Denoising Functional Maps: Diffusion Models for Shape Correspondence

2025-03-03

AI Summary

This work addresses the limited generalization capability and reliance on category-specific training data in point-to-point correspondence estimation between non-rigid shapes. We propose the first functional map learning framework based on denoising diffusion models. Methodologically, we directly model the low-dimensional functional map from template to target, bypassing explicit point-wise correspondence prediction. To mitigate the basis ambiguity inherent in spectral representations, we introduce a novel unsupervised, feature-driven sign correction mechanism for Laplacian eigenfunctions. Extensive evaluation on synthetic human meshes and cross-category deformable shapes—including non-isometric humans, anisotropic surfaces, and animal models—demonstrates significant performance gains over state-of-the-art methods. Our approach exhibits strong generalization and zero-shot cross-category transfer capability, requiring no category-specific training data.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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 approach 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.

Problem

• Overcoming limited generalization in existing shape correspondence methods
• Reducing reliance on category-specific training data for deformation models
• Resolving sign ambiguity in Laplacian eigenvector basis for functional maps

Innovation

• Using diffusion models to predict functional maps directly
• Employing a template-based approach to reduce map pairs
• Correcting eigenvector signs unsupervised via surface features