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

2026-06-29

AI Summary

Existing unsupervised methods for non-rigid 3D shape matching struggle with spectral basis alignment under challenging conditions such as partial occlusions, topological noise, and raw point clouds, leading to limited performance. This work proposes a novel unsupervised hypernetwork architecture that, for the first time, integrates hypernetworks with neural functional maps (NFM). By dynamically generating the weights of a multi-layer perceptron equipped with skip connections, the approach enables nonlinear refinement of the canonical functional map, thereby achieving robust spectral alignment. The method overcomes the inherent limitations of traditional linear functional mappings and significantly improves matching accuracy in complex scenarios. Moreover, it seamlessly integrates into existing unsupervised deep functional map pipelines without requiring architectural modifications.

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.

Problem

• 3D shape matching
• functional maps
• spectral bases
• intrinsic distortion
• unsupervised learning

Innovation

• hyper-network
• neural functional maps
• unsupervised 3D shape matching
• spectral alignment
• non-linear functional mapping