Möbius transformations for global intrinsic symmetry analysis

Vladimir G. Kim, Yaron Lipman, Xiaobai Chen, Thomas Allen Funkhouser

Research output: Contribution to journalArticle

31 Scopus citations

Abstract

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 Möbius 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 Möbius transformations,and 3) selects among those candidate Möbius transformations the one(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 Möbius group for enumerating potential self-mappings. During experiments with a benchmark set of meshes augmented with human-specified symmetric correspondences, we find that the algorithm is able to find intrinsic symmetries for a wide variety of object types with moderate deviations from perfect symmetry.

Original languageEnglish (US)
Pages (from-to)1689-1700
Number of pages12
JournalEurographics Symposium on Geometry Processing
Volume29
Issue number5
StatePublished - Dec 28 2010

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Geometry and Topology

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    Kim, V. G., Lipman, Y., Chen, X., & Funkhouser, T. A. (2010). Möbius transformations for global intrinsic symmetry analysis. Eurographics Symposium on Geometry Processing, 29(5), 1689-1700.