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open source pkg v1

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This commit is contained in:
Vijay Yadev
2020-08-04 19:12:31 -04:00
parent bef213dba9
commit c389fc2c47
3708 changed files with 1624220 additions and 1 deletions
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57
pkg/OpenFace/matlab_version/CCNF/CalcSigmaCCNFflat.m Normal file
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function [ SigmaInv] = CalcSigmaCCNFflat(alphas, betas, n, precalcQ2withoutBeta, precalc_eye, precalc_zeros)
%CALCSIGMAPRF Summary of this function goes here
% Detailed explanation goes here
% constructing the sigma
% A = zeros(n);
%
% for i=1:n
%
% A(i,i) = alphas' * mask(i,:)';
%
% end
% this is simplification of above code
% if(useIndicators)
% A = diag(mask * alphas);
% else
% A = sum(alphas) .* eye(n);
A = sum(alphas) .* precalc_eye;
% A = sum(alphas) * eye(n);
% not faster
% a = mtimesx(sum(alphas), eye(n), 'SPEED');
% a2 = mtimesx(sum(alphas), eye(n), 'SPEEDOMP');
% end
% calculating the B from the paper
% for i=1:n
% for j=1:n
%
% if(i == j)
% q2(i,j) = beta * (sum(S(i,:)) - S(i,i));
% else
% q2(i,j) = -beta * S(i,j);
% end
% end
% end
% the above code can be simplified by the following lines of code
% using the precalculated lower triangular elements of B without beta
Btmp = precalcQ2withoutBeta * betas;
% not faster
% Btmp = mtimesx(precalcQ2withoutBeta, betas, 'SPEED');
% Btmp = mtimesx(precalcQ2withoutBeta, betas, 'SPEEDOMP');
% now make it into a square symmetric matrix
% B = zeros(n,n);
B = precalc_zeros;
on = tril(true(n,n));
B(on) = Btmp;
B = B';
B(on) = Btmp;
SigmaInv = 2 * (A + B);
end

173
pkg/OpenFace/matlab_version/CCNF/CalculateSimilarities_sparsity.m Normal file
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function [ Similarities, PrecalcQ2s, PrecalcQ2sFlat, PrecalcYqDs ] = CalculateSimilarities_sparsity( n_sequences, x, similarityFNs, sparsityFNs, y, const)
%CALCULATESIMILARITIES Summary of this function goes here
% Detailed explanation goes here
K = numel(similarityFNs);
K2 = numel(sparsityFNs);
%calculate similarity measures for each of the sequences
Similarities = cell(n_sequences, 1);
PrecalcQ2s = cell(n_sequences,1);
PrecalcQ2sFlat = cell(n_sequences,1);
PrecalcYqDs = zeros(n_sequences, K + K2);
if(iscell(x))
for q = 1 : n_sequences
xq = x{q};
n = size(xq, 1);
Similarities{q} = zeros([n, n, K+K2]);
PrecalcQ2s{q} = cell(K+K2,1);
PrecalcQ2sFlat{q} = zeros((n*(n+1))/2,K+K2);
% go over all of the similarity metrics and construct the
% similarity matrices
if(nargin > 4)
yq = y{q};
end
for k=1:K
Similarities{q}(:,:,k) = similarityFNs{k}(xq);
S = Similarities{q}(:,:,k);
D = diag(sum(S));
% PrecalcQ2s{q}(:,:,k) = D - S;
PrecalcQ2s{q}{k} = D - S;
B = D - S;
% PrecalcQ2sFlat{q}{k} = PrecalcQ2s{q}{k}(logical(tril(ones(size(S)))));
PrecalcQ2sFlat{q}(:,k) = B(logical(tril(ones(size(S)))));
if(nargin > 4)
PrecalcYqDs(q,k) = -yq'*B*yq;
end
end
for k=1:K2
Similarities{q}(:,:,K+k) = sparsityFNs{k}(xq);
S = Similarities{q}(:,:,K+k);
D = diag(sum(S));
% PrecalcQ2s{q}(:,:,k) = D - S;
PrecalcQ2s{q}{K+k} = D + S;
B = D + S;
% PrecalcQ2sFlat{q}{k} = PrecalcQ2s{q}{k}(logical(tril(ones(size(S)))));
PrecalcQ2sFlat{q}(:,K+k) = B(logical(tril(ones(size(S)))));
if(nargin > 4)
PrecalcYqDs(q,K+k) = -yq'*B*yq;
end
end
end
elseif(~const)
sample_length = size(x,2)/n_sequences;
similarities = cell(K, 1);
sparsities = cell(K2, 1);
for q = 1 : n_sequences
beg_ind = (q-1)*sample_length + 1;
end_ind = q*sample_length;
% don't take the bias term
xq = x(2:end, beg_ind:end_ind);
Similarities{q} = zeros([sample_length, sample_length, K+K2]);
PrecalcQ2s{q} = cell(K+K2,1);
PrecalcQ2sFlat{q} = zeros((sample_length*(sample_length+1))/2,K+K2);
% go over all of the similarity metrics and construct the
% similarity matrices
if(nargin > 4)
yq = y(:,q);
end
for k=1:K
if(q==1)
similarities{k} = similarityFNs{k}(xq);
end
Similarities{q}(:,:,k) = similarities{k};
S = Similarities{q}(:,:,k);
D = diag(sum(S));
% PrecalcQ2s{q}(:,:,k) = D - S;
PrecalcQ2s{q}{k} = D - S;
B = D - S;
% PrecalcQ2sFlat{q}{k} = PrecalcQ2s{q}{k}(logical(tril(ones(size(S)))));
PrecalcQ2sFlat{q}(:,k) = B(logical(tril(ones(size(S)))));
if(nargin > 4)
PrecalcYqDs(q,k) = -yq'*B*yq;
end
end
for k=1:K2
% this is constant so don't need to recalc
if(q==1)
sparsities{k} = sparsityFNs{k}(xq);
end
Similarities{q}(:,:,K+k) = sparsities{k};
S = Similarities{q}(:,:,K+k);
D = diag(sum(S));
% PrecalcQ2s{q}(:,:,k) = D - S;
PrecalcQ2s{q}{K+k} = D + S;
B = D + S;
% PrecalcQ2sFlat{q}{k} = PrecalcQ2s{q}{k}(logical(tril(ones(size(S)))));
PrecalcQ2sFlat{q}(:,K+k) = B(logical(tril(ones(size(S)))));
if(nargin > 4)
PrecalcYqDs(q,K+k) = -yq'*B*yq;
end
end
end
else
sample_length = size(x,2)/n_sequences;
similarities = cell(K, 1);
sparsities = cell(K2, 1);
PrecalcQ2s = {cell(K+K2,1)};
PrecalcQ2sFlat = {zeros((sample_length*(sample_length+1))/2,K+K2)};
Similarities = {zeros([sample_length, sample_length, K+K2])};
beg_ind = 1;
end_ind = sample_length;
% don't take the bias term
xq = x(2:end, beg_ind:end_ind);
% go over all of the similarity metrics and construct the
% similarity matrices
for k=1:K
similarities{k} = similarityFNs{k}(xq');
Similarities{1}(:,:,k) = similarities{k};
S = Similarities{1}(:,:,k);
D = diag(sum(S));
PrecalcQ2s{1}{k} = D - S;
B = D - S;
% flatten the symmetric matrix to save space
PrecalcQ2sFlat{1}(:,k) = B(logical(tril(ones(size(S)))));
if(nargin > 4)
PrecalcYqDs(:,k) = diag(-y'*B*y);
end
end
for k=1:K2
% this is constant so don't need to recalc
sparsities{k} = sparsityFNs{k}(xq');
Similarities{1}(:,:,K+k) = sparsities{k};
S = Similarities{1}(:,:,K+k);
D = diag(sum(S));
% PrecalcQ2s{q}(:,:,k) = D - S;
PrecalcQ2s{1}{K+k} = D + S;
B = D + S;
% PrecalcQ2sFlat{q}{k} = PrecalcQ2s{q}{k}(logical(tril(ones(size(S)))));
PrecalcQ2sFlat{1}(:,K+k) = B(logical(tril(ones(size(S)))));
if(nargin > 4)
PrecalcYqDs(:,K+k) = diag(-y'*B*y);
end
end
end
end

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pkg/OpenFace/matlab_version/CCNF/similarity_neighbor_grid.m Normal file
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function [ SimilarityMatrix ] = similarity_neighbor_grid( x, side, types)
%SIMILARITYNEIGHBOR Summary of this function goes here
% Detailed explanation goes here
% this assumes that the patch is laid out with first column, then second
% column, ... final column (column major)
SimilarityMatrix = eye(side*side);
% types - 1 - horizontal, 2 - vertical, 3 - diagonal (bl-tr), 4 -
% diagonal (br - tl)
for t=1:numel(types)
if(types(t) == 1)
% for horizontal we want to link both neighbours
% (which are offset from the points by height)
i = 1:(side*side-side);
% create the neighboring links for i
SimilarityMatrix(sub2ind([side^2, side^2], i, i+side)) = 1;
SimilarityMatrix(sub2ind([side^2, side^2], i+side, i)) = 1;
% visualise
% vis = zeros(height, width)
% [i, j] = ind2sub([sz, sz], find(SimilarityMatrix(:)==1));
% i_2 = mod(i-1, width)+1;
% j_2 = floor((j-1)/height)+1;
% vis(sub2ind([width, height], i_2, j_2) = 1;
% imagesc(vis);
end
if(types(t) == 2)
% for vertical we want to link both neighbours except at edge
% cases which are mod(y_loc,side) = 0 as they are at the edges
i = 1:side*side;
i_to_rem = i(mod(i, side) == 0);
i_both = setdiff(i, i_to_rem);
% create the neighboring links for i
SimilarityMatrix(sub2ind([side^2, side^2], i_both+1, i_both)) = 1;
SimilarityMatrix(sub2ind([side^2, side^2], i_both, i_both+1)) = 1;
end
if(types(t) == 3)
% for diagonal to top right, and bottom left don't use right most column
i = 1:(side^2)-side;
i_to_rem = i(mod(i-1, side) == 0);
i_both = setdiff(i, i_to_rem);
% create the neighboring links for i
SimilarityMatrix(sub2ind([side^2, side^2], i_both+side-1, i_both)) = 1;
SimilarityMatrix(sub2ind([side^2, side^2], i_both, i_both+side-1)) = 1;
end
if(types(t) == 4)
% for diagonal to top left, and bottom right don't use right most column
i = 1:(side^2)-side;
i_to_rem = i(mod(i, side) == 0);
i_both = setdiff(i, i_to_rem);
% create the neighboring links for i
SimilarityMatrix(sub2ind([side^2, side^2], i_both+side+1, i_both)) = 1;
SimilarityMatrix(sub2ind([side^2, side^2], i_both, i_both+side+1)) = 1;
end
end
assert(isequal(SimilarityMatrix, SimilarityMatrix'));
end

