Nonlinear shape statistics in mumford–shah based segmentation

Daniel Cremers, Timo Kohlberger, Christoph Schnörr

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

57 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 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.

Original languageEnglish
Title of host publicationComputer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings
EditorsAnders Heyden, Gunnar Sparr, Mads Nielsen, Peter Johansen
PublisherSpringer Verlag
Number of pages16
ISBN (Print)9783540437444
StatePublished - 2003
Externally publishedYes
Event7th European Conference on Computer Vision, ECCV 2002 - Copenhagen, Denmark
Duration: 28 May 200231 May 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference7th European Conference on Computer Vision, ECCV 2002


  • Density estimation
  • Mercer kernels
  • Nonlinear statistics
  • Probabilistic kernel PCA
  • Segmentation
  • Shape learning
  • Variational methods


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