Nc; ic++)
|
||||
vecH_hatc[0][ic] = (double) rand() / (double) RAND_MAX;
|
||||
|
||||
epsilon = 0.000000001;
|
||||
i_max = 1000;
|
||||
|
||||
//sparsityMap = createIntMatrix(3*Nc*(kc+1), 3*Nc*(kc+1)+1);
|
||||
//getSparsityMap(3*Nc*(kc+1), 3*Nc*(kc+1), KK2c, sparsityMap);
|
||||
|
||||
//delta_err = conjgradient(3*Nc*(kc+1), KK2c, kk3c, i_max, epsilon, vecH_hatc);
|
||||
delta_err = conjgradient2(3*Nc*(kc+1), KK2c, kk3c, i_max, epsilon, kc, vecH_hatc);
|
||||
|
||||
if (delta_err>0.01)
|
||||
printf("Large CG error\n");
|
||||
|
||||
vecH_hat = mxCreateDoubleMatrix(3*Nc*(kc+1), 1, mxREAL);
|
||||
memcpy(mxGetPr(vecH_hat), vecH_hatc[0], sizeof(double)*3*Nc*(kc+1));
|
||||
|
||||
freeMatrix(KK2c);
|
||||
freeMatrix(kk3c);
|
||||
freeMatrix(vecH_hatc);
|
||||
|
||||
return vecH_hat;
|
||||
}
|
||||
@@ -0,0 +1,27 @@
|
||||
function vecH_hat = computeH(Xc, Yc, E_z, E_zz, RR)
|
||||
%vecH_hat = computeH(Xc, Yc, E_z, E_zz, RR)
|
||||
|
||||
fprintf('You are running the Matlab version of function ''computeH''. This program will run very slowly.... \nI recommend that you try to compile the CMEX code on your platform using command ''mex computeH.c'' (''mex computeH.c -l matlb'' under Unix)\n\n');
|
||||
|
||||
K = size(E_z,1);
|
||||
J = size(Xc,2);
|
||||
T = size(Xc,1);
|
||||
|
||||
KK2 = zeros(3*J*(K+1), 3*J*(K+1));
|
||||
KK3 = zeros(3*J, K+1);
|
||||
|
||||
for t=1:T
|
||||
P_t = [Xc(t,:); Yc(t,:)];
|
||||
|
||||
zz_hat_t = [1 E_z(:,t)'; E_z(:,t) E_zz((t-1)*K+1:t*K,:)];
|
||||
|
||||
R_t = [RR(t, :); RR(t+T, :)];
|
||||
|
||||
KK1 = kron(speye(J), R_t);
|
||||
|
||||
KK2 = KK2 + kron(zz_hat_t', KK1'*KK1);
|
||||
|
||||
KK3 = KK3 + KK1'* P_t(:) * [1 E_z(:,t)'];
|
||||
end
|
||||
|
||||
vecH_hat = pinv(KK2) * KK3(:);
|
||||
Binary file not shown.
@@ -0,0 +1,31 @@
|
||||
function loglik = compute_log_lik(P, S_bar, V, E_z, E_zz, RO, Tr, sigma_sq)
|
||||
|
||||
[K, T] = size(E_z);
|
||||
J = size(S_bar, 2);
|
||||
|
||||
M_t = zeros(2*J, K);
|
||||
|
||||
loglik = - 0.5*T * (2*J*log(sigma_sq));
|
||||
for t = 1:T,
|
||||
R_t = RO{t};
|
||||
|
||||
Sdef = S_bar;
|
||||
for kk = 1:K,
|
||||
Sdef = Sdef + E_z(kk,t)*V((kk-1)*3+[1:3],:);
|
||||
|
||||
M_t(1:J, kk) = (R_t(1,:)*V((kk-1)*3+[1:3],:))';
|
||||
M_t(J+1:end, kk) = (R_t(2,:)*V((kk-1)*3+[1:3], :))';
|
||||
end;
|
||||
|
||||
invSigmaSq_p = eye(2*J)./sigma_sq;
|
||||
|
||||
f_bar_t = R_t(1:2,:)*S_bar;
|
||||
f_bar_t = [f_bar_t(1,:) f_bar_t(2,:)]';
|
||||
|
||||
f_t = [P(t, :) P(t+T, :)]';
|
||||
t_vect_t = [Tr(t,1)*ones(J,1); Tr(t,2)*ones(J,1)];
|
||||
|
||||
covZ_t = E_zz((t-1)*K+1:t*K,:) - E_z(:,t)*E_z(:,t)';
|
||||
loglik = loglik - 0.5*(((f_t-f_bar_t-t_vect_t)./sigma_sq)'*(f_t-f_bar_t-t_vect_t)) + (((f_t-f_bar_t-t_vect_t)'./sigma_sq)*M_t*E_z(:,t)) ...
|
||||
- 0.5*trace(((M_t./sigma_sq)'*M_t) * E_zz((t-1)*K+1:t*K,:)) - 0.5*log(det(covZ_t));
|
||||
end
|
||||
161
pkg/OpenFace/model_training/pdm_generation/nrsfm-em/em_sfm.m
Normal file
161
pkg/OpenFace/model_training/pdm_generation/nrsfm-em/em_sfm.m
Normal file
@@ -0,0 +1,161 @@
|
||||
function [P3, S_bar, V, RO, Tr, Z, sigma_sq, phi, Q, mu0, sigma0] = em_sfm(P, MD, K, use_lds, tol, max_em_iter)
|
||||
|
||||
% Non-Rigid Structure From Motion with Gaussian/LDS Deformation Model
|
||||
% Copyright (c) by Lorenzo Torresani, Stanford University
|
||||
%
|
||||
% Based on the following paper:
|
||||
%
|
||||
% Lorenzo Torresani, Aaron Hertzmann and Christoph Bregler,
|
||||
% Learning Non-Rigid 3D Shape from 2D Motion, NIPS 16, 2003
|
||||
% http://cs.stanford.edu/~ltorresa/projects/learning-nr-shape/
|
||||
%
|
||||
% Please refer to this publication if you use this program for
|
||||
% research or for technical applications.
