Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching
This work addresses symmetry issues in shape matching for computer graphics and geometry processing, offering a more robust method for applications like 3D modeling and animation.
The paper tackles the problem of symmetry ambiguity in non-rigid shape matching by proposing a deep learning approach that learns orientation-aware features in an unsupervised setting, resulting in improved correspondence predictions without relying on unstable extrinsic descriptors.
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.