Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matching

Abstract

Functional maps are the cornerstone of recent non-rigid 3D shape matching methods due to their efficiency and performance. However, existing methods struggle with challenging scenarios, such as partiality, topological noise, and raw point clouds. A primary bottleneck is that significant intrinsic distortion prevents truncated spectral bases from being accurately aligned via linear transformations (i.e., functional maps). To address this, we introduce a hyper-network that predicts non-linear neural functional maps (NFM), learned in an unsupervised manner, to better align spectral bases. Specifically, we model the NFM as an MLP with skip-connection to refine standard FM and employ a hyper-network to predict its weights, conditioned on standard FM. Our framework is trained using a novel unsupervised spectral alignment loss. Experiments demonstrate that our approach can be seamlessly integrated into state-of-the-art unsupervised deep functional map pipelines, substantially improving matching accuracy in demanding scenarios.