77
pkg/OpenFace/matlab_version/CCNF/similarity_neighbor_grid_further.m Normal file
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function [ SimilarityMatrix ] = similarity_neighbor_grid_further( x, side, types, dist)
%SIMILARITYNEIGHBOR Summary of this function goes here
% Detailed explanation goes here
% this assumes that the patch is laid out with first column, then second
% column, ... final column (column major)
% dist = 2;
SimilarityMatrix = eye(side*side);
% types - 1 - horizontal, 2 - vertical, 3 - diagonal (bl-tr), 4 -
% diagonal (br - tl)
for t=1:numel(types)
if(types(t) == 1)
% for horizontal we want to link both neighbours
% (which are offset from the points by height)
i = 1:(side*side-side*dist);
% create the neighboring links for i
SimilarityMatrix(sub2ind([side^2, side^2], i, i+side*dist)) = 1;
SimilarityMatrix(sub2ind([side^2, side^2], i+side*dist, i)) = 1;
% visualise
% vis = zeros(height, width)
% [i, j] = ind2sub([sz, sz], find(SimilarityMatrix(:)==1));
% i_2 = mod(i-1, width)+1;
% j_2 = floor((j-1)/height)+1;
% vis(sub2ind([width, height], i_2, j_2) = 1;
% imagesc(vis);
end
if(types(t) == 2)
% for vertical we want to link both neighbours except at edge
% cases which are mod(y_loc,side) = 0 as they are at the edges
i = 1:side*side;
i_to_rem =[];
for s=1:dist
i_to_rem = union(i_to_rem, i(mod(i+s-1, side) == 0));
end
i_both = setdiff(i, i_to_rem);
% create the neighboring links for i
SimilarityMatrix(sub2ind([side^2, side^2], i_both+dist, i_both)) = 1;
SimilarityMatrix(sub2ind([side^2, side^2], i_both, i_both+dist)) = 1;
end
if(types(t) == 3)
% for diagonal to top right, and bottom left don't use right most column
i = 1:(side^2)-dist * side;
i_to_rem = [];
for s=1:dist
i_to_rem = union(i_to_rem,i(mod(i-s, side) == 0));
end
i_both = setdiff(i, i_to_rem);
% create the neighboring links for i
SimilarityMatrix(sub2ind([side^2, side^2], i_both+dist*side-dist, i_both)) = 1;
SimilarityMatrix(sub2ind([side^2, side^2], i_both, i_both+dist*side-dist)) = 1;
end
if(types(t) == 4)
% for diagonal to top left, and bottom right don't use right most column
i = 1:(side^2)-dist*side;
i_to_rem = [];
for s=1:dist
i_to_rem = union(i_to_rem, i(mod(i+s-1, side) == 0));
end
i_both = setdiff(i, i_to_rem);
% create the neighboring links for i
SimilarityMatrix(sub2ind([side^2, side^2], i_both+dist*side+dist, i_both)) = 1;
SimilarityMatrix(sub2ind([side^2, side^2], i_both, i_both+dist*side+ dist)) = 1;
end
end
assert(isequal(SimilarityMatrix, SimilarityMatrix'));
end

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pkg/OpenFace/matlab_version/CCNF/sparsity_grid.m Normal file
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function [ SparsityMatrix ] = sparsity_grid( x, side, width, width_end)
%SIMILARITYNEIGHBOR Summary of this function goes here
% Detailed explanation goes here
% this assumes that the patch is laid out with first column, then second
% column, ... final column (column major)
SimilarityMatrix = zeros(side*side);
for i=1:width
SimilarityMatrix = (similarity_neighbor_grid_further(x, side, [1,2,3,4], i) | SimilarityMatrix);
end
SimilarityMatrix_end = zeros(side*side);
for i=1:width_end
SimilarityMatrix_end = (similarity_neighbor_grid_further(x, side, [1,2,3,4], i) | SimilarityMatrix_end);
end
SparsityMatrix = double(SimilarityMatrix_end & (~SimilarityMatrix));
assert(isequal(SparsityMatrix, SparsityMatrix'));
end

50
pkg/OpenFace/matlab_version/OpenFace-license.txt Normal file
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OPENFACE
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9
pkg/OpenFace/matlab_version/PDM_helpers/AddOrthRow.m Normal file
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function [RotFull] = AddOrthRow(RotSmall)
% 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)
RotFull = zeros(3,3);
RotFull(1:2, :) = RotSmall;
RotFull(3,1) = RotSmall(1, 2) * RotSmall(2, 3) - RotSmall(1, 3) * RotSmall(2, 2);
RotFull(3,2) = RotSmall(1, 3) * RotSmall(2, 1) - RotSmall(1, 1) * RotSmall(2, 3);
RotFull(3,3) = RotSmall(1, 1) * RotSmall(2, 2) - RotSmall(1, 2) * RotSmall(2, 1);

22
pkg/OpenFace/matlab_version/PDM_helpers/AlignShapesKabsch.m Normal file
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function [ R, T ] = AlignShapesKabsch ( alignFrom, alignTo )
%ALIGN3DSHAPES Summary of this function goes here
% Detailed explanation goes here
dims = size(alignFrom, 2);
alignFromMean = alignFrom - repmat(mean(alignFrom), size(alignFrom,1),1);
alignToMean = alignTo - repmat(mean(alignTo), size(alignTo,1),1);
[U, ~, V] = svd( alignFromMean' * alignToMean);
% make sure no reflection is there
d = sign(det(V*U'));
corr = eye(dims);
corr(end,end) = d;
R = V*corr*U';
T = mean(alignTo) - (R * mean(alignFrom)')';
T = T';
end

30
pkg/OpenFace/matlab_version/PDM_helpers/AlignShapesWithScale.m Normal file
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function [ A, T, error, alignedShape ] = AlignShapesWithScale( alignFrom, alignTo )
%ALIGNSHAPESWITHSCALE Summary of this function goes here
% Detailed explanation goes here
numPoints = size(alignFrom,1);
meanFrom = mean(alignFrom);
meanTo = mean(alignTo);
alignFromMeanNormed = bsxfun(@minus, alignFrom, meanFrom);
alignToMeanNormed = bsxfun(@minus, alignTo, meanTo);
% scale now
sFrom = sqrt(sum(alignFromMeanNormed(:).^2)/numPoints);
sTo = sqrt(sum(alignToMeanNormed(:).^2)/numPoints);
s = sTo / sFrom;
alignFromMeanNormed = alignFromMeanNormed/sFrom;
alignToMeanNormed = alignToMeanNormed/sTo;
[R, t] = AlignShapesKabsch(alignFromMeanNormed, alignToMeanNormed);
A = s * R;
aligned = (A * alignFrom')';
T = mean(alignTo - aligned);
alignedShape = bsxfun(@plus, aligned, T);
error = sqrt(mean(sum((alignedShape - alignTo).^2,2)));
end

11
pkg/OpenFace/matlab_version/PDM_helpers/AxisAngle2Rot.m Normal file
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function [Rot] = AxisAngle2Rot(axisAngle)
theta = norm(axisAngle, 2);
nx = axisAngle / theta;
nx = [ 0 -nx(3) nx(2);
nx(3) 0 -nx(1);
-nx(2) nx(1) 0 ];
Rot = eye(3) + sin(theta) * nx + (1-cos(theta))*nx^2;

11
pkg/OpenFace/matlab_version/PDM_helpers/Euler2Rot.m Normal file
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function [Rot] = Euler2Rot(euler)
rx = euler(1);
ry = euler(2);
rz = euler(3);
Rx = [1 0 0; 0 cos(rx) -sin(rx); 0 sin(rx) cos(rx)];
Ry = [cos(ry) 0 sin(ry); 0 1 0; -sin(ry) 0 cos(ry)];
Rz = [cos(rz) -sin(rz) 0; sin(rz) cos(rz) 0; 0 0 1];
Rot = Rx * Ry * Rz;

7
pkg/OpenFace/matlab_version/PDM_helpers/GetShape3D.m Normal file
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function [shape3D] = GetShape3D(M, V, p)
shape3D = M + V * p;
shape3D = reshape(shape3D, numel(shape3D) / 3, 3);
end

20
pkg/OpenFace/matlab_version/PDM_helpers/GetShapeOrtho.m Normal file
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function [shape2D] = GetShapeOrtho(M, V, p, global_params)
% M - mean shape vector
% V - eigenvectors
% p - parameters of non-rigid shape
% V_exp
% p_exp
% global_params includes scale, euler rotation, translation,
% R - rotation matrix
% T - translation vector (tx, ty)
R = Euler2Rot(global_params(2:4));
T = [global_params(5:6); 0];
a = global_params(1);
shape3D = GetShape3D(M, V, p);
shape2D = bsxfun(@plus, a * R*shape3D', T);
shape2D = shape2D';
end

