Deep Shells: Unsupervised Shape Correspondence with Optimal Transport

TL;DR

This paper introduces an unsupervised deep learning method for 3D shape correspondence that leverages optimal transport and spectral features to improve accuracy and generalization without requiring initial pose guesses.

Contribution

It presents a fully differentiable, hierarchical matching pipeline based on entropy regularized optimal transport, replacing costly preprocessing steps in shape correspondence.

Findings

Outperforms state-of-the-art methods on multiple datasets

Achieves better results than recent supervised approaches

Demonstrates strong generalization to unseen shape variations

Abstract

We propose a novel unsupervised learning approach to 3D shape correspondence that builds a multiscale matching pipeline into a deep neural network. This approach is based on smooth shells, the current state-of-the-art axiomatic correspondence method, which requires an a priori stochastic search over the space of initial poses. Our goal is to replace this costly preprocessing step by directly learning good initializations from the input surfaces. To that end, we systematically derive a fully differentiable, hierarchical matching pipeline from entropy regularized optimal transport. This allows us to combine it with a local feature extractor based on smooth, truncated spectral convolution filters. Finally, we show that the proposed unsupervised method significantly improves over the state-of-the-art on multiple datasets, even in comparison to the most recent supervised methods. Moreover, we demonstrate compelling generalization results by applying our learned filters to examples that significantly deviate from the training set.