2008 Poster Sessions : Intrinsic Symmetries of Shapes

Student Name : Maks Ovsjanikov
Advisor : Leo Guibas
Research Areas: Graphics/HCI
Abstract
Although considerable attention in recent years has been given to the problem of symmetry detection for general shapes, few methods have been developed that aim to capture intrinsic symmetry of a shape rather than its extrinsic, or pose-dependent symmetry. The former notion is more general and extends more naturally to higher dimensional manifolds, where extrinsic symmetry is difficult to detect using existing methods. In this paper, we present a novel method for efficiently computing intrinsic symmetries of a shape which are invariant up to isometry preserving transformations. Our method is both computationally efficient and robust with respect to small non-isometric deformations, which include local topological changes. By combining the strengths of spectral methods with those of recently developed Generalized Multidimensional Scaling we are able to provide a smooth mapping from a shape onto itself as well as to quantatively characterize the set of intrinsic symmetries that the object possesses. This information can then be used to detect global structure of the shape as well as to quantify deviation from perfect symmetry.

Bio
Maks is a PhD candidate in the department of ICME at Stanford University.