Lie Bodies: A Manifold Representation of 3D Human Shape
7 October 2012
01:40
More info: http://ps.is.tue.mpg.de/project/Lie_Bodies Abstract: Three-dimensional object shape is commonly represented in terms of deformations of a triangular mesh from an exemplar shape. In particular, statistical generative models of human shape deformation are widely used in computer vision, graphics, ergonomics, and anthropometry. Existing models, however, are based on a Euclidean representation of shape deformations. In contrast, we argue that shape has a manifold structure: For example, averaging 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 ofLie 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. Similarly, interpolation between two mesh deformations results in a meaningful third deformation. 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. Paper: Lie Bodies: A Manifold Representation of 3D Human Shape Freifeld, O. and Black, M.J. In European Conf. on Computer Vision (ECCV), Springer-Verlag, Part I, LNCS 7572, pages 1-14, October 2012. http://files.is.tue.mpg.de/black/papers/FreifeldECCV2012.pdf