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.
翻译:许多自然形状的特征大多集中在空间的几个区域。例如,人类和动物有独特的头形,而椅子和飞机等无机物体则由具有具体几何特征的功能部分制成,这些特征往往具有很强的关联性 -- -- 在四重形体结构中面部特征的改变应导致身体结构的变化。然而,在形状模型应用中,这些类型的编辑属于最困难的特征;它们需要高度精确,但也需要对全球整体形状有高度的认识。即使在深层次的学习时代,获得满足这些要求的可操纵的表示是一个公开的问题,构成了严重的制约。在这项工作中,我们通过在线形体操作者(Mesh Laplaceian的变量)的系列中界定数据驱动模型来解决这一问题,其光谱捕捉到手形的全局和局部几何特性。在形状的形状中,这些对光谱的修改被转化成对相应表面表面的形态的精度有效的变形。通过明确将全球与地方表面特征脱钩,我们的管道允许进行本地的编辑,同时保持一种系统化的系统化的形态分析结构。