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pkg/OpenFace/matlab_version/PDM_helpers/ProcrustesAnalysis.m Normal file
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function [normX, normY, meanShape, Transform] = ProcrustesAnalysis(x, y, options)
% Translate all elements to origin and scale to 1
normX = zeros(size(x));
normY = zeros(size(y));
for i = 1:size(x,1)
offsetX = mean(x(i,:));
offsetY = mean(y(i,:));
Transform.offsetX(i) = offsetX;
Transform.offsetY(i) = offsetY;
normX(i,:) = x(i,:) - offsetX;
normY(i,:) = y(i,:) - offsetY;
% Get the Frobenius norm, to scale the shapes to unit size
scale = norm([normX(i,:) normY(i,:)], 'fro');
Transform.scale(i) = scale;
normX(i,:) = normX(i,:)/scale;
normY(i,:) = normY(i,:)/scale;
end
% Rotate elements untill all of them have the same orientation
% the initial estimate of rotation would be the first element
% if change is less than 1% stop (shouldn't take more than 2 steps)
change = 0.1;
meanShape = [ normX(1,:); normY(1,:) ]';
Transform.Rotation = zeros(size(x,1),1);
for i = 1:30
% align all of the shapes to the mean shape
% remember all orientations to get the mean one
orientations = zeros(size(normX,1),1);
for j = 1:size(x,1)
% do SVD of mean * X'
currentShape = [ normX(j,:); normY(j,:) ]';
[U, ~, V] = svd( meanShape' * currentShape);
rot = V*U';
if(asin(rot(2,1)) > 0)
orientations(j) = real(acos(rot(1,1)));
else
orientations(j) = real(-acos(rot(1,1)));
end
Transform.Rotation(j) = Transform.Rotation(j) + orientations(j);
currentShape = currentShape * rot;
normX(j,:) = currentShape(:,1)';
normY(j,:) = currentShape(:,2)';
end
% recalculate the mean shape;
oldMean = meanShape;
meanShape = [mean(normX); mean(normY)]';
% rotate the mean shape to mean rotation
meanOrientation = mean(orientations);
% Do this only the first time
if(i==1)
rotM = [ cos(-meanOrientation) -sin(-meanOrientation); sin(-meanOrientation) cos(-meanOrientation) ];
meanShape = meanShape * rotM;
end
% scale mean shape to unit
meanScale = norm(meanShape, 'fro');
meanShape = meanShape*(1/meanScale);
% find frobenious norm
diff = norm(oldMean - meanShape, 'fro');
if(diff/norm(oldMean,'fro') < change)
break;
end
end
% transform to tangent space to preserve linearities
% get the scaling factors for each shape
if(options.TangentSpaceTransform)
scaling = [ normX normY ] * [ meanShape(:,1)' meanShape(:,2)']';
for i=1:size(x,1)
normX(i,:) = normX(i,:) * (1 / scaling(i));
normY(i,:) = normY(i,:) * (1 / scaling(i));
end
end

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pkg/OpenFace/matlab_version/PDM_helpers/ProcrustesAnalysis3D.m Normal file
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function [ normX, normY, normZ, meanShape, Transform ] = ProcrustesAnalysis3D( x, y, z, tangentSpace, meanShape )
%PROCRUSTESANALYSIS3D Summary of this function goes here
% Detailed explanation goes here
meanProvided = false;
if(nargin > 4)
meanProvided = true;
end
% Translate all elements to origin
normX = zeros(size(x));
normY = zeros(size(y));
normZ = zeros(size(z));
for i = 1:size(x,1)
offsetX = mean(x(i,:));
offsetY = mean(y(i,:));
offsetZ = mean(z(i,:));
Transform.offsetX(i) = offsetX;
Transform.offsetY(i) = offsetY;
Transform.offsetZ(i) = offsetZ;
normX(i,:) = x(i,:) - offsetX;
normY(i,:) = y(i,:) - offsetY;
normZ(i,:) = z(i,:) - offsetZ;
end
% Rotate elements untill all of them have the same orientation
% the initial estimate of rotation would be the first element
% if change is less than 1% stop (shouldn't take more than 2 steps)
change = 0.1;
if(~meanProvided)
meanShape = [ mean(normX); mean(normY); mean(normZ) ]';
end
% scale all the shapes to mean shape
% Get the Frobenius norm, to scale the shapes to mean size (still want to
% retain mm)
meanScale = norm(meanShape, 'fro');
for i = 1:size(x,1)
scale = norm([normX(i,:) normY(i,:) normZ(i,:)], 'fro')/meanScale;
normX(i,:) = normX(i,:)/scale;
normY(i,:) = normY(i,:)/scale;
normZ(i,:) = normZ(i,:)/scale;
end
Transform.RotationX = zeros(size(x,1),1);
Transform.RotationY = zeros(size(x,1),1);
Transform.RotationZ = zeros(size(x,1),1);
for i = 1:30
% align all of the shapes to the mean shape
% remember all orientations to get the mean one (in euler angle form, pitch, yaw roll)
orientationsX = zeros(size(normX,1),1);
orientationsY = zeros(size(normX,1),1);
orientationsZ = zeros(size(normX,1),1);
for j = 1:size(x,1)
currentShape = [normX(j,:); normY(j,:); normZ(j,:)]';
% we want to align the current shape to the mean one
[ R, T ] = AlignShapesKabsch(currentShape, meanShape);
eulers = Rot2Euler(R);
orientationsX(j) = eulers(1);
orientationsY(j) = eulers(2);
orientationsZ(j) = eulers(3);
Transform.RotationX(j) = eulers(1);
Transform.RotationY(j) = eulers(2);
Transform.RotationZ(j) = eulers(3);
currentShape = R * currentShape';
normX(j,:) = currentShape(1,:);
normY(j,:) = currentShape(2,:);
normZ(j,:) = currentShape(3,:);
end
% recalculate the mean shape
% if(~meanProvided)
oldMean = meanShape;
meanShape = [mean(normX); mean(normY); mean(normZ)]';
meanScale = norm(meanShape, 'fro');
% end
for j = 1:size(x,1)
scale = norm([normX(j,:) normY(j,:) normZ(j,:)], 'fro')/meanScale;
normX(j,:) = normX(j,:)/scale;
normY(j,:) = normY(j,:)/scale;
normZ(j,:) = normZ(j,:)/scale;
end
if(i==1 && ~meanProvided)
% rotate the mean shape to mean rotation
meanOrientationX = mean(orientationsX);
meanOrientationY = mean(orientationsY);
meanOrientationZ = mean(orientationsZ);
R = Euler2Rot([meanOrientationX, meanOrientationY, meanOrientationZ]);
meanShape = (R * meanShape')';
end
% find frobenious norm
diff = norm(oldMean - meanShape, 'fro');
if(diff/norm(oldMean,'fro') < change)
break;
end
end
% transform to tangent space to preserve linearities
% get the scaling factors for each shape
if(tangentSpace)
[ normX, normY, normZ] = TangentSpaceTransform(normX, normY, normZ, meanShape);
end
end

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pkg/OpenFace/matlab_version/PDM_helpers/Rot2AxisAngle.m Normal file
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function [ axisAngle ] = Rot2AxisAngle( Rot )
%ROT2AXISANGLE Summary of this function goes here
% Detailed explanation goes here
theta = acos((trace(Rot) - 1) / 2);
vec = 1.0/(2*sin(theta));
vec = vec * [Rot(3,2) - Rot(2,3), Rot(1,3) - Rot(3,1), Rot(2,1) - Rot(1,2)];
axisAngle = vec * theta;
end

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pkg/OpenFace/matlab_version/PDM_helpers/Rot2Euler.m Normal file
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function [euler] = Rot2Euler(R)
q0 = sqrt( 1 + R(1,1) + R(2,2) + R(3,3) ) / 2;
q1 = (R(3,2) - R(2,3)) / (4*q0) ;
q2 = (R(1,3) - R(3,1)) / (4*q0) ;
q3 = (R(2,1) - R(1,2)) / (4*q0) ;
yaw = asin(2*(q0*q2 + q1*q3));
pitch= atan2(2*(q0*q1-q2*q3), q0*q0-q1*q1-q2*q2+q3*q3);
roll = atan2(2*(q0*q3-q1*q2), q0*q0+q1*q1-q2*q2-q3*q3);
euler = [pitch, yaw, roll];

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pkg/OpenFace/matlab_version/PDM_helpers/TangentSpaceTransform.m Normal file
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function [ transformedX, transformedY, transformedZ ] = TangentSpaceTransform( x, y, z, meanShape )
%TANGENTSPACETRANSFORM Summary of this function goes here
% Detailed explanation goes here
scaling = [ x y z] * [ meanShape(:,1)' meanShape(:,2)' meanShape(:,3)']';
for i=1:size(x,1)
x(i,:) = x(i,:) * (1 / scaling(i));
y(i,:) = y(i,:) * (1 / scaling(i));
z(i,:) = z(i,:) * (1 / scaling(i));
end
transformedX = x * mean(scaling);
transformedY = y * mean(scaling);
transformedZ = z * mean(scaling);
end

345
pkg/OpenFace/matlab_version/PDM_helpers/fit_PDM_ortho_proj_to_2D.m Normal file
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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)
%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;
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=1:1000
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]);
[params, p_global] = CalcReferenceUpdate(p_delta, params, p_global);
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 = OrthonormaliseRotation(R_delta);
% Combine rotations
R_final = R * R_delta;
% Extract euler angle
euler = 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

