Lie Bodies: A Manifold Representation of 3D Human Shape


Conference Paper


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.

Author(s): Oren Freifeld and Michael J. Black
Book Title: European Conf. on Computer Vision (ECCV)
Pages: 1--14
Year: 2012
Month: October

Series: Part I, LNCS 7572
Editors: {A. Fitzgibbon et al. (Eds.)}
Publisher: Springer-Verlag

Department(s): Perceiving Systems
Research Project(s): Learning on Manifolds
Lie Bodies
Bibtex Type: Conference Paper (inproceedings)
Paper Type: Conference

Links: pdf
supplemental material
eigenshape video


  title = {Lie Bodies: A Manifold Representation of {3D} Human Shape},
  author = {Freifeld, Oren and Black, Michael J.},
  booktitle = {European Conf. on Computer Vision (ECCV)},
  pages = {1--14},
  series = {Part I, LNCS 7572},
  editors = {{A. Fitzgibbon et al. (Eds.)}},
  publisher = {Springer-Verlag},
  month = oct,
  year = {2012},
  month_numeric = {10}