Point distribution model: Difference between revisions

Revision as of 12:07, 12 March 2008

Revision as of 11:37, 7 April 2008

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# 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.

An eigenvector, interpreted in euclidean space, can be seen as a sequence of n euclidean vectors associated to corresponding landmark and designating a compound move for the whole shape. Global nonlinear variation is usually well handled provided nonlinear variation is kept to a reasonable level. Typically, a twisting nematode worm opensis used as an example in the roadteaching toof [[kernel PCA]]-based methods.

Due to the PCA properties: eigenvectors are mutually orthogonal, form a basis of the training set cloud in the shape space, and cross at the 0 in this space, which represents the mean shape. Also, PCA is a traditional way of fitting a closed ellipsoid to a Gaussian cloud of points (whatever their dimension): this suggests the concept of bounded variation.