论文标题
对称音量图：订单不变的体积网格对应与自由边界
Symmetric Volume Maps: Order-Invariant Volumetric Mesh Correspondence with Free Boundary
论文作者
论文摘要
尽管形状对应是几何处理中的一个核心问题，但此任务的大多数方法仅适用于二维表面。在二维情况下没有出现的独特挑战。在这项工作中，我们提出了一种在表示四面体网格的体积之间映射的方法。我们的配方最小化了旨在对称提取地图的失真能量，即不依赖源和目标域的排序。我们伴随我们的方法进行了理论讨论，描述了这种对称性假设的后果，这使我们选择了一个有利于等距对应关系的对称的ARAP能量。我们的最终公式在与边界匹配的同时，优化了近乎等值线。我们在不同的几何数据集上演示了我们的方法，从而产生与边界紧密保持一致的低距离匹配。
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted from simulation, medical imaging, and volume rendering--presents unique challenges that do not appear in the two-dimensional case. In this work, we propose a method for mapping between volumes represented as tetrahedral meshes. Our formulation minimizes a distortion energy designed to extract maps symmetrically, i.e., without dependence on the ordering of the source and target domains. We accompany our method with theoretical discussion describing the consequences of this symmetry assumption, leading us to select a symmetrized ARAP energy that favors isometric correspondences. Our final formulation optimizes for near-isometry while matching the boundary. We demonstrate our method on a diverse geometric dataset, producing low-distortion matchings that align closely to the boundary.
