FRIDU: Functional Map Refinement with Guided Image Diffusion
This addresses shape correspondence refinement for computer graphics or geometry processing, but appears incremental as it builds on existing functional map and diffusion model techniques.
The paper tackles the problem of refining correspondence maps between shapes by training an image diffusion model in the functional map space, conditioned on an initial map, and shows it is competitive with state-of-the-art methods.
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.