A Fourier-theoretic approach for inferring symmetries

Authors:
Xiaoye Jiang;Jian Sun;Leonidas Guibas
Affiliations:
Institute for Computational and Mathematical Engineering, Stanford University, USA;Mathematical Sciences Center, Tsinghua University, China;Computer Science Department, Stanford University, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2014

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Abstract

In this paper, we propose a novel Fourier-theoretic approach for estimating the symmetry group G of a geometric object X. Our approach takes as input a geometric similarity matrix between low-order combinations of features of X and then searches within the tree of all feature permutations to detect the sparse subset that defines the symmetry group G of X. Using the Fourier-theoretic approach, we construct an efficient marginal-based search strategy, which can recover the symmetry group G effectively. The framework introduced in this paper can be used to discover symmetries of more abstract geometric spaces and is robust to deformation noise. Experimental results show that our approach can fully determine the symmetries of various geometric objects.