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pkg/OpenFace/matlab_version/PDM_helpers/fit_PDM_ortho_proj_to_2D_no_reg.m Normal file
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function [ a, R, T, T3D, params, error, shapeOrtho ] = fit_PDM_ortho_proj_to_2D_no_reg( M, E, V, shape2D)
%FITPDMTO2DSHAPE Summary of this function goes here
% Detailed explanation goes here
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;
R = eye(3);
T = [tx; ty];
params = zeros(size(E));
currShape = getShapeOrtho(M, V, params, R, T, a);
currError = getRMSerror(currShape, shape2D);
reg_rigid = zeros(6,1);
regFactor = 0.25;
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]);
% not to overshoot
p_delta = 0.5 * p_delta;
[params, p_global] = CalcReferenceUpdate(p_delta, params, p_global);
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
T3D = [0;0;0];
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 = OrthonormaliseRotation(R_delta);
% Combine rotations
R_final = R * R_delta;
% Extract euler angle
euler = 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

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pkg/OpenFace/matlab_version/PDM_helpers/iterate_piece_wise.m Normal file
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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

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pkg/OpenFace/matlab_version/PDM_helpers/writeMatrix.m Normal file
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% 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

37
pkg/OpenFace/matlab_version/PDM_helpers/writeMatrixBin.m Normal file
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% for easier readibility write them row by row
function writeMatrixBin(fileID, M, type)
% 4 bytes each for the description
fwrite(fileID, size(M,1), 'uint');
fwrite(fileID, size(M,2), 'uint');
fwrite(fileID, type, 'uint');
% Convert the matrix to OpenCV format (row minor as opposed to column
% minor)
M = M';
% type 0 - uint8, 1 - int8, 2 - uint16, 3 - int16, 4 - int, 5 -
% float32, 6 - float64
% Write out the matrix itself
switch type
case 0
type = 'uint8';
case 1
type = 'int8';
case 2
type = 'uint16';
case 3
type = 'int16';
case 4
type = 'int';
case 5
type = 'float32';
case 6
type = 'float64';
otherwise
type = 'float32';
end
fwrite(fileID, M, type);
end

32
pkg/OpenFace/matlab_version/copyright.txt Normal file
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Copyright (C) 2017, University of Southern California, University of Cambridge, and Carnegie Mellon University, all rights reserved
ACADEMIC OR NON-PROFIT ORGANIZATION NONCOMMERCIAL RESEARCH USE ONLY
THIS SOFTWARE IS PROVIDED "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
Notwithstanding the license granted herein, Licensee acknowledges that certain components of the Software may be covered by so-called “open source” software licenses (“Open Source Components”), which means any software licenses approved as open source licenses by the Open Source Initiative or any substantially similar licenses, including without limitation any license that, as a condition of distribution of the software licensed under such license, requires that the distributor make the software available in source code format. Carnegie Mellon shall provide a list of Open Source Components for a particular version of the Software upon Licensee’s request. Licensee will comply with the applicable terms of such licenses and to the extent required by the licenses covering Open Source Components, the terms of such licenses will apply in lieu of the terms of this Agreement. To the extent the terms of the licenses applicable to Open Source Components prohibit any of the restrictions in this License Agreement with respect to such Open Source Component, such restrictions will not apply to such Open Source Component. To the extent the terms of the licenses applicable to Open Source Components require Carnegie Mellon to make an offer to provide source code or related information in connection with the Software, such offer is hereby made. Any request for source code or related information should be directed to Tadas Baltrusaitis. Licensee acknowledges receipt of notices for the Open Source Components for the initial delivery of the Software.
// License can be found in OpenFace-license.txt
//
// * Any publications arising from the use of this software, including but
// not limited to academic journal and conference publications, technical
// reports and manuals, must cite at least one of the following works:
//
// OpenFace 2.0: Facial Behavior Analysis Toolkit
// Tadas Baltrušaitis, Amir Zadeh, Yao Chong Lim, and Louis-Philippe Morency
// in IEEE International Conference on Automatic Face and Gesture Recognition, 2018
//
// Convolutional experts constrained local model for facial landmark detection.
// A. Zadeh, T. Baltrušaitis, and Louis-Philippe Morency,
// in Computer Vision and Pattern Recognition Workshops, 2017.
//
// Rendering of Eyes for Eye-Shape Registration and Gaze Estimation
// Erroll Wood, Tadas Baltrušaitis, Xucong Zhang, Yusuke Sugano, Peter Robinson, and Andreas Bulling
// in IEEE International. Conference on Computer Vision (ICCV), 2015
//
// Cross-dataset learning and person-specific normalisation for automatic Action Unit detection
// Tadas Baltrušaitis, Marwa Mahmoud, and Peter Robinson
// in Facial Expression Recognition and Analysis Challenge,
// IEEE International Conference on Automatic Face and Gesture Recognition, 2015
//
///////////////////////////////////////////////////////////////////////////////

97
pkg/OpenFace/matlab_version/demo/face_image_demo.m Normal file
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clear
addpath('../PDM_helpers/');
addpath(genpath('../fitting/'));
addpath('../models/');
addpath(genpath('../face_detection'));
addpath('../CCNF/');
%% loading the patch experts
% Default OpenFace landmark model, using CE-CLM patch experts
[patches, pdm, clmParams, early_term_params] = Load_CECLM_general();
% faster but less accurate
%[patches, pdm, clmParams] = Load_CLNF_general();
% even faster but even less accurate
%[patches, pdm, clmParams] = Load_CLM_general();
% Using a multi-view approach
views = [0,0,0; 0,-30,0; 0,30,0; 0,0,30; 0,0,-30;];
views = views * pi/180;
% Dependencies for face detection (MatConvNet), remove if not present
setup_mconvnet;
addpath('../face_detection/mtcnn/');
%%
root_dir = '../../samples/';
images = dir([root_dir, '*.jpg']);
verbose = true;
for img=1:numel(images)
image_orig = imread([root_dir images(img).name]);
% Face detectiopn
[bboxs] = detect_faces(image_orig, 'mtcnn');
% If MTCNN detector not available, can use the cascaded regression one
% [bboxs] = detect_faces(image_orig, 'cascade');
if(size(image_orig,3) == 3)
image_gray = rgb2gray(image_orig);
else
image_gray = image_orig;
end
%%
if(verbose)
f = figure;
if(max(image_orig(:)) > 1)
imshow(double(image_orig)/255, 'Border', 'tight');
else
imshow(double(image_orig), 'Border', 'tight');
end
axis equal;
hold on;
end
for i=1:size(bboxs,1)
% Convert from the initial detected shape to CLM model parameters,
% if shape is available
bbox = bboxs(i,:);
if(exist('early_term_params', 'var'))
[shape,~,~,lhood,lmark_lhood,view_used] =...
Fitting_from_bb_multi_hyp(image_gray, [], bbox, pdm, patches, clmParams, views, early_term_params);
else
[shape,~,~,lhood,lmark_lhood,view_used] =...
Fitting_from_bb_multi_hyp(image_gray, [], bbox, pdm, patches, clmParams, views);
end
% shape correction for matlab format
shape = shape + 1;
if(verbose)
% valid points to draw (not to draw self-occluded ones)
v_points = logical(patches(1).visibilities(view_used,:));
try
plot(shape(v_points,1), shape(v_points',2),'.r','MarkerSize',20);
plot(shape(v_points,1), shape(v_points',2),'.b','MarkerSize',10);
catch warn
end
end
end
hold off;
end

93
pkg/OpenFace/matlab_version/demo/face_image_demo_eyes.m Normal file
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clear
addpath('../PDM_helpers/');
addpath(genpath('../fitting/'));
addpath('../models/');
addpath(genpath('../face_detection'));
addpath('../CCNF/');
%% loading the patch experts
% Default OpenFace landmark model, using CE-CLM patch experts
[patches, pdm, clmParams, early_term_params] = Load_CECLM_general();
% faster but less accurate
%[patches, pdm, clmParams] = Load_CLNF_general();
% even faster but even less accurate
%[patches, pdm, clmParams] = Load_CLM_general();
% Using a multi-view approach
views = [0,0,0; 0,-30,0; 0,30,0; 0,0,30; 0,0,-30;];
views = views * pi/180;
% Load the eye landmark models that will be used
[ clmParams_eye, pdm_right_eye, pdm_left_eye, ...
patches_left_eye, patches_right_eye,...
left_eye_inds_in_68, right_eye_inds_in_68,...
left_eye_inds_in_28, right_eye_inds_in_28] = Load_eye_models();
%%
% root_dir = 'C:\Users\Tadas\Dropbox\AAM\test data\gaze_original\p00/';
% images = dir([root_dir, '*.jpg']);
%root_dir = './sample_eye_imgs/';
%images = dir([root_dir, '/*.png']);
root_dir = '../../samples/';
images = dir([root_dir, '*.jpg']);
verbose = true;
for img=1:numel(images)
image_orig = imread([root_dir images(img).name]);
% Face detection
[bboxs] = detect_faces(image_orig, 'mtcnn');
% If MTCNN detector not available, can use the cascaded regression one
% [bboxs] = detect_faces(image_orig, 'cascade');
if(size(image_orig,3) == 3)
image_gray = rgb2gray(image_orig);
else
image_gray = image_orig;
end
%%
if(verbose)
f = figure;
if(max(image_orig(:)) > 1)
imshow(double(image_orig)/255, 'Border', 'tight');
else
imshow(double(image_orig), 'Border', 'tight');
end
axis equal;
hold on;
end
for i=1:size(bboxs,1)
% Convert from the initial detected shape to CLM model parameters,
% if shape is available
bbox = bboxs(i,:);
[shape,~,~,lhood,lmark_lhood,view_used] = Fitting_from_bb_multi_hyp(image_gray, [], bbox, pdm, patches, clmParams, views);
% Perform eye fitting now
[shape, shape_r_eye] = Fitting_from_bb_hierarch(image_gray, pdm, pdm_right_eye, patches_right_eye, clmParams_eye, shape, right_eye_inds_in_68, right_eye_inds_in_28);
[shape, shape_l_eye] = Fitting_from_bb_hierarch(image_gray, pdm, pdm_left_eye, patches_left_eye, clmParams_eye, shape, left_eye_inds_in_68, left_eye_inds_in_28);
% Convert it to matlab convention
shape_r_eye = shape_r_eye + 1;
shape_l_eye = shape_l_eye + 1;
plot(shape_l_eye(9:20,1), shape_l_eye(9:20,2), '.g', 'MarkerSize',7);
plot(shape_l_eye(1:8,1), shape_l_eye(1:8,2), '.b', 'MarkerSize',7);
plot(shape_r_eye(9:20,1), shape_r_eye(9:20,2), '.g', 'MarkerSize',7);
plot(shape_r_eye(1:8,1), shape_r_eye(1:8,2), '.b', 'MarkerSize',7);
end
hold off;
end

