Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning

• URL: http://arxiv.org/abs/2403.01781v1
• Date: Mon, 4 Mar 2024 07:21:07 GMT
• Title: Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning
• Authors: Tung Le, Khai Nguyen, Shanlin Sun, Nhat Ho, Xiaohui Xie
• Abstract summary: We present an unsupervised shape matching framework that integrates functional map regularizers with a novel OT-based loss derived from SWD. We also introduce an adaptive refinement process utilizing entropy regularized OT, further refining feature alignments for accurate point-to-point correspondences. Our method demonstrates superior performance in non-rigid shape matching, including near-isometric and non-isometric scenarios.
• Score: 43.6925865296259
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the realm of computer vision and graphics, accurately establishing correspondences between geometric 3D shapes is pivotal for applications like object tracking, registration, texture transfer, and statistical shape analysis. Moving beyond traditional hand-crafted and data-driven feature learning methods, we incorporate spectral methods with deep learning, focusing on functional maps (FMs) and optimal transport (OT). Traditional OT-based approaches, often reliant on entropy regularization OT in learning-based framework, face computational challenges due to their quadratic cost. Our key contribution is to employ the sliced Wasserstein distance (SWD) for OT, which is a valid fast optimal transport metric in an unsupervised shape matching framework. This unsupervised framework integrates functional map regularizers with a novel OT-based loss derived from SWD, enhancing feature alignment between shapes treated as discrete probability measures. We also introduce an adaptive refinement process utilizing entropy regularized OT, further refining feature alignments for accurate point-to-point correspondences. Our method demonstrates superior performance in non-rigid shape matching, including near-isometric and non-isometric scenarios, and excels in downstream tasks like segmentation transfer. The empirical results on diverse datasets highlight our framework's effectiveness and generalization capabilities, setting new standards in non-rigid shape matching with efficient OT metrics and an adaptive refinement module.

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