|
||||
%
|
||||
%
|
||||
% INPUT:
|
||||
%
|
||||
% P - (2*T) x J tracking matrix: P([t t+T],:) contains the 2D projections of the J points at time t
|
||||
% MD - T x J missing data binary matrix: MD(t, j)=1 if no valid data is available for point j at time t, 0 otherwise
|
||||
% K - number of deformation basis
|
||||
% use_lds - set to 1 to model deformations using a linear dynamical system; set to 0 otherwise
|
||||
% tol - termination tolerance (proportional change in likelihood)
|
||||
% max_em_iter - maximum number of EM iterations
|
||||
%
|
||||
%
|
||||
% OUTPUT:
|
||||
%
|
||||
% P3 - (3*T) x J 3D-motion matrix: ( P3([t t+T t+2*T],:) contains the 3D coordinates of the J points at time t )
|
||||
% S_bar - shape average: 3 x J matrix
|
||||
% V - deformation shapes: (3*K) x J matrix ( V((n-1)*3+[1:3],:) contains the n-th deformation basis )
|
||||
% RO - rotation: cell array ( RO{t} gives the rotation matrix at time t )
|
||||
% Tr - translation: T x 2 matrix
|
||||
% Z - deformation weights: T x K matrix
|
||||
% sigma_sq - variance of the noise in feature position
|
||||
% phi - LDS transition matrix
|
||||
% Q - LDS state noise matrix
|
||||
% mu0 - initial state mean
|
||||
% sigma0 - initial state variance
|
||||
|
||||
if mod(size(P,1), 1) ~= 0,
|
||||
fprintf('Error: size(P) must be (2*T)xJ\n');
|
||||
return;
|
||||
end
|
||||
if (size(P,1)/2 ~= size(MD,1)) | (size(P,2) ~= size(MD,2))
|
||||
fprintf('Error: Size incompatibility between P and MD\n');
|
||||
return;
|
||||
end
|
||||
if mod(K, 1) ~= 0,
|
||||
fprintf('Error: K must be an integer value\n');
|
||||
return;
|
||||
end
|
||||
|
||||
[T, J] = size(MD);
|
||||
r = 3*(K + 1); % motion rank
|
||||
|
||||
P_hat = P; % if any of the points are missing, P_hat will be updated during the M-step
|
||||
|
||||
% uses rank 3 factorization to get a first initialization for rotation and S_bar
|
||||
[R_init, Trvect, S_bar] = rigidfac(P_hat, MD);
|
||||
|
||||
Tr(:,1) = Trvect(1:T);
|
||||
Tr(:,2) = Trvect(T+1:2*T);
|
||||
|
||||
R = zeros(2*T, 3);
|
||||
% enforces rotation constraints
|
||||
for t = 1:T,
|
||||
Ru = R_init(t,:);
|
||||
Rv = R_init(T+t,:);
|
||||
Rz = cross(Ru,Rv); if det([Ru;Rv;Rz])<0, Rz = -Rz; end;
|
||||
RO_approx = apprRot([Ru;Rv;Rz]);
|
||||
RO{t} = RO_approx;
|
||||
R(t,:) = RO_approx(1,:);
|
||||
R(t+T,:) = RO_approx(2,:);
|
||||
end;
|
||||
|
||||
% given the initial estimates of rotation, translation and shape average, it initializes
|
||||
% deformation shapes and weights through LSQ minimization of the reprojection error
|
||||
[V, Z] = init_SB(P_hat, Tr, R, S_bar, K);
|
||||
|
||||
% initializes sigma_sq
|
||||
E_zz_init = cov(Z);
|
||||
E_zz_init = repmat(E_zz_init, T, 1);
|
||||
sigma_sq = mstep_update_noisevar(P_hat, S_bar, V, Z', E_zz_init, RO, Tr);
|
||||
|
||||
if use_lds,
|
||||
[phi, mu0, sigma0, Q] = init_lds(P_hat, S_bar, V, R, Tr, sigma_sq);
|
||||
else
|
||||
phi = [];
|
||||
mu0 = [];
|
||||
sigma0 = [];
|
||||
Q = [];
|
||||
end
|
||||
|
||||
loglik = 0;
|
||||
annealing_const = 60;
|
||||
max_anneal_iter = round(max_em_iter/2);
|
||||
|
||||
for em_iter=1:max_em_iter,
|
||||
if use_lds,
|
||||
[E_z, E_zz, y, M, xt_n, Pt_n, Ptt1_n, xt_t1, Pt_t1] = estep_lds_compute_Z_distr(P_hat, S_bar, V, R, Tr, phi, mu0, sigma0, Q, sigma_sq);
|
||||
|
||||
[phi, Q, sigma_sq, mu0, sigma0] = mstep_lds_update(y, M, xt_n, Pt_n, Ptt1_n);
|
||||
else
|
||||
% computes the hidden variables distributions
|
||||
[E_z, E_zz] = estep_compute_Z_distr(P_hat, S_bar, V, R, Tr, sigma_sq); % (Eq 17-18)
|
||||
end
|
||||
Z = E_z';
|
||||
|
||||
% updates shape basis
|
||||
[S_bar, V] = mstep_update_shapebasis(P_hat, E_z, E_zz, R, Tr, S_bar, V); % (Eq 21)
|
||||
|
||||
% fills in missing points
|
||||
if sum(MD(:))>0,
|
||||
P_hat = mstep_update_missingdata(P_hat, MD, S_bar, V, E_z, RO, Tr); % (Eq 25)
|
||||
end
|
||||
|
||||
% updates rotation
|
||||
[RO, R] = mstep_update_rotation(P_hat, S_bar, V, E_z, E_zz, RO, Tr); % (Eq 24)
|
||||
|
||||
% updates translation
|
||||
Tr = mstep_update_transl(P_hat, S_bar, V, E_z, RO); % (Eq 23)
|
||||
|
||||
if ~use_lds,
|
||||
% updates noise variance
|
||||
sigma_sq = mstep_update_noisevar(P_hat, S_bar, V, E_z, E_zz, RO, Tr); % (Eq 22)
|
||||
if em_iter < max_anneal_iter,
|
||||
sigma_sq = sigma_sq * (1 + annealing_const*(1 - em_iter/max_anneal_iter));
|
||||
end
|
||||
|
||||
oldloglik = loglik;
|
||||
% computes log likelihood
|
||||
loglik = compute_log_lik(P_hat, S_bar, V, E_z, E_zz, RO, Tr, sigma_sq);
|
||||
|
||||
fprintf('LogLik(%d): %f\n', em_iter, loglik);
|
||||
|
||||
if (em_iter <= 2),
|
||||
loglikbase = loglik;
|
||||
elseif (loglik < oldloglik)
|
||||
fprintf('Violation');
|
||||
% keyboard;
|
||||
elseif 0 & ((loglik-loglikbase)<(1 + tol)*(oldloglik-loglikbase)),
|
||||
fprintf('\n');
|
||||
break;
|
||||
end
|
||||
else
|
||||
