ReMatching: Low-Resolution Representations for Scalable Shape Correspondence

We introduce \emph{ReMatching}, a new approach to the functional map framework that, by exploiting a novel and appropriate remeshing paradigm (\emph{Re}), enables us to target shape-matching tasks (\emph{Matching}) even on high-resolution meshes (\emph{Matching}) on which the original functional map framework does not apply or requires a massive computational cost. Instead, with our solution, we propose a time-efficient and metric-preserving remeshing algorithm that builds up a low-resolution geometry while acting conservatively on the lower frequencies of the shape and its Laplacian spectrum. Thanks to this last property, we can translate the functional maps optimization problem on this sparse representation, and thus, we can efficiently compute correspondences with functional map approaches. Finally, we design a robust technique for extending the estimate correspondence to wildly dense meshes. Through quantitative and qualitative evaluation and compared to existing alternatives, we show that our method is more efficient and effective, outperforming state-of-the-art pipelines in terms of quality and computational cost.