We present a variational integration of nonlinear shape statistics into a Mumford-Shah based segmentation process. The nonlinear statistics are derived from a set of training silhouettes by a novel method of density estimation which can be considered as an extension of kernel PCA to a stochastic framework.

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 distance and 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 can fairly well be learned and represented in a completely unsupervised way.

Biological vision is characterized by an intricate interplay of external sensory input and previously acquired internal representations of the world. In this work, we present a computer vision model for image segmentation which allows to combine external visual input and internally represented shape knowledge in a unifying energy functional. We explain how prior shape information is acquired. Numerical examples show how the relative weight of prior information affects the outcome of segmentation. A method to include translation invariance claries the way in which shape knowledge is acquired. The behavior of our method in a real-world scenario is demonstrated.

We present a variational integration of nonlinear shape statistics into a Mumford{Shah based segmentation process. The nonlinear statistics are derived from a set of training silhouettes by a novel method of density estimation which can be considered as an extension of kernel PCA to a stochastic framework.