fprintf('Iteration %d/%d\n', em_iter, max_em_iter);
|
||||
end
|
||||
end
|
||||
|
||||
P3 = zeros(3*T, J);
|
||||
for t = 1:T,
|
||||
z_t = Z(t,:);
|
||||
Rf = [R(t,:); R(t+T,:)];
|
||||
S = S_bar;
|
||||
for kk = 1:K,
|
||||
S = S+z_t(kk)*V((kk-1)*3+[1:3],:);
|
||||
end;
|
||||
S = RO{t}*S;
|
||||
|
||||
P3([t t+T t+2*T], :) = S + [Tr(t, [1 2]) -mean(S(3,:))]'*ones(1,J);
|
||||
end
|
||||
@@ -0,0 +1,37 @@
|
||||
function [E_z, E_zz] = estep_compute_Z_distr(P, S_bar, V, RR, Tr, sigma_sq)
|
||||
%[E_z, E_zz] = estep_compute_Z_distr(P, S_bar, V, RR, Tr, sigma_sq)
|
||||
|
||||
% Computes the distribution over Z given the current parameter estimates (see Eq 17-18)
|
||||
|
||||
K = size(V,1)/3;
|
||||
[T, J] = size(P);
|
||||
T = T/2;
|
||||
|
||||
Pc = P - Tr(:)*ones(1,J);
|
||||
|
||||
M_t = zeros(2*J, K);
|
||||
P_hat_t = zeros(2*J, 1);
|
||||
|
||||
E_z = zeros(K, T);
|
||||
E_zz = zeros(T*K, K);
|
||||
|
||||
invSigmaSq_p = eye(2*J)./sigma_sq;
|
||||
for t=1:T,
|
||||
R_t = [RR(t,:); RR(t+T,:)];
|
||||
|
||||
for kk = 1:K,
|
||||
M_t(1:J, kk) = (R_t(1,:)*V(1+(kk-1)*3:kk*3, :))';
|
||||
M_t(J+1:end, kk) = (R_t(2,:)*V(1+(kk-1)*3:kk*3, :))';
|
||||
end
|
||||
P_hat_t(1:J) = (R_t(1,:)*S_bar)';
|
||||
P_hat_t(J+1:end) = (R_t(2,:)*S_bar)';
|
||||
|
||||
%beta_t = M_t' * inv(M_t*M_t' + sigma_sq*eye(2*J)); % (Eq 16)
|
||||
% Can be computed much more efficiently using the matrix inversion lemma:
|
||||
AA = M_t./sigma_sq;
|
||||
beta_t = M_t'*(invSigmaSq_p - AA*inv(eye(K) + M_t'*M_t./sigma_sq)*AA'); % (Eq 16)
|
||||
|
||||
E_z(:, t) = beta_t*([Pc(t, :) Pc(t+T, :)]' - P_hat_t); % (Eq 17)
|
||||
E_zz((t-1)*K+1:t*K,:) = eye(K) - beta_t*M_t + E_z(:,t)*E_z(:,t)'; % (Eq 18)
|
||||
end
|
||||
|
||||
@@ -0,0 +1,46 @@
|
||||
function [E_z, E_zz, y, M, xt_n, Pt_n, Ptt1_n, xt_t1, Pt_t1] = sfm_lds_Estep(P, S_bar, V, RR, Tr, phi, mu0, sigma0, Q, sigma_sq)
|
||||
%[E_z, E_zz, y, M, xt_n, Pt_n, Ptt1_n, xt_t1, Pt_t1] = sfm_lds_Estep(P, S_bar, V, RR, Tr, phi, mu0, sigma0, Q, sigma_sq)
|
||||
|
||||
K = size(V,1)/3;
|
||||
[T, J] = size(P);
|
||||
T = T/2;
|
||||
|
||||
Pc = P - [Tr(:,1); Tr(:,2)]*ones(1,J);
|
||||
|
||||
M_t = zeros(2*J, K);
|
||||
P_hat_t = zeros(2*J, 1);
|
||||
|
||||
E_z = zeros(K, T);
|
||||
E_zz = zeros(T*K, K);
|
||||
|
||||
invSigmaSq_p = eye(2*J)./sigma_sq;
|
||||
|
||||
M = cell(1, T+1);
|
||||
M{1} = [];
|
||||
y = zeros(2*J, T+1);
|
||||
y(:,1) = 0;
|
||||
for t=1:T,
|
||||
Pt = [P(t,:) P(t+T,:)]';
|
||||
|
||||
Rt = [RR(t,:); RR(t+T,:)];
|
||||
|
||||
for kk = 1:K,
|
||||
M_t(1:J, kk) = (Rt(1,:)*V(1+(kk-1)*3:kk*3, :))';
|
||||
M_t(J+1:end, kk) = (Rt(2,:)*V(1+(kk-1)*3:kk*3, :))';
|
||||
end
|
||||
P_hat_t(1:J) = (Rt(1,:)*S_bar)';
|
||||
P_hat_t(J+1:end) = (Rt(2,:)*S_bar)';
|
||||
|
||||
y(:, t+1) = Pt - P_hat_t;
|
||||
|
||||
M{t+1} = M_t;
|
||||
end
|
||||
|
||||
maxIter = 20;
|
||||
[xt_n, Pt_n, Ptt1_n, xt_t1, Pt_t1] = kalmansmooth(y, M, maxIter, phi, mu0, sigma0, Q, sigma_sq, K, 2*J, T);
|
||||
|
||||
E_z = xt_n(:,2:end);
|
||||
for t=1:T,
|
||||
E_zz((t-1)*K+1:t*K,:) = Pt_n{t+1} + E_z(:,t)*E_z(:,t)';
|
||||
end
|
||||
|
||||
68
pkg/OpenFace/model_training/pdm_generation/nrsfm-em/findG.m
Normal file
68
pkg/OpenFace/model_training/pdm_generation/nrsfm-em/findG.m
Normal file
@@ -0,0 +1,68 @@
|
||||
function G = findG(Rhat)
|
||||
|
||||
[F,D] = size(Rhat); F = F/2;
|
||||
|
||||
% Build matrix Q such that Q * v = [1,...,1,0,...,0] where v is a six
|
||||
% element vector containg all six distinct elements of the Matrix C
|
||||
|
||||
%clear Q
|
||||
for f = 1:F,
|
||||
g = f + F;
|
||||
h = g + F;
|
||||
Q(f,:) = zt2(Rhat(f,:), Rhat(f,:));
|
||||
Q(g,:) = zt2(Rhat(g,:), Rhat(g,:));
|
||||
Q(h,:) = zt2(Rhat(f,:), Rhat(g,:));
|
||||
end
|
||||
|
||||
% Solve for v
|
||||
rhs = [ones(2*F,1); zeros(F,1)];
|
||||
v = Q \ rhs;
|
||||
|
||||
% C is a symmetric 3x3 matrix such that C = G * transpose(G)
|
||||
n = 1;
|
||||
for x = 1:D,
|
||||
for y = x:D,
|
||||
C(x,y) = v(n); C(y,x) = v(n);
|
||||
n = n+1;
|
||||
end;
|
||||
end;
|
||||
|
||||
e = eig(C);
|
||||
%disp(e)
|
||||
|
||||
if (any(e<= 0)),
|
||||
[uu,dd,vv] = svd(C);
|
||||
G = uu*sqrt(dd);
|
||||
cc = G*G';
|
||||
err = sum((cc(:)-C(:)).^2);
|
||||
%if err>0.03,
|
||||
if 0 & err>30,
|
||||
G = [];
|
||||
dbstack; keyboard
|
||||
end;
|
||||
else
|
||||
G = sqrtm(C);
|
||||
end
|
||||
|
||||
%neg = 0;
|
||||
%if e(1) <= 0, neg = 1; end
|
||||
%if e(2) <= 0, neg = 1; end
|
||||
%if e(3) <= 0, neg = 1; end
|
||||
%if neg == 1, G = [];
|
||||
%else G = sqrtm(C);
|
||||
%end
|
||||
|
||||
%-------------------------------------------------
|
||||
|
||||
function M = zt2(i,j)
|
||||
|
||||
D = length(i);
|
||||
M = [];
|
||||
for x = 1:D,
|
||||
for y = x:D,
|
||||
if x==y, M = [M, i(x)*j(y)];
|
||||
else, M = [M, i(x)*j(y)+i(y)*j(x)];
|
||||
end;
|
||||
end;
|
||||
end;
|
||||
|
||||
@@ -0,0 +1,33 @@
|
||||
function [V, Z] = init_SB(P, Tr, RR, S_bar, K)
