Möbius Transformations for Global Intrinsic Symmetry Analysis

Symposium on Geometry Processing

Publication date: July 28, 2010

Vladimir Kim, Yaron Lipman, Xiaobai Chen, Thomas Funkhouser

The goal of our work is to develop an algorithm for automatic and robust detection of global intrinsic symmetries in 3D surface meshes. Our approach is based on two core observations. First, symmetry invariant point sets can be detected robustly using critical points of the Average Geodesic Distance (AGD) function. Second, intrinsic symmetries are self-isometries of surfaces and as such are contained in the low dimensional group of Mobius transformations. Based on these observations, we propose an algorithm that: 1) generates a set of symmetric points by detecting critical points of the AGD function, 2) enumerates small subsets of those feature points to generate candidate Mobius transformations,and 3) selects among those candidate Mobius transformation(s) that best map the surface onto itself. The main advantages of this algorithm stem from the stability of the AGD in predicting potential symmetric point features and the low dimensionality of the Mobius group for enumerating potential self-mappings. During experiments with a wide variety of meshes augmented with human-specified symmetric correspondences, we find that the algorithm is able to find intrinsic symmetries in large collection of shape classes and under

Learn More