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: https://sonsang.github.io/dmesh-project.

翻译：我们提出了一种可微分表示方法DMesh，适用于通用三维三角网格。DMesh同时考虑了网格的几何与连接信息。在我们的设计中，首先基于加权Delaunay三角剖分（WDT）得到一组紧致镶嵌定义域的凸四面体，并基于WDT以可微分方式构建网格面上存在概率的公式。这使得DMesh能够以可微分方式表示各种拓扑结构的网格，并允许我们利用基于梯度的优化方法，根据点云、多视角图像等多种观测数据重建网格。完整论文及源代码见：https://sonsang.github.io/dmesh-project。