|
||||
%[V, Z] = init_SB(P, Tr, RR, S_bar, K)
|
||||
|
||||
[T, J] = size(P);
|
||||
T = T/2;
|
||||
|
||||
V = zeros(3*K, J);
|
||||
Z = zeros(T, K);
|
||||
|
||||
W_tilda = P - RR*S_bar - [Tr(:,1); Tr(:,2)]*ones(1,J);
|
||||
for kk=1:K, % iterates over deformations
|
||||
V_kk = zeros(T, 3*J);
|
||||
for t=1:T,
|
||||
try
|
||||
V_kk_t = pinv(RR([t t+T], :))*W_tilda([t t+T], :);
|
||||
catch err
|
||||
fprintf('Wrong at %d\n', t);
|
||||
end
|
||||
V_kk(t,:) = V_kk_t(:)';
|
||||
end
|
||||
|
||||
[a,b,c] = svd(V_kk, 0);
|
||||
sqrtb = sqrt(b(1,1));
|
||||
|
||||
Z(:, kk) = a(:,1) * sqrtb;
|
||||
new_V_kk = sqrtb * c(:,1)';
|
||||
|
||||
V((kk-1)*3+1:kk*3, :) = reshape(new_V_kk, 3, J);
|
||||
|
||||
for t = 1:T,
|
||||
W_tilda([t t+T], :) = W_tilda([t t+T], :) - RR([t t+T], :)*(Z(t,kk)*V((kk-1)*3+1:kk*3, :));
|
||||
end
|
||||
end
|
||||
@@ -0,0 +1,41 @@
|
||||
function [phiIn, mu0In, sigma0In, QIn] = iit_lds(P, S_bar, V, RR, Tr, sigma_sq)
|
||||
|
||||
K = size(V,1)/3;
|
||||
[T, J] = size(P);
|
||||
T = T/2;
|
||||
|
||||
y = zeros(2*J, T);
|
||||
P_hat_t = zeros(2*J, 1);
|
||||
M_t = zeros(2*J, K);
|
||||
|
||||
for t=1:T,
|
||||
Pt = [P(t,:) P(t+T,:)]';
|
||||
|
||||
Rt = [RR(t,:); RR(t+T,:)];
|
||||
|
||||
P_hat_t(1:J,1) = (Rt(1,:)*S_bar)';
|
||||
P_hat_t(J+1:end,1) = (Rt(2,:)*S_bar)';
|
||||
|
||||
|
||||
for kk = 1:K,
|
||||
M_t(1:J, kk) = (Rt(1,:)*V(1+(kk-1)*3:kk*3, :))';
|
||||
M_t(J+1:end, kk) = (Rt(2,:)*V(1+(kk-1)*3:kk*3, :))';
|
||||
end
|
||||
M{t} = M_t;
|
||||
|
||||
y(:, t) = Pt - P_hat_t;
|
||||
end
|
||||
|
||||
A = eye(2*J)./sigma_sq;
|
||||
for t=1:T,
|
||||
temp1 = A*M{t};
|
||||
temp2 = A - temp1*inv(eye(K)+M{t}'*temp1)*temp1';
|
||||
temp1b(t,:) = y(:,t)'*temp2*M{t};
|
||||
end
|
||||
mu0In = mean(temp1b)';
|
||||
Q = cov(temp1b);
|
||||
QIn = Q;
|
||||
t1 = temp1b(1:T-1,:);
|
||||
t2 = temp1b(2:T,:);
|
||||
phiIn = inv(t1'*t1+Q)*t1'*t2;
|
||||
sigma0In = QIn;
|
||||
BIN
pkg/OpenFace/model_training/pdm_generation/nrsfm-em/jaws.mat
Normal file
BIN
pkg/OpenFace/model_training/pdm_generation/nrsfm-em/jaws.mat
Normal file
Binary file not shown.
@@ -0,0 +1,69 @@
|
||||
function [xt_n, Pt_n, Ptt1_n, xt_t1, Pt_t1] = kalmansmooth(y, M, maxIter, phi, mu0, sigma0, Q, sigma_sq, p, q, n)
|
||||
|
||||
% Adapted from code written by Hrishi Deshpande
|
||||
|
||||
% Based on eqn (A3)-(A12) of Appendix A in Shumway, R.H. & Stoffer, D.S. (1982),
|
||||
% "An approach to time series smoothing and forecasting using the EM algorithm", Journal of Time Series Analysis, 3, 253-264
|
||||
|
||||
%- - - - - - - - - - - - - - - -
|
||||
% Forward steps. Eqns (A3)-(A7).
|
||||
|
||||
xt_t1 = zeros(p, n+1); % t = 0, 1, ..., n
|
||||
Pt_t1 = cell (1, n+1); % t = 0, 1, ..., n
|
||||
K = cell (1, n+1); % t = 0, 1, ..., n
|
||||
xt_t = zeros(p, n+1); % t = 0, 1, ..., n
|
||||
Pt_t = cell (1, n+1); % t = 0, 1, ..., n
|
||||
|
||||
t = 0; tIdx = t+1;
|
||||
xt_t(:,tIdx) = mu0;
|
||||
Pt_t{tIdx} = sigma0;
|
||||
for t = 1:n
|
||||
tIdx = t+1;
|
||||
|
||||
xt_t1(:,tIdx) = phi*xt_t(:,tIdx-1); % (A3)
|
||||
Pt_t1{tIdx} = phi*Pt_t{tIdx-1}*phi' + Q; % (A4)
|
||||
if 1,
|
||||
K{tIdx} = Pt_t1{tIdx}*M{tIdx}' * inv(M{tIdx}*Pt_t1{tIdx}*M{tIdx}' + sigma_sq*eye(q)); % (A5)
|
||||
else
|
||||
% Using the Matrix Inversion Lemma
|
||||
% (see http://www-2.cs.cmu.edu/afs/cs.cmu.edu/user/zoubin/www/SALD/week5b.pdf)
|
||||
invR = eye(q)./sigma_sq; AA = inv(inv(Pt_t1{tIdx}) + M{tIdx}'*invR*M{tIdx}); BB = (invR - invR*M{tIdx}*AA*M{tIdx}'*invR);
|
||||
K{tIdx} = Pt_t1{tIdx}*M{tIdx}' * BB; % (A5)
|
||||
end
|
||||
xt_t(:,tIdx) = xt_t1(:,tIdx) + K{tIdx}*(y(:,tIdx) - M{tIdx}*xt_t1(:,tIdx)); % (A6)
|
||||
Pt_t{tIdx} = Pt_t1{tIdx} - K{tIdx}*M{tIdx}*Pt_t1{tIdx}; % (A7)
|
||||
end
|
||||
|
||||
|
||||
%- - - - - - - - - - - - - - - -
|
||||
% Backward steps. Eqns (A8)-(A10)
|
||||
|
||||
Jt = cell (1, n+1); % t = 0, 1, ..., n
|
||||
xt_n = zeros(p, n+1); % t = 0, 1, ..., n
|
||||
Pt_n = cell (1, n+1); % t = 0, 1, ..., n
|
||||
|
||||
t=n; tIdx = t+1;
|
||||
xt_n(:,tIdx) = xt_t(:,tIdx); % (A9)
|
||||
Pt_n{tIdx} = Pt_t{tIdx}; % (A10)
|
||||
|
||||
for t=n:-1:1
|
||||
tIdx = t+1;
|
||||
|
||||
Jt{tIdx-1} = Pt_t{tIdx-1}*phi'*inv(Pt_t1{tIdx}); % (A8)
|
||||
xt_n(:,tIdx-1) = xt_t(:,tIdx-1) + Jt{tIdx-1}*(xt_n(:,tIdx) - phi*xt_t(:,tIdx-1)); % (A9)
|
||||
Pt_n{tIdx-1} = Pt_t{tIdx-1} + Jt{tIdx-1} * (Pt_n{tIdx} - Pt_t1{tIdx}) * Jt{tIdx-1}'; % (A10)
|
||||
end
|
||||
|
||||
|
||||
%- - - - - - - - - - - - - - - -
|
||||
% Backward steps. Eqns (A11)-(A12)
|
||||
|
||||
Ptt1_n = cell(1, n+1); % t = 0, 1, ..., n
|
||||
|
||||
t = n; tIdx = t+1;
|
||||
Ptt1_n{tIdx} = (eye(p) - K{tIdx}*M{tIdx}) * phi * Pt_t{tIdx-1}; % (A12)
|
||||
for t=n:-1:2
|
||||
tIdx = t+1;
|
||||
Ptt1_n{tIdx-1} = Pt_t{tIdx-1}*Jt{tIdx-2}' + ...
|
||||
Jt{tIdx-1}*(Ptt1_n{tIdx} - phi*Pt_t{tIdx-1})*Jt{tIdx-2}'; % (A11)
|
||||
end
|
||||
Binary file not shown.
