DMesh: A Differentiable Mesh Representation

TL;DR

DMesh introduces a differentiable representation for 3D meshes that captures geometry and connectivity, enabling gradient-based reconstruction from various observations like point clouds and images.

Contribution

It proposes a novel differentiable mesh representation using Weighted Delaunay Triangulation, allowing flexible topology handling and reconstruction via gradient optimization.

Findings

Enables mesh reconstruction from point clouds and images.

Supports various topologies through differentiable face probability.

Provides a new framework for gradient-based 3D mesh optimization.

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 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.