sustaining_gazes/matlab_version/pdm_generation/PDM_helpers/ProcrustesAnalysis.m

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2016-04-28 21:40:36 +02:00
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