A Probabilistic Framework for Partial Intrinsic Symmetries in Geometric Data

Abstract

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 sumproduct 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. 1.