Nonlinear Shape Statistics in Mumford-Shah Based Segmentation

We present a variational integration of nonlinear shape statistics into a Mumford-Shah based segmentation process. The non-linear 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.

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