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.

翻译：我们提出了一种名为 \emph{ReMatching} 的功能映射框架新方法，通过利用一种新颖且合适的重新网格化范式（\emph{Re}），该方法能够在原始功能映射框架无法应用或需要巨大计算成本的高分辨率网格（\emph{Matching}）上，解决形状匹配任务（\emph{Matching}）。相反，我们的解决方案提出了一种时间高效且保度量的重新网格化算法，该算法在构建低分辨率几何结构的同时，对形状及其拉普拉斯谱的低频部分采取保守处理。得益于这一特性，我们可以将功能映射优化问题迁移至该稀疏表示上，从而高效地利用功能映射方法计算对应关系。最后，我们设计了一种鲁棒的技术，用于将估计的对应关系扩展到高密度网格。通过定量与定性评估，并与现有替代方案进行比较，我们证明了我们的方法在效率与有效性上均更优，在质量和计算成本方面超越了现有最先进的管线。