Lie bodies: A manifold representation of 3D human shape

Oren Freifeld, Michael J. Black

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

53 Scopus citations

Abstract

Three-dimensional object shape is commonly represented in terms of deformations of a triangular mesh from an exemplar shape. Existing models, however, are based on a Euclidean representation of shape deformations. In contrast, we argue that shape has a manifold structure: For example, summing the shape deformations for two people does not necessarily yield a deformation corresponding to a valid human shape, nor does the Euclidean difference of these two deformations provide a meaningful measure of shape dissimilarity. Consequently, we define a novel manifold for shape representation, with emphasis on body shapes, using a new Lie group of deformations. This has several advantages. First we define triangle deformations exactly, removing non-physical deformations and redundant degrees of freedom common to previous methods. Second, the Riemannian structure of Lie Bodies enables a more meaningful definition of body shape similarity by measuring distance between bodies on the manifold of body shape deformations. Third, the group structure allows the valid composition of deformations. This is important for models that factor body shape deformations into multiple causes or represent shape as a linear combination of basis shapes. Finally, body shape variation is modeled using statistics on manifolds. Instead of modeling Euclidean shape variation with Principal Component Analysis we capture shape variation on the manifold using Principal Geodesic Analysis. Our experiments show consistent visual and quantitative advantages of Lie Bodies over traditional Euclidean models of shape deformation and our representation can be easily incorporated into existing methods.

Original languageEnglish
Title of host publicationComputer Vision, ECCV 2012 - 12th European Conference on Computer Vision, Proceedings
Pages1-14
Number of pages14
EditionPART 1
DOIs
StatePublished - 30 Oct 2012
Externally publishedYes
Event12th European Conference on Computer Vision, ECCV 2012 - Florence, Italy
Duration: 7 Oct 201213 Oct 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume7572 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th European Conference on Computer Vision, ECCV 2012
Country/TerritoryItaly
CityFlorence
Period7/10/1213/10/12

Keywords

  • Lie group
  • Shape deformation
  • Statistics on manifolds

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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