Nonlinear Shape Statistics in Mumford—Shah Based Segmentation

Applications of the nonlinear shape statistics in segmentation and tracking of 2D and 3D objects demonstrate that the segmentation process can incorporate knowledge on a large variety of complex real-world shapes.

Abstract

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. The idea is to assume that the training data forms a Gaussian distribution after a nonlinear mapping to a potentially higher-dimensional feature space. Due to the strong nonlinearity, the corresponding density estimate in the original space is highly non–Gaussian. It can capture essentially arbitrary data distributions (e.g. multiple clusters, ring- or banana–shaped manifolds). Applications of the nonlinear shape statistics in segmentation and tracking of 2D and 3D objects demonstrate that the segmentation process can incorporate knowledge on a large variety of complex real—world shapes. It makes the segmentation process robust against misleading information due to noise, clutter and occlusion.