Learning-based Real-time Detection of Intrinsic Reflectional Symmetry

Abstract

Reflectional symmetry is ubiquitous in nature. While extrinsic reflectional symmetry can be easily parametrized and detected, intrinsic symmetry is much harder due to the high solution space. Previous works usually solve this problem by voting or sampling, which suffer from high computational cost and randomness. In this paper, we propose a learning-based approach to intrinsic reflectional symmetry detection. Instead of directly finding symmetric point pairs, we parametrize this self-isometry using a functional map matrix, which can be easily computed given the signs of Laplacian eigenfunctions under the symmetric mapping. Therefore, we train a novel deep neural network to predict the sign of each eigenfunction under symmetry, which in addition takes the first few eigenfunctions as intrinsic features to characterize the mesh while avoiding coping with the connectivity explicitly. Our network aims at learning the global property of functions, and consequently converts the problem defined on the manifold to the functional domain. By disentangling the prediction of the matrix into separated basis, our method generalizes well to new shapes and is invariant under perturbation of eigenfunctions. Through extensive experiments, we demonstrate the robustness of our method in challenging cases, including different topology and incomplete shapes with holes. By avoiding random sampling, our learning-based algorithm is over 100 times faster than state-of-the-art methods, and meanwhile, is more robust, achieving higher correspondence accuracy in commonly used metrics.