Denoising Functional Maps: Diffusion Models for Shape Correspondence

• URL: http://arxiv.org/abs/2503.01845v2
• Date: Wed, 02 Apr 2025 14:01:32 GMT
• Title: Denoising Functional Maps: Diffusion Models for Shape Correspondence
• Authors: Aleksei Zhuravlev, Zorah Lähner, Vladislav Golyanik,
• Abstract summary: We propose a fundamentally new approach to shape correspondence based on denoising diffusion models.<n>We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned.<n>Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals.
• Score: 25.50153593846352
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these limitations, we propose a fundamentally new approach to shape correspondence based on denoising diffusion models. In our method, a diffusion model learns to directly predict the functional map, a low-dimensional representation of a point-wise map between shapes. We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned. First, the maps refer to a template rather than shape pairs. Second, the functional map is defined in a basis of eigenvectors of the Laplacian, which is not unique due to sign ambiguity. Therefore, we introduce an unsupervised approach to select a specific basis by correcting the signs of eigenvectors based on surface features. Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals compared to existing descriptor-based and large-scale shape deformation methods. See our project page for the source code and the datasets.

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