@@ -0,0 +1,37 @@
|
||||
function [phi, Q, sigma_sq, mu0, sigma0] = mstep_lds_update(y, M, xt_n, Pt_n, Ptt1_n)
|
||||
|
||||
% Adapted from code written by Hrishi Deshpande
|
||||
|
||||
% M-step as described in Shumway, R.H. & Stoffer, D.S. (1982), "An approach to time series smoothing and forecasting using the EM algorithm",
|
||||
% Journal of Time Series Analysis, 3, 253-264
|
||||
|
||||
q = size(y, 1);
|
||||
n = size(y, 2)-1;
|
||||
p = size(M{2}, 2);
|
||||
|
||||
%- - - - - - - - - -
|
||||
% Eqns (9)-(11)
|
||||
A = zeros(p); B = zeros(p); C = zeros(p);
|
||||
for t=1:n
|
||||
tIdx = t+1;
|
||||
A = A + Pt_n{tIdx-1} + xt_n(:,tIdx-1) * xt_n(:,tIdx-1)';
|
||||
B = B + Ptt1_n{tIdx} + xt_n(:,tIdx) * xt_n(:,tIdx-1)';
|
||||
C = C + Pt_n{tIdx} + xt_n(:,tIdx) * xt_n(:,tIdx)';
|
||||
end
|
||||
|
||||
%- - - - - - - - - -
|
||||
% Eqns (12)-(14)
|
||||
invA = inv(A);
|
||||
phi = B * invA;
|
||||
Q = (C - B*invA*B') / n;
|
||||
R = zeros(q);
|
||||
for t=1:n
|
||||
tIdx = t+1;
|
||||
R = R + (y(:,tIdx)-M{tIdx}*xt_n(:,tIdx)) * (y(:,tIdx)-M{tIdx}*xt_n(:,tIdx))' + ...
|
||||
M{tIdx}*Pt_n{tIdx}*M{tIdx}';
|
||||
end
|
||||
R = R / n;
|
||||
R = eye(q)*mean(diag(R));
|
||||
sigma_sq = R(1,1);
|
||||
mu0 = xt_n(:, 1); % (Eq 22, Ghahramani 1996)
|
||||
sigma0 = Pt_n{1}; % (Eq 24, Ghahramani 1996)
|
||||
@@ -0,0 +1,30 @@
|
||||
function P_hat = mstep_update_missingdata(P, MD, S_bar, V, E_z, RO, Tr)
|
||||
% P_hat = mstep_update_missingdata(P, MD, S_bar, V, E_z, RO, Tr)
|
||||
|
||||
% Fills in missing data using Eq 25
|
||||
|
||||
[K, T] = size(E_z);
|
||||
J = size(S_bar, 2);
|
||||
|
||||
ind = find(sum(MD')>0);
|
||||
|
||||
P_hat = P;
|
||||
for kk = 1:length(ind),
|
||||
|
||||
t = ind(kk);
|
||||
|
||||
missingpoints_t = find(MD(t, :));
|
||||
|
||||
for s=1:length(missingpoints_t),
|
||||
j = missingpoints_t(s);
|
||||
|
||||
H_j = [S_bar(:,j) reshape(V(:,j), 3, K)]; % H_j is 3x(K+1)
|
||||
|
||||
S_tj = H_j*[1; E_z(:,t)]; % S_tj is 3x1
|
||||
|
||||
newf_t = RO{t}(1:2,:) * S_tj + Tr(t,:)';
|
||||
|
||||
P_hat([t t+T], j) = newf_t;
|
||||
end
|
||||
end
|
||||
|
||||
@@ -0,0 +1,39 @@
|
||||
function sigma_sq = mstep_update_noisevar_md(P, S_bar, V, E_z, E_zz, RO, Tr)
|
||||
%sigma_sq = mstep_update_noisevar(P, S_bar, V, E_z, E_zz, RO, Tr)
|
||||
|
||||
% Updates noise variance (Eq 22)
|
||||
|
||||
[K, T] = size(E_z);
|
||||
J = size(S_bar, 2);
|
||||
|
||||
M_t = zeros(2*J, K);
|
||||
|
||||
sigma_sq = 0;
|
||||
for t = 1:T,
|
||||
R_t = RO{t};
|
||||
|
||||
Sdef = S_bar;
|
||||
for kk = 1:K,
|
||||
Sdef = Sdef + E_z(kk,t)*V((kk-1)*3+[1:3],:);
|
||||
|
||||
M_t(1:J, kk) = (R_t(1,:)*V((kk-1)*3+[1:3],:))';
|
||||
M_t(J+1:end, kk) = (R_t(2,:)*V((kk-1)*3+[1:3], :))';
|
||||
end;
|
||||
|
||||
f_bar_t = R_t(1:2,:)*S_bar;
|
||||
f_bar_t = [f_bar_t(1,:) f_bar_t(2,:)]';
|
||||
|
||||
f_t = [P(t, :) P(t+T, :)]';
|
||||
t_vect_t = [Tr(t,1)*ones(J,1); Tr(t,2)*ones(J,1)];
|
||||
|
||||
s1 = (f_t - f_bar_t - t_vect_t)'*(f_t - f_bar_t - t_vect_t);
|
||||
|
||||
s2 = 2*(f_t - f_bar_t - t_vect_t)'*M_t*E_z(:,t);
|
||||
|
||||
s3 = trace(M_t'*M_t*E_zz((t-1)*K+1:t*K,:));
|
||||
|
||||
sigma_sq = sigma_sq + (s1 - s2 + s3);
|
||||
end
|
||||
|
||||
sigma_sq = sigma_sq/(2*J*T);
|
||||
|
||||
@@ -0,0 +1,63 @@
|
||||
function [newRO, newRR] = mstep_update_rotation(P, S_bar, V, E_z, E_zz, RO, Tr)
|
||||
%[newRO, newRR] = mstep_update_rotation(P, S_bar, V, E_z, E_zz, RO, Tr)
|
||||
|
||||
% Linearizes the expression in Eq 24 using exponential maps and
|
||||
% solves for an improved rotation
|
||||
|
||||
% update step
|
||||
tw_step = 0.3;
|
||||
|
||||
[K, T] = size(E_z);
|
||||
J = size(S_bar, 2);
|
||||
|
||||
Pc = P - Tr(:)*ones(1,J);
|
||||
|
||||
newRR = zeros(2*T,3);
|
||||
newRO = RO;
|
||||
|
||||
for iter=1:1,
|
||||
for t = 1:T,
|
||||
A = zeros(3);
|
||||
B = zeros(2,3);
|
||||
|
||||
zz_hat_t = [1 E_z(:,t)'; E_z(:,t) E_zz((t-1)*K+1:t*K,:)];
|
||||
|
||||
for j=1:J,
|
||||
H_j = [S_bar(:,j) reshape(V(:,j), 3, K)];
|
||||
|
||||
A = A + H_j*zz_hat_t*H_j';
|
||||
|
||||
B = B + ([Pc(t,j); Pc(t+T,j)] * [1 E_z(:,t)'] * H_j');
|
||||
end
|
||||
|
||||
oldRO_t = RO{t};
|
||||
|
||||
C = oldRO_t*A;
|
||||
D = B - oldRO_t(1:2,:)*A;
|
||||
|
||||
% now we solve the system: [1 0 0; 0 1 0]*twist*C = D
|
||||
CC = [0 C(3,1) -C(2,1)
|
||||
-C(3,1) 0 C(1,1)
|
||||
0 C(3,2) -C(2,2)
|
||||
-C(3,2) 0 C(1,2)
|
||||
0 C(3,3) -C(2,3)
|
||||
-C(3,3) 0 C(1,3)];
|
||||
|
||||
DD = D(:);
|
||||
|
||||
% twist optimization
|
||||
twist_vect = tw_step*pinv(CC)*DD;
|
||||
|
||||
