Abstract This paper pursues an accurate, reliable dense partial shape correspondence between non-rigid shapes. The method presented here is based on the recently proposed partial functional maps framework. The key novelty of our approach comes from its capability to integrate the eigenvalue equivalence of the Hamiltonian operator with the optimization formula of functional maps. We also use the map refinement approach based upon the new iterative upsampling method called ZoomOut in conjunction with several search algorithms. The technique we proposed allows us to obtain a high-quality partial correspondence that promotes the smoothness and the semantic accuracy of the maps, even in such cases of non-rigid transformations that are robust to large deformations and topological noise. Extensive experiments on standard non-rigid correspondence benchmarks show that our method achieves state-of-the-art results both qualitatively and quantitatively.

中文翻译：

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通过全谱特征值对齐和上采样细化的部分 3D 形状函数对应

摘要 本文追求非刚性形状之间准确、可靠的密集部分形状对应关系。这里介绍的方法基于最近提出的部分功能映射框架。我们的方法的关键新颖之处在于它能够将哈密顿算子的特征值等价与函数映射的优化公式相结合。我们还使用基于称为 ZoomOut 的新迭代上采样方法结合多种搜索算法的地图细化方法。我们提出的技术使我们能够获得高质量的部分对应关系，从而提高地图的平滑度和语义准确性，即使在对大变形和拓扑噪声具有鲁棒性的非刚性变换的情况下也是如此。