open source pkg v1

pkg/OpenFace/matlab_version/PDM_helpers/ProcrustesAnalysis.m

@@ -0,0 +1,103 @@
+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
+