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.
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Cremers, D., Kohlberger, T., Schnörr, C. (2002). Nonlinear Shape Statistics in Mumford—Shah Based Segmentation. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47967-8_7
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