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Just fixing the reference to Principal Component Analysis |
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Point Distribution Models rely on [[Landmark point]]s. A landmark is an annotating point posed by an anatomist onto a given locus for every shape instance across the training set population. For instance, the same landmark will designate the tip of the index in a training set of 2D hands outlines. [[Principal Component Analysis]] (PCA), for instance, is a relevant tool for studying correlations of movement between groups of landmarks among the training set population. Typically, it might detect that all the landmarks located along the same finger move exactly together across the training set examples showing different finger spacing for a flat-posed hands collection.
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* '''2:''' align the clouds of landmark using the [[Generalized procrustes analysis]] (minimization of overall distance between landmarks of same label). The big idea is that shape information is not related to affine pose parameters, which need to be removed before any shape study. A mean shape can now be computed in averaging the aligned landmark positions.
* '''3:''' now the shape outlines are reduced to sequences of n landmarks, we can see the training set as a 2n or 3n (2D/3D) space where any shape instance is a single dot. Assuming the scattering is gaussian in this space, PCA
* '''4:''' PCA computes normalized eigenvectors and eigenvalues of the training set covariance matrix. Each eigenvector describe a principal mode of variation along the set, the corresponding eigenvalue indicating the importance of this mode in the shape space scattering. Since correlation was found between landmarks, the total variation of the space is concentrated on the very first eigenvectors, showing a very fast descent. Otherwise correlation was not found, suggesting the training set shows no variation or the landmarks are not properly posed.
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