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pkg/OpenFace/matlab_version/demo/face_image_depth_demo.m Normal file
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clear
addpath('../PDM_helpers/');
addpath(genpath('../fitting/'));
addpath('../models/');
addpath(genpath('../face_detection'));
addpath('../CCNF/');
%% loading the patch experts
[clmParams, pdm] = Load_CLM_params_66();
% A CLM-Z model trained on Multi-PIE and BU-4DFE
[patches] = Load_Patch_Experts( '../models/clmz/', 'svr_patches_multi_pie_*.mat', '../models/clmz/', 'svr_depth_patches_*.mat', clmParams);
clmParams.multi_modal_types = patches(1).multi_modal_types;
%%
images = {'sample_depth_imgs/1.jpg', 'sample_depth_imgs/2.jpg', 'sample_depth_imgs/3.jpg', 'sample_depth_imgs/4.jpg', 'sample_depth_imgs/5.jpg'};
images_depth = {'sample_depth_imgs/1d.png', 'sample_depth_imgs/2d.png', 'sample_depth_imgs/3d.png', 'sample_depth_imgs/4d.png', 'sample_depth_imgs/5d.png'};
verbose = true;
for img=1:numel(images)
image_orig = imread(images{img});
image_depth = imread(images_depth{img});
% Need to convert from the disparity to depth values, and threshold
image_depth = 10000./(image_depth);
image_depth(image_depth > 300) = 0;
% First attempt to use the Matlab one (fastest but not as accurate, if not present use yu et al.)
[bboxs] = detect_faces(image_orig, {'cascade', 'zhu'});
if(size(image_orig,3) == 3)
image = rgb2gray(image_orig);
end
%%
if(verbose)
f = figure;
if(max(image(:)) > 1)
imshow(double(image_orig)/255, 'Border', 'tight');
else
imshow(double(image_orig), 'Border', 'tight');
end
axis equal;
hold on;
end
for i=1:size(bboxs,2)
% Convert from the initial detected shape to CLM model parameters
bbox = bboxs(:,i);
% Use the initial global and local params for clm fitting in the image
[shape,~,~,lhood,lmark_lhood,view_used] = Fitting_from_bb(image, image_depth, bbox, pdm, patches, clmParams);
% shape correction for matlab format
shape = shape + 1;
if(verbose)
% valid points to draw (not to draw self-occluded ones)
v_points = logical(patches(1).visibilities(view_used,:));
try
plot(shape(v_points,1), shape(v_points',2),'.r','MarkerSize',20);
plot(shape(v_points,1), shape(v_points',2),'.b','MarkerSize',10);
catch warn
end
end
end
hold off;
end

202
pkg/OpenFace/matlab_version/demo/face_video_demo.m Normal file
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clear
addpath('../PDM_helpers/');
addpath(genpath('../fitting/'));
addpath('../models/');
addpath(genpath('../face_detection'));
addpath('../CCNF/');
%%
vid_dir = '../../samples/';
vids = cat(1, dir([vid_dir, '*.avi']), dir([vid_dir, '*.wmv']));
%%
verbose = true;
record = true;
%% loading the patch experts
% Default OpenFace landmark model, using CE-CLM patch experts
[patches, pdm, clmParams, early_term_params] = Load_CECLM_general();
% faster but less accurate
%[patches, pdm, clmParams] = Load_CLNF_general();
% even faster but even less accurate
%[patches, pdm, clmParams] = Load_CLM_general();
% load the face validator and add its dependency
load('../face_validation/trained/faceCheckers.mat', 'faceCheckers');
addpath(genpath('../face_validation'));
od = cd('../face_validation/');
setup;
cd(od);
% Setup the face detector (remove the setup mconvnet if not using
% MatConvNet)
setup_mconvnet;
addpath('../face_detection/mtcnn/');
%%
for v=1:numel(vids)
% load the video
vr = VideoReader([vid_dir, vids(v).name]);
[~,fname,~] = fileparts(vids(v).name);
if(record)
if(~exist('./tracked_vids', 'file'))
mkdir('tracked_vids');
end
writerObj = VideoWriter(sprintf('./tracked_vids/%s.avi', fname));
open(writerObj);
end
det = false;
initialised = false;
nFrames = vr.NumberOfFrames;
% Read one frame at a time.
all_local_params = zeros(nFrames, numel(pdm.E));
all_global_params = zeros(nFrames,6);
for i = 1 : nFrames
% if this version throws a "Dot name reference on non-scalar structure"
% error change obj.NumberOfFrames to obj(1).NumberOfFrames (in two
% places in read function) or surround it with an empty try catch
% statement
image_orig = read(vr, i);
if((~det && mod(i,4) == 0) || ~initialised)
% Face detection
[bboxs] = detect_faces(image_orig, 'mtcnn');
% If MTCNN detector not available, can use the cascaded regression one
% [bboxs] = detect_faces(image_orig, 'cascade');
if(~isempty(bboxs))
% Pick the biggest face for tracking
[~,ind] = max(bboxs(:,3) - bboxs(:,1));
bbox = bboxs(ind,:);
% Discard overly small detections
if(bbox(3) - bbox(1) > 40)
% Either infer the local and global shape parameters
% from the detected landmarks or just using the
% bounding box
num_points = numel(pdm.M) / 3;
M = reshape(pdm.M, num_points, 3);
width_model = max(M(:,1)) - min(M(:,1));
height_model = max(M(:,2)) - min(M(:,2));
a = (((bbox(3) - bbox(1)) / width_model) + ((bbox(4) - bbox(2))/ height_model)) / 2;
tx = (bbox(3) + bbox(1))/2;
ty = (bbox(4) + bbox(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;
% visualisation
g_param_n = [a, 0, 0, 0, tx, ty]';
l_param_n = zeros(size(pdm.E));
% If tracking has not started trust the detection
if(~initialised)
g_param = g_param_n;
l_param = l_param_n;
det = true;
initialised = true;
else
% If tracking has already started double check the
% detection
shape_new = GetShapeOrtho(pdm.M, pdm.V, params, g_param_n);
dec = face_check_cnn(image, shape_new, g_param, faceCheckers);
if(dec < 0.5)
det = true;
g_param = g_param_n;
l_param = l_param_n;
else
det = false;
end
end
end
end
end
if(size(image_orig,3) == 3)
image = rgb2gray(image_orig);
else
image = image_orig;
end
d_image = [];
if(initialised)
[shape,g_param,l_param,lhood,lmark_lhood,view_used] = Fitting_from_bb(image, d_image, bbox, pdm, patches, clmParams, 'gparam', g_param, 'lparam', l_param);
all_local_params(i,:) = l_param;
all_global_params(i,:) = g_param;
dec = face_check_cnn(image, shape, g_param, faceCheckers);
if(dec < 0.5)
clmParams.window_size = [19,19; 17,17;];
clmParams.numPatchIters = 2;
det = true;
else
clmParams.window_size = [21,21; 19,19; 17,17;];
clmParams.numPatchIters = 3;
det = false;
end
end
if(verbose)
try
if(max(image_orig(:)) > 1)
imshow(double(image_orig)/255, 'Border', 'tight');
else
imshow(double(image_orig), 'Border', 'tight');
end
axis equal;
hold on;
if(initialised)
plot(shape(:,1), shape(:,2),'.r','MarkerSize',20);
plot(shape(:,1), shape(:,2),'.b','MarkerSize',10);
end
hold off;
drawnow expose;
pause(0.01);
if(record)
frame = getframe;
writeVideo(writerObj,frame);
end
catch warn
fprintf('%s', warn.message);
end
end
end
if(record)
close(writerObj);
end
close all;
experiments.local_params = all_local_params;
experiments.global_params = all_global_params;
end

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pkg/OpenFace/matlab_version/demo/setup_mconvnet.m Normal file
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function setup(varargin)
try
run D:\soft\matconvnet-master\matconvnet-master\matlab/vl_setupnn ;
addpath D:\soft\matconvnet-master\matconvnet-master\examples ;
opts.useGpu = false ;
opts.verbose = false ;
opts = vl_argparse(opts, varargin) ;
try
vl_nnconv(single(1),single(1),[]) ;
catch
warning('VL_NNCONV() does not seem to be compiled. Trying to compile it now.') ;
vl_compilenn('enableGpu', opts.useGpu, 'verbose', opts.verbose) ;
end
if opts.useGpu
try
vl_nnconv(gpuArray(single(1)),gpuArray(single(1)),[]) ;
catch
vl_compilenn('enableGpu', opts.useGpu, 'verbose', opts.verbose) ;
warning('GPU support does not seem to be compiled in MatConvNet. Trying to compile it now') ;
end
end
catch
fprintf('Could not setup MatConvNet, face detection will be slower, install the library and set the right location for it in setup_mconvnet.m\n');
end

