Nonlinear shape statistics via kernel spaces

Abstract

We present a novel approach for representing shape knowledge in terms of example views of 3D objects. Typically, such data sets exhibit a highly nonlinear structure with distinct clusters in the shape vector space, preventing the usual encoding by linear principal component analysis (PCA). For this reason, we propose a nonlinear Mercer-kernel PCA scheme which takes into account both the projection distanceand the within-subspace distance in a high-dimensional feature space. The comparison of our approach with supervised mixture models indicates that the statistics of example views of distinct 3D objects canfairly well be learned and represented in a completely unsupervised way.