用图像扩散模型精修形状对应关系，提升精度与效率。
FRIDU: Functional Map Refinement with Guided Image Diffusion
- 将函数映射视为2D图像，直接在函数空间训练扩散模型。
- 以初始误差映射为条件，生成更准确的对应关系，性能媲美顶尖方法。
- 支持正交性、对易性等目标引导，适合几何处理研究者使用。
我们提出一种新方法，用于精修两个形状之间的对应关系。将对应关系表示为函数映射（即基变换矩阵）时，可将其视为二维图像。基于此视角，我们在函数映射空间中直接训练图像扩散模型，使其能够根据不准确的初始映射生成高精度映射。训练完全在函数空间进行，因此极为高效。推理时，利用当前函数映射对应的点对点映射作为扩散过程中的引导信号，该引导还可额外促进函数映射的正交性及与拉普拉斯-贝尔特拉米算子的对易性。实验表明，该方法在映射精修任务上具有与最先进方法相当的性能，且引导扩散模型为函数映射处理提供了有前景的新路径。
原文摘要 · Abstract (English)
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.
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