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611.427551, 169.405777, 139.934357, 143.002686
597.747803, 170.652832, 142.568161, 144.064026
591.493286, 168.764069, 141.392029, 148.815384
587.829956, 172.080215, 141.274521, 147.066238
585.645935, 171.767395, 138.113724, 147.305756
576.570190, 162.877823, 145.016159, 155.517502
574.303345, 161.519363, 144.964691, 155.179031
575.342651, 173.268265, 135.329468, 137.861603
567.317749, 164.882797, 138.514191, 148.434616
555.128845, 165.218658, 142.956039, 151.123489
548.543335, 165.538361, 147.115982, 151.091888
548.695984, 162.272736, 140.393555, 147.741226
539.999817, 165.589859, 141.810822, 143.310760
534.897217, 164.702377, 140.027740, 141.293106
522.120361, 156.415085, 148.772232, 150.519394
524.142151, 156.964539, 141.861176, 149.615402
509.797272, 155.903839, 142.478546, 145.138107
505.582733, 155.779449, 142.547974, 148.568726
495.112518, 156.392853, 143.831985, 147.925323
485.452484, 151.438385, 147.727493, 149.950027
482.728882, 150.751205, 143.091995, 149.219971
473.837189, 153.620178, 142.500305, 148.657730
465.685394, 147.710632, 147.149338, 150.373840
461.350098, 147.729645, 146.493225, 153.788834
462.089722, 147.866257, 140.295517, 152.459885
463.929901, 145.834427, 138.935425, 152.069901
460.144257, 150.774933, 139.893188, 143.474854
452.185394, 151.040039, 145.720795, 147.369980
455.230408, 153.891815, 141.036514, 144.773880
450.566040, 151.399124, 142.886948, 146.546234
447.377075, 148.692047, 147.441788, 152.999924
449.446411, 147.333740, 141.760208, 151.339615
451.778564, 147.140518, 140.940140, 152.857697
449.847321, 147.605392, 140.210739, 149.239990
447.923523, 147.564804, 142.147507, 150.817474
451.850677, 156.355301, 135.599411, 144.253250
446.433441, 152.300476, 139.277115, 146.991638
440.085754, 145.413055, 144.012817, 151.149994
439.996735, 142.865967, 144.797562, 151.610397
438.609833, 143.314316, 145.229370, 152.793854
438.190186, 144.458679, 144.965118, 152.767273
442.658051, 156.574448, 139.285172, 140.276001
443.097504, 153.709885, 141.639725, 142.286545
443.246857, 150.768387, 140.892593, 149.176468
445.156494, 146.465698, 142.946609, 155.646667
445.156982, 147.113892, 142.129547, 156.867294
439.889069, 143.918655, 145.975220, 157.953278
442.245422, 142.599426, 140.361176, 150.698730
442.444122, 147.303162, 136.118408, 137.714539
448.172455, 146.251999, 138.871948, 150.619827
448.107391, 148.751724, 140.643875, 147.012421
454.269531, 145.583405, 141.279175, 149.890045
463.808044, 143.209778, 136.288483, 145.866867
463.736511, 143.020645, 142.957611, 146.397522
472.938446, 138.146759, 143.231812, 146.635345
474.717377, 137.092316, 141.740356, 147.427551
487.584717, 136.972900, 139.958313, 150.112793
496.932251, 135.994217, 138.237350, 149.719055
505.235840, 135.716415, 137.655670, 148.409866
512.708679, 140.414871, 137.100647, 147.717270
518.079102, 138.296753, 138.184479, 145.364838
524.192322, 151.022995, 140.231308, 136.041138
537.688721, 139.533875, 137.192261, 147.414764
542.746155, 137.970398, 139.318161, 145.822495
551.208679, 142.812180, 132.986130, 138.302505
557.734741, 143.530121, 136.203369, 146.694504
559.549927, 138.899063, 140.233521, 148.942978
566.269226, 139.378021, 139.950684, 149.555984
573.254883, 142.305481, 143.123001, 154.287506
577.604492, 148.294067, 136.392700, 145.949524
581.017151, 148.394516, 135.136292, 146.146149
581.264648, 149.166412, 137.171524, 148.151321
583.014038, 147.691711, 137.204285, 147.670227
584.541077, 146.935623, 137.944427, 147.754456
585.698853, 146.983978, 137.912918, 148.325317
584.131653, 146.411743, 140.990921, 151.263321
584.343567, 148.620819, 139.587631, 148.019379
582.229980, 150.542328, 137.798065, 145.942001
581.407349, 151.061340, 138.129410, 146.652786
579.286865, 153.834854, 140.044495, 146.591125
578.491821, 153.179260, 138.071518, 145.821838
570.068787, 153.856766, 143.440247, 144.001343
568.226563, 159.011841, 141.068237, 144.027451
570.086426, 165.281967, 139.475174, 141.692291
570.546448, 174.937897, 136.794556, 138.637939
566.238464, 178.696472, 138.543869, 138.962677
566.916504, 175.634094, 143.928284, 147.696213
570.375671, 177.471359, 143.050232, 147.980927
572.449219, 175.591232, 142.936310, 144.052002
580.013367, 173.893066, 140.217194, 145.382141
582.966125, 173.186279, 139.685928, 147.325363
582.643799, 175.531311, 137.722900, 147.259430
585.692749, 169.387833, 136.538055, 143.150742
580.985352, 165.304642, 139.870346, 147.309311
574.339111, 164.807846, 141.336258, 145.674637
567.032959, 170.987289, 147.792358, 145.996841
569.825378, 170.776398, 142.544479, 147.096939
563.164551, 180.178558, 143.847885, 140.503510
562.776733, 179.975861, 142.508560, 146.268021
559.510925, 187.198486, 143.472366, 140.583023
550.054382, 186.063721, 140.706253, 136.175934
545.378662, 187.454391, 143.570984, 139.346725
540.597473, 189.720108, 143.508163, 137.405899
528.301453, 191.015961, 148.627502, 140.011002
526.857849, 195.514893, 142.961334, 134.874313
519.004578, 197.525543, 145.435913, 134.977234
514.071777, 199.661102, 145.418777, 134.353958
509.649780, 204.860550, 149.929291, 140.336594
500.340363, 196.979294, 154.262375, 137.523438
499.208221, 197.775436, 154.535095, 139.651962
503.444733, 197.765320, 146.323807, 135.836456
502.876953, 197.440033, 145.623077, 135.867996
504.725861, 195.997620, 144.785431, 135.608810
506.837128, 194.159256, 143.627121, 134.820053
509.151489, 189.009476, 142.124847, 135.008865
508.945374, 176.958862, 150.943985, 142.532104
520.451111, 177.306076, 136.936829, 131.409515
519.302368, 171.502319, 140.195709, 138.030807
778.886292, 358.252991, 19.571171, 18.291252
748.817871, 334.276276, 32.136009, 31.412342
536.892151, 173.328629, 139.043579, 144.682953
751.499756, 335.415009, 30.534380, 27.874126
777.161499, 364.114380, 26.395163, 26.797106
779.681458, 363.315918, 24.582714, 25.175161
541.281921, 182.748672, 141.784744, 154.046921
538.002136, 186.609833, 146.656982, 156.526031
536.553955, 189.268585, 144.618027, 154.480087
533.361816, 189.010971, 147.255798, 158.210022
532.538879, 190.401474, 145.989426, 156.801285
541.210693, 187.293396, 140.128296, 153.972092
540.089172, 181.209564, 138.279114, 152.326019
536.200439, 183.544037, 138.486343, 147.494949
523.751221, 171.515961, 145.695557, 154.506836
520.329346, 162.682373, 142.775894, 148.297745
512.218140, 160.815872, 140.359970, 144.133469
502.735870, 157.765472, 144.175430, 146.237045
492.335388, 155.636551, 145.971252, 148.126343
480.095123, 155.606293, 150.713440, 150.294907
477.683746, 147.597595, 138.686081, 142.663879
468.964203, 143.879547, 137.430771, 137.273941
461.497650, 141.177155, 135.703278, 134.059769
456.325958, 145.673874, 138.765625, 137.652603
448.558197, 137.764618, 139.069183, 137.217819
444.235260, 138.451843, 143.618805, 142.018631
441.501007, 139.900116, 140.645203, 140.341537
432.946289, 136.414825, 138.027222, 136.016205
427.624146, 136.634140, 137.551682, 134.123581
422.156677, 140.834503, 135.237152, 130.977631
417.163818, 144.353180, 139.835037, 130.963913
406.862518, 147.441360, 154.209579, 141.547089
404.311493, 150.044220, 144.990112, 135.533936
408.075836, 154.341476, 139.667725, 135.926544
403.688477, 152.638229, 143.532196, 139.456711
403.943848, 152.118011, 142.682526, 137.992645
403.020874, 152.984497, 142.499023, 137.496368
408.416931, 156.264099, 142.186279, 138.476135
403.552368, 150.497955, 143.943008, 135.368042
406.400635, 153.927963, 146.256607, 142.565994
409.317627, 152.897675, 144.015808, 134.117844
413.397156, 153.120483, 143.490417, 136.688934
415.019012, 151.877838, 143.267319, 135.391037
417.346954, 150.932419, 144.243790, 137.074844
424.101166, 154.037521, 146.767929, 146.850571
431.278076, 145.394745, 144.470642, 142.795044
441.149414, 140.664185, 141.079224, 145.603622
447.325043, 137.850067, 139.600616, 142.435760
456.738647, 137.704163, 137.536987, 140.748184
463.091522, 143.212769, 136.141556, 143.216217
465.257751, 145.834885, 141.183792, 149.480881
466.599213, 149.000931, 143.329666, 150.119247
467.741425, 153.331787, 143.595840, 156.540909
473.271027, 155.200867, 140.375214, 152.459702
467.934174, 161.743240, 143.558884, 155.150665
461.292847, 171.644608, 152.070953, 157.334274
464.187439, 175.258499, 147.115982, 151.781296