twh = [0 -twist_vect(3) twist_vect(2)
|
||||
twist_vect(3) 0 -twist_vect(1)
|
||||
-twist_vect(2) twist_vect(1) 0 ];
|
||||
dR = expm(twh);
|
||||
newRO_t = dR*oldRO_t;
|
||||
|
||||
newRO{t} = newRO_t;
|
||||
newRR(t,:) = newRO_t(1,:);
|
||||
newRR(t+T,:) = newRO_t(2,:);
|
||||
end
|
||||
|
||||
RO = newRO;
|
||||
end
|
||||
@@ -0,0 +1,23 @@
|
||||
function [newS_bar, newV] = mstep_update_shapebasis(P, E_z, E_zz, RR, Tr, S_bar, V)
|
||||
%[newS_bar, newV] = mstep_update_shapebasis(P, E_z, E_zz, RR, Tr, S_bar, V)
|
||||
|
||||
% Computes an improved version of S_bar and V (Eq 21)
|
||||
|
||||
% E_z is KxT, E_zz is a (F*K)xK matrix
|
||||
% V is (3*K)xJ and S_bar is 3xJ
|
||||
|
||||
K = size(E_z,1);
|
||||
[T, J] = size(P); T = T/2;
|
||||
|
||||
Uc = P(1:T, :) - Tr(:,1)*ones(1,J);
|
||||
Vc = P(T+1:2*T, :) - Tr(:,2)*ones(1,J);
|
||||
|
||||
vecH_hat = computeH(Uc, Vc, E_z, E_zz, RR);
|
||||
|
||||
H_hat = reshape(vecH_hat, 3*J, K+1);
|
||||
|
||||
newS_bar = reshape(H_hat(:,1), 3, J);
|
||||
newV = zeros(3*K, J);
|
||||
for kk=1:K,
|
||||
newV((kk-1)*3+[1:3],:) = reshape(H_hat(:,kk+1), 3, J);
|
||||
end
|
||||
@@ -0,0 +1,22 @@
|
||||
function Tr = mstep_update_transl(P, S_bar, V, E_z, RO)
|
||||
% Tr = mstep_update_transl(P, S_bar, V, E_z, RO)
|
||||
|
||||
% Updates translation using Eq 23
|
||||
|
||||
[K, T] = size(E_z);
|
||||
J = size(S_bar, 2);
|
||||
|
||||
Tr = zeros(T, 2);
|
||||
for t = 1:T,
|
||||
Sdef = S_bar;
|
||||
for kk = 1:K,
|
||||
Sdef = Sdef + E_z(kk,t)*V((kk-1)*3+[1:3],:);
|
||||
end;
|
||||
|
||||
R_t = RO{t};
|
||||
XY = R_t(1:2,:)*Sdef;
|
||||
|
||||
t_t = sum(P([t t+T], :) - XY, 2)./J;
|
||||
|
||||
Tr(t, :) = t_t';
|
||||
end
|
||||
@@ -0,0 +1,22 @@
|
||||
Copyright © 2003 Lorenzo Torresani, Aaron Hertzmann, Chris Bregler
|
||||
|
||||
This software was written by
|
||||
|
||||
Lorenzo Torresani
|
||||
Dept of Computer Science
|
||||
Stanford University
|
||||
ltorresa@cs.stanford.edu
|
||||
|
||||
This software is research code, meant for free non-commercial use
|
||||
and distribution. I cannot promise that it works and I cannot guarantee
|
||||
I will maintain it.
|
||||
|
||||
If you want to experiment with this code, please refer to this paper:
|
||||
|
||||
Lorenzo Torresani, Aaron Hertzmann and Christoph Bregler,
|
||||
Learning Non-Rigid 3D Shape from 2D Motion, NIPS 16, 2003
|
||||
http://cs.stanford.edu/~ltorresa/projects/learning-nr-shape/
|
||||
|
||||
If you find bugs, please send me an email at ltorresa@cs.stanford.edu.
|
||||
|
||||
Please email me if you get cool results or if you use this software for your research!
|
||||
@@ -0,0 +1,52 @@
|
||||
function [P3, S_bar, V, Z, RO, Tr] = random_nr_motion(T, J, K, state)
|
||||
% [P3, S_bar, V, Z, RO, Tr] = random_nr_motion(T, J, K, state)
|
||||
%
|
||||
% INPUT:
|
||||
%
|
||||
% T - number of frames
|
||||
% J - number of points
|
||||
% K - number of deformation basis
|
||||
%
|
||||
% OUTPUT:
|
||||
%
|
||||
% P3 - (3*T) x J 3D-motion matrix: P3([t t+T t+2*T],:) contains the 3D coordinates of the J points at time t
|
||||
% S_bar - shape average: 3 x J matrix
|
||||
% V - deformation shapes: (3*K) x J matrix ( V((n-1)*3+[1:3],:) contains the n-th deformation basis )
|
||||
% Z - deformation weights: T x K matrix
|
||||
% RO - rotation: cell array ( RO{t} gives the rotation matrix at time t )
|
||||
% Tr - translation: T x 2 matrix
|
||||
|
||||
rand('state', state);
|
||||
randn('state', state);
|
||||
|
||||
S_bar = rand(3, J);
|
||||
|
||||
[q,r] = qr(rand(3*J));
|
||||
|
||||
V = zeros(3*K, J);
|
||||
for kk=1:K,
|
||||
V(1+(kk-1)*3:3*kk, :) = reshape(q(:,kk), 3, J);
|
||||
end
|
||||
|
||||
Z = randn(T,K);
|
||||
Tr = randn(T,2);
|
||||
|
||||
a = (rand(T,1)-0.5)*2*pi;
|
||||
b = (rand(T,1)-0.5)*2*pi;
|
||||
c = (rand(T,1)-0.5)*2*pi;
|
||||
P3 = zeros(3*T, J);
|
||||
for t=1:T,
|
||||
R1 = [1 0 0; 0 cos(a(t)) -sin(a(t)); 0 sin(a(t)) cos(a(t))];
|
||||
R2 = [cos(b(t)) 0 sin(b(t)); 0 1 0; -sin(b(t)) 0 cos(b(t))];
|
||||
R3 = [cos(c(t)) -sin(c(t)) 0; sin(c(t)) cos(c(t)) 0; 0 0 1];
|
||||
|
||||
RO{t} = R1*R2*R3;
|
||||
|
||||
Sdef = S_bar;
|
||||
for kk = 1:K,
|
||||
Sdef = Sdef+Z(t,kk)*V((kk-1)*3+[1:3],:);
|
||||
end;
|
||||
Sdef = RO{t}*Sdef +[Tr(t,:)'; 0]*ones(1, J);
|
||||
|
||||
P3([t t+T t+2*T], :) = Sdef;
|
||||
end
|
||||
@@ -0,0 +1,83 @@
|
||||
% Random Shapes Demo
|
||||
%
|
||||
% Copyright (c) by Lorenzo Torresani, Stanford University
|
||||
%
|
||||
% A demo of Non-Rigid Structure From Motion on artificial random
|
||||
% shapes.
