FRIDU: Functional Map Refinement with Guided Image Diffusion

TL;DR

This paper introduces FRIDU, a diffusion-based method for refining shape correspondence maps by treating them as images in the functional space, leading to more accurate and efficient map refinement.

Contribution

The paper presents a novel diffusion model approach that refines functional maps directly in their image space, guided by initial maps and functional constraints.

Findings

Competitive with state-of-the-art map refinement methods

Efficient training in functional space

Guided diffusion improves map accuracy

Abstract

We propose a novel approach for refining a given correspondence map between two shapes. A correspondence map represented as a functional map, namely a change of basis matrix, can be additionally treated as a 2D image. With this perspective, we train an image diffusion model directly in the space of functional maps, enabling it to generate accurate maps conditioned on an inaccurate initial map. The training is done purely in the functional space, and thus is highly efficient. At inference time, we use the pointwise map corresponding to the current functional map as guidance during the diffusion process. The guidance can additionally encourage different functional map objectives, such as orthogonality and commutativity with the Laplace-Beltrami operator. We show that our approach is competitive with state-of-the-art methods of map refinement and that guided diffusion models provide a promising pathway to functional map processing.