Spectral geometric methods have brought revolutionary changes to the field of geometry processing -- however, when the data to be processed exhibits severe partiality, such methods fail to generalize. As a result, there exists a big performance gap between methods dealing with complete shapes, and methods that address missing geometry. In this paper, we propose a possible way to fill this gap. We introduce the first method to compute compositions of non-rigidly deforming shapes, without requiring to solve first for a dense correspondence between the given partial shapes. We do so by operating in a purely spectral domain, where we define a union operation between short sequences of eigenvalues. Working with eigenvalues allows to deal with unknown correspondence, different sampling, and different discretization (point clouds and meshes alike), making this operation especially robust and general. Our approach is data-driven, and can generalize to isometric and non-isometric deformations of the surface, as long as these stay within the same semantic class (e.g., human bodies), as well as to partiality artifacts not seen at training time.

中文翻译：

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部分可变形3D形状的光谱并集

光谱几何方法给几何处理领域带来了革命性的变化-但是，当要处理的数据表现出严重的局部性时，这种方法就无法推广。结果，在处理完整形状的方法与解决缺少的几何形状的方法之间存在很大的性能差距。在本文中，我们提出了一种可能的方法来填补这一空白。我们介绍了第一种方法来计算非刚性变形形状的成分，而无需首先求解给定局部形状之间的密集对应关系。我们通过在纯光谱域中进行操作来实现，在光谱域中，我们定义了特征值的短序列之间的并集操作。使用特征值可以处理未知的对应关系，不同的采样和不同的离散化（点云和网格都一样），使此操作特别健壮和通用。我们的方法是数据驱动的，并且可以推广到表面的等距变形和非等距变形，只要这些变形保持在相同的语义类别（例如人体）之内，以及在训练时看不到的局部伪像即可。