Unsupervised Learning of Robust Spectral Shape Matching

TL;DR

This paper introduces an unsupervised deep learning method for robust 3D shape matching that directly predicts accurate point-wise correspondences without post-processing, outperforming previous methods across diverse datasets.

Contribution

It presents a novel unsupervised loss coupling functional maps and point-wise maps, enabling direct point-wise correspondence prediction for various challenging shape matching scenarios.

Findings

Outperforms previous state-of-the-art methods on nine datasets.

Effective for near-isometric, non-isometric, partial, and noisy shapes.

Achieves high accuracy without supervised training or post-processing.

Abstract

We propose a novel learning-based approach for robust 3D shape matching. Our method builds upon deep functional maps and can be trained in a fully unsupervised manner. Previous deep functional map methods mainly focus on predicting optimised functional maps alone, and then rely on off-the-shelf post-processing to obtain accurate point-wise maps during inference. However, this two-stage procedure for obtaining point-wise maps often yields sub-optimal performance. In contrast, building upon recent insights about the relation between functional maps and point-wise maps, we propose a novel unsupervised loss to couple the functional maps and point-wise maps, and thereby directly obtain point-wise maps without any post-processing. Our approach obtains accurate correspondences not only for near-isometric shapes, but also for more challenging non-isometric shapes and partial shapes, as well as shapes with different discretisation or topological noise. Using a total of nine diverse datasets, we extensively evaluate the performance and demonstrate that our method substantially outperforms previous state-of-the-art methods, even compared to recent supervised methods. Our code is available at https://github.com/dongliangcao/Unsupervised-Learning-of-Robust-Spectral-Shape-Matching.