461.985291, 176.699844, 148.897171, 154.667236
472.301025, 171.824524, 141.310425, 152.430389
469.150177, 175.627701, 142.244980, 152.563980
465.068420, 179.507050, 144.840942, 155.854919
464.720947, 183.424026, 140.585953, 147.777283
459.489685, 184.518616, 146.727448, 151.399048
456.038879, 183.941849, 146.103058, 152.966934
454.219666, 186.241379, 146.978790, 152.253571
456.448608, 187.871399, 142.536667, 150.533157
451.139587, 181.490814, 147.494278, 153.627380
450.098846, 184.494125, 145.761871, 151.435287
447.017059, 185.153259, 145.614502, 154.153168
443.222290, 188.183792, 144.959732, 152.587479
444.523163, 187.991348, 143.844421, 148.155884
441.826813, 186.274704, 144.869354, 149.928238
443.819702, 183.835846, 138.412888, 146.353424
438.145508, 189.796234, 145.472992, 147.736084
440.075317, 182.583511, 140.611145, 148.308182
440.700317, 180.041107, 139.553619, 149.103516
434.178070, 183.026382, 143.134567, 147.776932
436.369171, 183.909134, 137.952713, 144.603928
430.317047, 175.657776, 148.020065, 155.248489
436.126404, 171.779388, 146.942993, 154.934753
437.960205, 175.139267, 147.117172, 155.929321
443.753357, 171.106323, 145.225464, 157.136032
447.020233, 170.204681, 141.420532, 152.423630
451.259430, 168.125610, 142.089951, 154.409210
455.384613, 174.677521, 141.805817, 153.370361
462.430450, 167.222229, 141.732788, 155.066605
468.674316, 164.478973, 143.579865, 157.622818
475.610718, 166.666901, 145.493820, 159.847336
480.493439, 165.764542, 145.005539, 159.353561
484.805084, 167.086487, 143.004929, 157.048172
489.569092, 166.954712, 141.570892, 154.430435
496.161102, 161.654495, 142.647522, 154.418579
503.435577, 161.622955, 141.473297, 152.123642
504.770203, 158.761597, 142.948853, 153.109009
510.731720, 154.729919, 140.740189, 150.850662
510.486481, 149.430359, 146.327164, 153.865067
518.076355, 146.669067, 143.422150, 153.118149
526.524231, 142.856140, 141.392273, 148.540970
534.400452, 139.695099, 140.175308, 148.700012
544.333679, 141.473663, 142.477631, 149.197815
551.959229, 142.785980, 141.348236, 149.712952
563.795959, 142.711884, 136.878601, 146.947830
565.888123, 143.967194, 137.946060, 148.439880
572.763245, 142.624939, 144.808304, 154.133713
584.241699, 139.851486, 138.146484, 145.374786
592.878540, 141.765076, 135.700195, 138.099655
599.368164, 136.383163, 139.476425, 142.375610
605.757019, 145.497925, 140.085510, 137.097366
611.439026, 139.174683, 146.054504, 141.864288
621.527222, 142.625427, 134.844254, 141.601974
623.749451, 135.159653, 141.071945, 146.172501
626.122070, 137.349762, 140.071976, 145.511856
632.138062, 143.849716, 142.326660, 142.722260
634.859009, 147.425690, 135.456863, 139.222412
636.664124, 139.497620, 140.567520, 144.779205
638.835632, 142.092712, 141.382187, 143.054031
643.268066, 142.598862, 139.156860, 140.499390
650.086548, 144.734680, 135.579666, 139.723892
649.311829, 144.545746, 136.115219, 139.452637
653.477966, 156.337448, 137.581955, 140.558777
651.337830, 150.822739, 141.863754, 145.872971
653.287659, 151.744827, 138.047256, 140.313843
653.253174, 150.140427, 140.210709, 143.003784
654.446228, 154.432190, 140.776764, 137.930008
656.250244, 158.817520, 134.039719, 134.576080
653.755066, 157.834030, 130.014359, 133.930084
653.273682, 156.100677, 132.780853, 137.953705
647.732971, 154.024353, 136.381546, 140.067017
644.928345, 157.283371, 135.757599, 138.095230
640.906311, 165.885620, 141.048447, 139.818649
639.942078, 166.738358, 140.006760, 144.773468
638.775085, 166.963348, 140.316681, 143.744888
638.625610, 169.601074, 138.065155, 143.046539
640.344788, 168.940338, 135.770889, 139.702271
637.150635, 170.370132, 140.811539, 142.824463
638.793213, 169.372681, 138.108429, 142.008759
636.091309, 167.210266, 143.476776, 144.517410
635.418396, 168.997452, 143.166473, 143.551224
638.431335, 169.053635, 138.857956, 143.317459
640.987732, 165.125305, 135.395554, 138.939240
640.867310, 167.810242, 133.966003, 136.463486
636.109009, 165.043396, 138.794128, 139.278366
635.068909, 167.730469, 138.720535, 142.351364
635.349243, 164.236465, 141.323090, 143.656982
636.344971, 162.974487, 138.629440, 145.144638
634.275024, 160.084198, 141.437134, 145.709106
636.485901, 162.144150, 142.268066, 145.582382
638.031189, 156.882141, 137.557755, 148.308929
638.897583, 156.471954, 136.388733, 145.275085
638.295715, 155.473526, 139.067337, 145.389130
642.692627, 157.472534, 134.463120, 142.974731
642.460876, 156.770050, 142.013138, 140.480301
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153.789505, 164.184906, 268.025696, 272.426117
153.942123, 163.291931, 266.064117, 271.447449
148.995316, 159.290100, 272.252808, 274.595886
149.253998, 161.512909, 277.128723, 281.871674
134.378998, 158.088837, 284.888458, 288.109375
140.491638, 162.237488, 282.667175, 279.678864
144.242340, 161.300079, 271.258057, 276.959778
147.456039, 159.974426, 277.479218, 276.675598
146.599030, 156.647736, 278.516785, 280.595184
152.858368, 159.316025, 263.785828, 266.677795
156.245514, 158.330383, 267.443695, 271.749847
150.852325, 157.261353, 267.417664, 278.067169
150.057861, 151.494141, 278.414185, 286.241119
154.731796, 157.162491, 269.109344, 277.930267
155.397842, 158.833984, 268.884125, 273.308716
155.353058, 160.073792, 272.072937, 273.829010
156.462509, 160.198181, 273.335815, 273.974487
150.808884, 154.714432, 273.327332, 279.219360
144.707993, 149.984497, 283.355469, 283.664703
154.233551, 153.975952, 263.716644, 269.600861
152.638763, 154.380066, 266.026611, 273.629456
149.755829, 156.567871, 270.565308, 281.521851
147.860840, 161.038818, 267.775543, 274.915833
152.285629, 158.454041, 266.115326, 272.308105
154.399948, 158.787079, 263.894989, 268.692932
149.472610, 159.309174, 256.929077, 262.198883
147.260605, 158.548737, 257.176270, 264.812225
137.774811, 157.821503, 277.788147, 281.682251
136.247101, 158.847595, 276.108459, 280.639252
138.652512, 155.266205, 274.160522, 276.331665
151.104355, 158.000839, 259.922363, 266.828003
156.646500, 156.047226, 246.754868, 256.261322
149.733932, 147.682693, 262.532867, 266.728302
143.752243, 141.386780, 280.357544, 289.132019
150.097839, 144.615784, 265.152252, 272.988861
150.286896, 148.130066, 265.945770, 275.203583
140.652954, 150.008850, 281.546143, 289.096039
145.232925, 150.113632, 278.436279, 280.971893
144.150803, 143.968536, 278.746552, 286.325623
148.675812, 153.484131, 264.702759, 271.358337
149.215973, 154.383545, 267.505371, 271.842285
142.220825, 154.653107, 275.459808, 280.385712
149.189011, 156.500854, 267.367645, 274.020050
153.997849, 156.885132, 264.992126, 270.524719
152.156158, 155.799622, 265.068207, 273.984406
152.634033, 151.141632, 269.971039, 276.897614
141.440903, 149.036987, 287.571716, 287.373993
154.334488, 151.239136, 266.165619, 269.593292
153.941437, 149.138138, 266.957031, 273.891754
147.727646, 144.511444, 284.117462, 286.868225
156.280914, 144.794128, 278.606445, 286.078613
157.422348, 144.850616, 279.803070, 289.218170
159.559021, 147.225616, 276.223785, 289.010162
163.299484, 157.590775, 268.561279, 282.817596
168.305634, 162.613159, 257.436523, 277.365387
164.079666, 163.809479, 261.548248, 281.439880
165.948013, 164.095917, 276.093719, 292.308533
160.879745, 159.930511, 278.695923, 293.682281
157.819305, 162.216873, 276.275391, 282.553833
160.722885, 151.330109, 269.964813, 281.550293
152.681091, 150.771408, 276.266266, 287.531433
149.754410, 155.523209, 263.523407, 270.803223
148.765686, 155.601410, 263.689972, 272.454590
144.697617, 155.918335, 265.102051, 272.877319
143.040283, 156.252045, 264.406067, 272.231262
136.753510, 153.672394, 275.979340, 281.307861
140.377441, 155.158966, 273.435425, 280.428986
146.324799, 156.420441, 268.320587, 275.277863
149.219742, 164.095886, 256.943726, 265.823761
150.894394, 161.546173, 261.916962, 267.470154
150.730865, 158.819901, 261.233093, 266.167572
152.539505, 159.079422, 262.702728, 268.062866
159.089844, 159.181732, 264.078033, 269.903503
161.582428, 159.869522, 260.897308, 267.145294
162.815048, 163.134277, 253.908890, 263.741241
161.636230, 163.180664, 257.427979, 261.563568
158.078293, 161.480103, 255.840179, 262.184082
161.541061, 167.637421, 255.283279, 260.633331
166.059708, 167.571518, 252.427155, 258.010193
