具有全局相干性的局部形状模拟：一种逆谱方法
Localized Shape Modelling with Global Coherence: An Inverse Spectral Approach
摘要：
许多自然形状的大部分特征都集中在空间的几个区域上。例如，人类和动物具有独特的头部形状，而椅子和飞机等无机物体则由具有特定几何特征的局部功能部件组成。通常，这些特征是密切相关的--四足动物面部特征的改变应该会引起身体结构的变化。然而，在形状建模应用程序中，这些类型的编辑是最困难的;它们需要高精度，但也需要对整个形状的全局感知。即使在深度学习时代，获得满足这些要求的可操纵表示也是一个开放的问题，带来了重大的限制。在这项工作中，我们通过定义一个数据驱动的模型上的一个家庭的线性算子（网格拉普拉斯算子的变体），其光谱捕获全局和局部几何特性的形状在手，解决了这个问题。对这些光谱的修改被转换为相应表面的语义上有效的变形。通过显式地将全局与局部表面特征解耦，我们的管道允许执行局部编辑，同时保持全局风格的一致性。我们经验性地展示了我们的基于学习的模型如何推广到训练时看不到的形状表示，并且我们系统地分析了不同形状类别的局部算子的不同选择。
英文摘要：
Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of well-localized functional parts with specific geometric features. Often, these features are strongly correlated -- a modification of facial traits in a quadruped should induce changes to the body structure. However, in shape modelling applications, these types of edits are among the hardest ones; they require high precision, but also a global awareness of the entire shape. Even in the deep learning era, obtaining manipulable representations that satisfy such requirements is an open problem posing significant constraints. In this work, we address this problem by defining a data-driven model upon a family of linear operators (variants of the mesh Laplacian), whose spectra capture global and local geometric properties of the shape at hand. Modifications to these spectra are translated to semantically valid deformations of the corresponding surface. By explicitly decoupling the global from the local surface features, our pipeline allows to perform local edits while simultaneously maintaining a global stylistic coherence. We empirically demonstrate how our learning-based model generalizes to shape representations not seen at training time, and we systematically analyze different choices of local operators over diverse shape categories.
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