Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching

TL;DR

This paper introduces a deep learning method for shape matching that addresses symmetry ambiguities by learning orientation-aware features using complex functional maps and a vector field loss, improving robustness and stability.

Contribution

It proposes a novel unsupervised deep learning approach leveraging complex functional maps and a vector field loss to handle shape symmetries in non-rigid shape matching.

Findings

Improved shape matching accuracy on symmetric shapes

Robustness to discretization changes due to DiffusionNet backbone

Effective orientation preservation without extrinsic descriptors

Abstract

State-of-the-art fully intrinsic networks for non-rigid shape matching often struggle to disambiguate the symmetries of the shapes leading to unstable correspondence predictions. Meanwhile, recent advances in the functional map framework allow to enforce orientation preservation using a functional representation for tangent vector field transfer, through so-called complex functional maps. Using this representation, we propose a new deep learning approach to learn orientation-aware features in a fully unsupervised setting. Our architecture is built on top of DiffusionNet, making it robust to discretization changes. Additionally, we introduce a vector field-based loss, which promotes orientation preservation without using (often unstable) extrinsic descriptors.