|
||||
%
|
||||
%
|
||||
% The 3D reconstruction technique is based on the following paper:
|
||||
%
|
||||
% Lorenzo Torresani, Aaron Hertzmann and Christoph Bregler,
|
||||
% Learning Non-Rigid 3D Shape from 2D Motion, NIPS 16, 2003
|
||||
% http://cs.stanford.edu/~ltorresa/projects/learning-nr-shape/
|
||||
%
|
||||
%
|
||||
% Function em_sfm implements the algorithm "EM-Gaussian" and "EM-LDS" described
|
||||
% in the paper
|
||||
%
|
||||
% I recommend that you try to compile the CMEX code for the function computeH:
|
||||
% type 'mex computeH.c' in the Matlab Command Window ('mex computeH.c -l matlb' under Unix)
|
||||
%
|
||||
|
||||
T = 100; % number of frames
|
||||
J = 60; % number of points
|
||||
K = 5; % number of deformation shapes
|
||||
|
||||
state = 1000; % random generator state
|
||||
|
||||
% generates a random sequence of non-rigid 3D motion according to
|
||||
% the deformation model described by Eq (2) and (3)
|
||||
[P3_gt, S_bar_gt, V_gt, Z_gt, RO_gt, Tr_gt] = random_nr_motion(T, J, K, state);
|
||||
|
||||
% 2D motion resulting from orthographic projection (Eq (1))
|
||||
p2_obs = P3_gt(1:2*T, :);
|
||||
|
||||
% removes 40% of the data
|
||||
missingdata_rate = 0.4;
|
||||
if missingdata_rate>0,
|
||||
rp = randperm(T*J);
|
||||
ind_md = rp(1:round(T*J*missingdata_rate));
|
||||
MD = zeros(T, J);
|
||||
MD(ind_md) = 1;
|
||||
[i_md, j_md] = ind2sub([T J], ind_md);
|
||||
p2_obs(sub2ind([2*T J], [i_md i_md+T], [j_md j_md])) = 0; % set to 0 the values corresponding to missing data
|
||||
else
|
||||
MD = zeros(T, J);
|
||||
end
|
||||
|
||||
% runs the non-rigid structure from motion algorithm with different number of deformation shapes
|
||||
max_em_iter = 50;
|
||||
use_lds = 0; % doesn't use LDS since the data was generated at random, w/o temporal smoothness
|
||||
tol = 0.001;
|
||||
k_values = [K-1:K+1];
|
||||
Zcoords_gt = P3_gt(2*T+1:3*T,:) - mean(P3_gt(2*T+1:3*T,:),2)*ones(1,J);
|
||||
Zdist = max(Zcoords_gt,[],2) - min(Zcoords_gt,[],2); % size of the 3D shape along the Z axis for each time frame
|
||||
ze = [];
|
||||
fprintf('3D reconstruction with %f missing data...\n', missingdata_rate*100);
|
||||
for kk=k_values,
|
||||
[P3, S_hat, V, RO, Tr, Z] = em_sfm(p2_obs, MD, kk, use_lds, tol, max_em_iter);
|
||||
|
||||
% Compares it with ground truth.
|
||||
% Note that there are still 2 ambiguities that cannot be resolved:
|
||||
% 1. depth direction (i.e. the shape could be "flipped" along the Z axis) -> we test both possibilities
|
||||
% 2. Z translation -> we subtract the mean of the Z coords to evaluate reconstruction results
|
||||
Zcoords_em = P3(2*T+1:3*T,:) - mean(P3(2*T+1:3*T,:),2)*ones(1,J);
|
||||
|
||||
Zerror1 = mean( mean(abs(Zcoords_em - Zcoords_gt), 2)./Zdist );
|
||||
Zerror2 = mean( mean(abs(-Zcoords_em - Zcoords_gt), 2)./Zdist );
|
||||
|
||||
avg_zerror = 100*min(Zerror1, Zerror2);
|
||||
|
||||
ze = [ze avg_zerror];
|
||||
|
||||
hold off;
|
||||
plot(k_values(1:length(ze)), ze, '-o');
|
||||
title(['3D reconstruction with ' num2str(missingdata_rate*100) '% missing data'], 'fontweight', 'bold');
|
||||
xlabel('K (number of deformation shapes)');
|
||||
ylabel('% Z error');
|
||||
grid on;
|
||||
drawnow;
|
||||
end
|
||||
|
||||
|
||||
@@ -0,0 +1,4 @@
|
||||
See randomshapes_demo.m and shark_demo.m for more information.
