Shape statistics in kernel space for variational image segmentation

Daniel Cremers, Timo Kohlberger, Christoph Schnörr

Research output: Contribution to journalArticlepeer-review

195 Scopus citations


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 probabilistic framework. We assume that the training data forms a Gaussian distribution after a nonlinear mapping to a higher-dimensional feature space. Due to the strong nonlinearity, the corresponding density estimate in the original space is highly non-Gaussian. 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.

Original languageEnglish
Pages (from-to)1929-1943
Number of pages15
JournalPattern Recognition
Issue number9
StatePublished - Sep 2003
Externally publishedYes


  • Density estimation
  • Diffusion snakes
  • Image segmentation
  • Nonlinear shape statistics
  • Probabilistic kernel PCA
  • Variational methods


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