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 select triangular faces on the tetrahedra to define the final mesh. We formulate probability of faces to exist on the actual surface 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: https://sonsang.github.io/dmesh-project.

翻译：我们提出了一种用于通用三维三角网格的可微分表示方法——DMesh。DMesh同时考虑了网格的几何信息与连接关系。在我们的设计中，首先基于加权Delaunay三角剖分（WDT）得到一组紧密镶嵌该区域的凸四面体，然后选取四面体上的三角面片来定义最终网格。我们基于WDT以可微分的方式定义了实际表面上面片存在的概率。这使得DMesh能够以可微分的方式表示各种拓扑结构的网格，并允许我们通过基于梯度的优化方法，在点云、多视角图像等多种观测条件下重建网格。源代码及完整论文详见：https://sonsang.github.io/dmesh-project。