Point distribution model: Difference between revisions

Revision as of 00:43, 9 January 2017

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==Discussion==

An eigenvector, interpreted in [[euclidean space]], can be seen as a sequence of <math>k</math> 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]] worm is used as an example in the teaching of [[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.