|
||||
|
||||
I recommend that you try to compile the CMEX code for the function computeH:
|
||||
type 'mex computeH.c' in the Matlab Command Window ('mex computeH.c -l matlb' under Unix)
|
||||
@@ -0,0 +1,39 @@
|
||||
function [R, Tr, S] = rigidfac(P, MD)
|
||||
% [R, Tr, S] = rigidfac(P, MD)
|
||||
%
|
||||
% Computes rank 3 factorization: P = R*S + Tr
|
||||
|
||||
Pnew = P;
|
||||
|
||||
[T, J] = size(Pnew); T = T/2;
|
||||
|
||||
|
||||
if sum(MD(:)) > 0, % if there is missing data, then it uses an iterative solution to get a rough initialization for the missing points
|
||||
[i,j] = find(MD==1);
|
||||
ind = sub2ind(size(P), [i; i+T], [j; j]);
|
||||
numIter = 10;
|
||||
else
|
||||
numIter = 1;
|
||||
ind = [];
|
||||
end
|
||||
|
||||
r = 3;
|
||||
for iter=1:numIter,
|
||||
Tr = Pnew*ones(J,1)/J;
|
||||
Pnew_c = Pnew - Tr*ones(1,J);
|
||||
|
||||
[a,b,c] = svd(Pnew_c,0);
|
||||
|
||||
smallb = b(1:r,1:r);
|
||||
sqrtb = sqrt(smallb);
|
||||
Rhat = a(:,1:r) * sqrtb;
|
||||
Shat = sqrtb * c(:,1:r)';
|
||||
|
||||
P_approx = Rhat*Shat + Tr*ones(1,J);
|
||||
|
||||
Pnew(ind) = P_approx(ind);
|
||||
end
|
||||
|
||||
G = findG(Rhat);
|
||||
R = Rhat*G;
|
||||
S = inv(G)*Shat;
|
||||
@@ -0,0 +1,60 @@
|
||||
% Shark Demo
|
||||
%
|
||||
% Copyright (c) by Lorenzo Torresani, Stanford University
|
||||
%
|
||||
% A demo of Non-Rigid Structure From Motion on artificial shark sequence
|
||||
%
|
||||
%
|
||||
% The 3D reconstruction technique is based on the following paper:
|
||||
%
|
||||
% Lorenzo Torresani, Aaron Hertzmann and Christoph Bregler,
|
||||
% Learning Non-Rigid 3D Shape from 2D Motion, NIPS 16, 2003
|
||||
% http://cs.stanford.edu/~ltorresa/projects/learning-nr-shape/
|
||||
%
|
||||
%
|
||||
% Function em_sfm implements the algorithms "EM-Gaussian" and "EM-LDS" described
|
||||
% in the paper
|
||||
%
|
||||
% I recommend that you try to compile the CMEX code for the function computeH:
|
||||
% type 'mex computeH.c' in the Matlab Command Window ('mex computeH.c -l matlb' under Unix)
|
||||
%
|
||||
|
||||
% loads the matrix P3_gt containing the ground thruth data: P3_gt([t t+T t+2*T],:) contains the 3D coordinates of the J points at time t
|
||||
% (T is the number of frames, J is the number of points)
|
||||
load('jaws.mat');
|
||||
[T, J] = size(P3_gt); T = T/3;
|
||||
|
||||
% 2D motion resulting from orthographic projection (Eq (1))
|
||||
p2_obs = P3_gt(1:2*T, :);
|
||||
|
||||
% runs the non-rigid structure from motion algorithm
|
||||
use_lds = 1;
|
||||
max_em_iter = 60;
|
||||
tol = 0.0001;
|
||||
K = 2; % number of deformation shapes
|
||||
Zcoords_gt = P3_gt(2*T+1:3*T,:) - mean(P3_gt(2*T+1:3*T,:),2)*ones(1,J);
|
||||
Zdist = max(Zcoords_gt,[],2) - min(Zcoords_gt,[],2); % size of the 3D shape along the Z axis for each time frame
|
||||
MD = zeros(T,J);
|
||||
|
||||
[P3, S_hat, V, RO, Tr, Z] = em_sfm(p2_obs, MD, K, use_lds, tol, max_em_iter);
|
||||
|
||||
%% Compares it with ground truth.
|
||||
% Note that there are still 2 unresolvable ambiguities:
|
||||
% 1. depth direction (i.e. the shape could be "flipped" along the Z axis) -> we test both possibilities
|
||||
% 2. Z translation -> we subtract the mean of the Z coords to evaluate reconstruction results
|
||||
Zcoords_em = P3(2*T+1:3*T,:) - mean(P3(2*T+1:3*T,:),2)*ones(1,J);
|
||||
|
||||
Zerror1 = mean( mean(abs(Zcoords_em - Zcoords_gt), 2)./Zdist );
|
||||
Zerror2 = mean( mean(abs(-Zcoords_em - Zcoords_gt), 2)./Zdist );
|
||||
|
||||
if Zerror2 < Zerror1,
|
||||
avg_zerror = 100*Zerror2;
|
||||
P3(2*T+1:3*T,:) = -(P3(2*T+1:3*T,:) - mean(P3(2*T+1:3*T,:),2)*ones(1,J));
|
||||
else
|
||||
avg_zerror = 100*Zerror1;
|
||||
P3(2*T+1:3*T,:) = P3(2*T+1:3*T,:) - mean(P3(2*T+1:3*T,:),2)*ones(1,J);
|
||||
end
|
||||
fprintf('Average reconstruction error in Z: %f%%\n', avg_zerror);
|
||||
|
||||
vis_reconstruction(P3_gt, P3);
|
||||
|
||||
@@ -0,0 +1,59 @@
|
||||
function vis_reconstruction(P3_gt, P3_rec)
|
||||
|
||||
[T, J] = size(P3_gt); T = T/3;
|
||||
|
||||
xmin = min(min(P3_gt(1:T,:)));
|
||||
xmax = max(max(P3_gt(1:T,:)));
|
||||
xmin = xmin - (xmax-xmin)*0.1;
|
||||
xmax = xmax + (xmax-xmin)*0.1;
|
||||
ymin = min(min(P3_gt(T+1:2*T,:)));
|
||||
ymax = max(max(P3_gt(T+1:2*T,:)));
|
||||
ymin = ymin - (ymax-ymin)*0.1;
|
||||
ymax = ymax + (ymax-ymin)*0.1;
|
||||
zmin = min(min(P3_gt(2*T+1:3*T,:)));
|
||||
zmax = max(max(P3_gt(2*T+1:3*T,:)));
|
||||
zmin = zmin - (zmax-zmin)*0.1;
|
||||
zmax = zmax + (zmax-zmin)*0.1;
|
||||
|
||||
figure(3);
|
||||
hold off;
|
||||
plot([xmin xmax], [ymin ymin], 'k-');
|
||||
hold on;
|
||||
axis equal;
|
||||
axis off;
|
||||
set(gcf, 'color', [1 1 1]);
|
||||
plot([xmin xmax], [ymax ymax], 'k-');
|
||||
plot([xmin xmin], [ymin ymax], 'k-');
|
||||
plot([xmax xmax], [ymin ymax], 'k-');
|
||||
delta = ymin-zmax-10;
|
||||
plot([xmin xmax], [zmin zmin]+delta, 'k-');
|
||||
plot([xmin xmax], [zmax zmax]+delta, 'k-');
|
||||
plot([xmin xmin], [zmin zmax]+delta, 'k-');
|
||||
plot([xmax xmax], [zmin zmax]+delta, 'k-');
|
||||
ht1=text((xmin+xmax)/2, ymax-10, 'Input 2D tracks', 'HorizontalAlignment', 'center', 'fontweight', 'bold', 'fontname', 'verdana');
|
||||
ht2=text((xmin+xmax)/2, zmax+delta-10, '3D shape', 'HorizontalAlignment', 'center', 'fontweight', 'bold', 'fontname', 'verdana');
|
||||
|
||||
|
||||
for t=1:T
|
||||
if t>1,
|
||||
delete(hs1);
|
||||
delete(hs2);
|
||||
delete(hs3);
|
||||
end
|
||||
hs1 = plot(P3_gt(t,:), P3_gt(t+T,:), 'g.');
|
||||
hs2 = plot(P3_gt(t,:), P3_gt(t+2*T,:)-mean(P3_gt(t+2*T,:))+delta, 'b.');
|
||||
hs3 = plot(P3_rec(t,:), P3_rec(t+2*T,:)-mean(P3_rec(t+2*T,:))+delta, 'ro');
|
||||
if t==1,
|
||||
hh=legend([hs2,hs3],'ground truth', 'reconstruction', 4);
|
||||
set(hh, 'fontname', 'verdana');
|
||||
end
|
||||
drawnow;
|
||||
|
||||
I = getframe;
|
||||
|
||||
if 0,
|
||||
str = sprintf('frame%04d', t);
|
||||
imwrite(I.cdata, [str '.jpg'], 'Quality', 100);
|
||||
end
|
||||
end
|
||||
|
||||
BIN
pkg/OpenFace/model_training/pdm_generation/tri_68.mat
Normal file
BIN
pkg/OpenFace/model_training/pdm_generation/tri_68.mat
Normal file
Binary file not shown.
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user