Nonlinear shape statistics via kernel spaces

Daniel Cremers, Timo Kohlberger, Christoph Schnörr

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

11 Scopus citations

Abstract

We present a novel approach for representing shape knowledge in terms of example views of 3D objects. Typically, such data sets exhibit a highly nonlinear structure with distinct clusters in the shape vector space, preventing the usual encoding by linear principal component analysis (PCA). For this reason, we propose a nonlinear Mercer-kernel PCA scheme which takes into account both the projection distanceand the within-subspace distance in a high-dimensional feature space. The comparison of our approach with supervised mixture models indicates that the statistics of example views of distinct 3D objects canfairly well be learned and represented in a completely unsupervised way.

Original languageEnglish
Title of host publicationPattern Recognition - 23rd DAGM Symposium, Proceedings
EditorsBernd Radig, Stefan Florczyk
PublisherSpringer Verlag
Pages269-276
Number of pages8
ISBN (Print)3540425969
DOIs
StatePublished - 2001
Externally publishedYes
Event23rd German Association for Pattern Recognition Symposium, DAGM 2001 - Munich, Germany
Duration: 12 Sep 200114 Sep 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2191
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd German Association for Pattern Recognition Symposium, DAGM 2001
Country/TerritoryGermany
CityMunich
Period12/09/0114/09/01

Keywords

  • Kernel PCA
  • Mercer kernels
  • Nonlinear density estimation
  • Nonlinear shape statistics
  • Shape learning
  • Variational methods

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