Abstract
We present a differentiable representation, DMesh, for general 3D triangular meshes. DMesh considers both the geometry and connectivity information of a mesh. In our design, we first get a set of convex tetrahedra that compactly tessellates the domain based on Weighted Delaunay Triangulation (WDT), and formulate probability of faces to exist on our desired mesh in a differentiable manner based on the WDT. This enables DMesh to represent meshes of various topology in a differentiable way, and allows us to reconstruct the mesh under various observations, such as point cloud and multi-view images using gradient-based optimization. The source code and full paper is available at: this https URL.
Abstract (translated)
我们提出了一个可导的三角形网格表示器DMesh，用于描述任意3D三角网格。DMesh同时考虑了网格的形状和拓扑信息。在我们的设计中，我们首先通过加权Delaunay三角化（WDT）得到一系列凸四边形，然后以WDT的方式将网格域紧凑地仿射理化，并在WDT的基础上以不同的方式计算网格中面存在的概率。这使得DMesh能够以不同方式表示各种拓扑结构的网格，并使用基于梯度的优化方法重构网格。源代码和完整论文可在以下链接找到：https:// this URL。
URL
https://arxiv.org/abs/2404.13445
