A probabilistic framework for partial intrinsic symmetries in geometric data

In this paper, we present a novel algorithm for partial intrinsic symmetry detection in 3D geometry. Unlike previous work, our algorithm is based on a conceptually simple and straightforward probabilistic formulation of partial shape matching: based on a Markov random field model, we obtain a probability distribution over all possible intrinsic matches of a shape to itself, which reveals the symmetry structure of the object. Rather than examining this exponentially sized distribution directly, which is infeasible, we approximate marginals of this distribution using sum-product loopy belief propagation and show how the symmetry information can subsequently be extracted from this condensed representation. Using a parallel implementation on graphics hardware, we are able to extract symmetries of deformable shapes in general poses efficiently. We apply our algorithm on several standard 3D models, demonstrating that a concise probabilistic model yields a practical and general symmetry detection algorithm.