163.333588, 166.380356, 252.870209, 257.579926
162.891144, 166.929062, 253.797302, 257.980713
158.246155, 165.862549, 258.649048, 263.356537
155.254135, 163.177917, 263.527161, 266.973114
144.525452, 159.275238, 271.128143, 278.355835
143.880188, 159.409500, 266.981537, 273.503143
144.857925, 158.375366, 272.011749, 272.630493
142.655136, 156.009567, 276.161469, 278.311707
135.557541, 149.608322, 281.595123, 286.238098
144.775513, 152.624741, 282.461273, 285.753326
131.818466, 144.216034, 295.250214, 303.730804
140.719147, 150.107529, 286.477783, 289.975067
142.391266, 148.592972, 284.797974, 290.490143
141.906006, 146.792572, 286.878845, 292.127380
145.337555, 147.820053, 284.002289, 289.416718
149.186218, 150.645721, 280.942688, 284.738190
144.280304, 149.491440, 283.484467, 290.058563
147.707993, 152.307953, 277.817749, 284.347443
145.700760, 154.093353, 277.766754, 283.629639
148.215225, 157.116486, 271.264923, 276.801300
133.851273, 157.442535, 275.093079, 286.411621
135.523193, 158.733032, 274.136139, 289.790802
139.025177, 163.780365, 264.276306, 276.366394
134.983780, 153.906586, 269.835083, 278.912811
135.759949, 153.845856, 269.114563, 277.952972
136.430588, 157.561615, 269.625366, 279.561249
133.714340, 156.556229, 276.610413, 280.599670
140.730820, 153.511658, 263.920502, 265.013153
140.914185, 147.714798, 275.540314, 279.860596
140.635818, 146.764130, 275.146851, 280.856262
137.892181, 148.467621, 278.703003, 285.183167
153.522507, 157.334015, 262.033630, 267.273804
151.503281, 156.284866, 264.402161, 269.690155
151.754761, 156.921494, 264.888031, 270.489166
139.043137, 150.831787, 268.042145, 273.804535
138.702026, 158.148315, 270.280945, 278.183136
137.835098, 161.603149, 273.399292, 279.721252
131.603088, 157.474640, 272.620422, 275.758209
134.356094, 164.492844, 271.672699, 277.113800
135.456787, 165.048538, 270.361725, 277.063110
136.033218, 164.472931, 270.191742, 276.877960
136.679810, 164.217270, 270.368164, 277.470062
135.275848, 163.803696, 269.772034, 276.955902
134.936340, 163.583099, 267.940918, 276.590149
135.754959, 163.405487, 268.454590, 276.970154
134.744141, 163.476471, 268.299591, 276.177490
137.210632, 161.527435, 261.827118, 269.458466
147.493576, 166.323944, 266.999420, 271.613251
135.980392, 158.371887, 272.472015, 277.726685
138.747192, 155.223511, 259.506378, 262.917450
135.262390, 151.752289, 263.224701, 264.712891
134.019943, 153.383667, 262.332275, 264.286163
135.190964, 158.984619, 261.589233, 268.952118
128.681656, 153.885529, 274.718658, 280.374481
126.068680, 152.127838, 279.707489, 288.474213
149.244461, 160.485260, 263.145630, 266.683441
149.033798, 162.564575, 259.583923, 262.964722
130.298904, 155.847702, 279.386292, 289.344696
138.590714, 150.990295, 277.204956, 286.795441
146.270508, 149.623489, 272.003967, 285.537872
146.227203, 149.843063, 269.294952, 279.949066
148.568024, 149.384796, 265.219696, 272.536346
146.564270, 152.590393, 266.763031, 270.955292
147.212921, 154.194229, 267.392151, 271.364807
147.766632, 153.869003, 269.215607, 274.140625
134.895630, 152.295105, 273.051239, 277.409821
143.412201, 153.033569, 277.862549, 283.596893
143.228836, 153.440079, 275.127594, 286.855560
147.295059, 151.804352, 268.919373, 277.344177
147.828339, 153.721619, 265.509674, 269.385376
148.469604, 151.836670, 272.201324, 276.022400
149.437790, 152.609680, 270.581024, 276.008514
149.760193, 154.077393, 269.323395, 274.354401
151.272430, 152.120880, 265.322968, 273.667145
149.429626, 152.684402, 265.227661, 273.783112
151.826447, 154.025635, 262.960541, 272.651672
150.393204, 152.112717, 266.795288, 275.377991
155.594086, 158.035660, 263.610748, 270.334717
156.322754, 161.572067, 258.091278, 266.112122
149.180374, 160.112427, 260.904999, 269.197205
145.454269, 157.209290, 261.118103, 266.480133
144.644653, 157.547287, 263.208008, 269.265656
139.833069, 154.033661, 267.818329, 279.524078
152.599030, 160.085632, 262.534882, 267.050812
152.423355, 158.652878, 262.039001, 265.801239
152.190536, 155.074875, 261.176147, 262.991608
128.006668, 150.757690, 280.147278, 285.399200
123.533470, 148.787888, 280.333374, 286.646942
123.767342, 152.055359, 273.235138, 278.432434
120.753525, 150.153946, 276.350769, 279.082489
126.296051, 150.169296, 277.586090, 281.296539
131.918686, 150.390839, 287.626678, 287.057068
128.432434, 147.463898, 293.384583, 300.464996
149.656677, 152.318237, 274.889771, 280.176361
148.664185, 152.931549, 277.046295, 282.199310
146.350479, 155.823868, 278.052704, 282.649689
146.459183, 155.695618, 275.323761, 283.319489
147.177795, 156.349213, 273.985474, 282.099304
147.610428, 156.695862, 273.871399, 281.571106
148.017502, 157.247971, 273.189880, 280.316376
144.380905, 158.357971, 277.782257, 279.846497
145.863098, 159.928925, 276.610687, 277.874237
148.181808, 159.574127, 274.145081, 276.005371
149.069305, 159.531097, 273.516632, 275.579865
149.501404, 159.718201, 272.312042, 275.900604
148.572937, 159.207352, 274.328491, 277.849670
148.115677, 158.182251, 274.786133, 279.570679
148.929001, 158.298004, 274.009705, 276.510590
156.879303, 162.154785, 266.348083, 269.655457
154.892685, 160.054352, 268.718079, 271.375641
150.344635, 154.968460, 269.847412, 273.753479
146.813263, 154.218353, 270.018982, 277.427856
143.619370, 153.194275, 265.903107, 268.135040
146.421280, 154.769623, 268.144287, 267.484161
152.790680, 159.132019, 261.500000, 263.617706
131.680588, 154.051743, 283.372833, 287.447388
125.328209, 153.505051, 290.615204, 298.346405
136.354538, 158.985535, 278.294067, 285.070221
129.234726, 159.526047, 270.182251, 272.645386
126.741814, 153.920013, 277.177277, 281.080994
122.879105, 151.328644, 286.863983, 288.729950
121.392044, 146.163788, 290.690582, 296.945160
125.937233, 149.315002, 281.443146, 285.892609
115.446152, 148.162628, 285.701752, 290.580322
121.191429, 149.959076, 290.372681, 299.351135
129.776672, 149.307007, 288.684357, 295.172607
126.354271, 149.784073, 294.359772, 303.406006
126.392242, 151.422729, 291.179047, 299.642059
126.215248, 151.386093, 290.904694, 299.287903
129.600220, 157.518158, 276.980499, 283.249359
122.997261, 147.655029, 288.862000, 297.156830
128.100525, 152.521393, 283.432343, 297.244415
128.991898, 153.184784, 282.313202, 287.726624
129.595337, 154.386719, 282.138763, 284.634796
126.313446, 154.163101, 283.890594, 285.115692
128.826599, 153.262604, 283.586060, 290.470825
125.918434, 149.190094, 285.331757, 291.094940
136.918625, 151.961853, 265.885925, 274.855896
137.050018, 150.306244, 268.707306, 278.202850
143.104691, 154.433716, 270.561035, 283.162781
144.395981, 159.067078, 268.075470, 276.715057
145.787521, 156.997086, 270.328949, 277.232300
142.160049, 150.765259, 276.424866, 284.406494
146.806305, 156.491272, 269.416992, 279.646667
140.561020, 159.381363, 269.560364, 275.616486
141.313980, 159.261963, 267.011139, 275.372192
144.009705, 162.057037, 273.967712, 276.059113
142.917740, 159.994446, 271.233978, 273.747528
142.051468, 160.936340, 273.554199, 277.836700
144.346817, 161.909210, 270.859772, 277.650116
139.423553, 159.466034, 268.813965, 277.916229
137.165894, 157.230881, 271.956238, 281.435608
132.932007, 155.459930, 280.314301, 288.227661
127.324409, 152.681274, 288.710266, 296.604889
126.678688, 149.364319, 287.237854, 294.569946
135.953400, 153.130951, 271.767151, 278.822601
129.399704, 149.261520, 283.855835, 286.790253
127.523758, 149.963181, 286.079407, 285.349792
120.798065, 149.943314, 286.696533, 285.741821
115.234123, 148.333160, 274.313904, 277.548828
125.070412, 142.706833, 269.291168, 273.751953
127.844658, 136.755280, 262.310303, 265.613922
126.598305, 134.304810, 276.690735, 271.843048
124.186111, 132.295135, 265.028564, 267.940155
111.912872, 126.389290, 286.045074, 289.672180
122.089394, 136.946808, 277.014038, 285.151306
133.388779, 139.185623, 271.740204, 280.994293
126.145920, 135.539139, 273.018280, 280.155548
142.191345, 144.041351, 256.996796, 256.580872
145.362732, 148.700317, 256.742035, 258.235992
133.104736, 143.334167, 277.053711, 277.801758
132.369202, 142.730850, 273.960205, 278.472473
131.861389, 144.204742, 273.473907, 277.573578
133.826065, 146.602661, 280.906738, 286.304718
135.631851, 146.736145, 274.515381, 281.095917

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