Learning Deformable Tetrahedral Meshes for 3D Reconstruction

Previous work on neural 3D reconstruction demonstrated benefits, but also limitations, of point cloud, voxel, surface mesh, and implicit function representations. We introduce \emph{Deformable Tetrahedral Meshes} (DefTet) as a particular parameterization that utilizes volumetric tetrahedral meshes for the reconstruction problem. Unlike existing volumetric approaches, DefTet optimizes for both vertex placement and occupancy, and is differentiable with respect to standard 3D reconstruction loss functions. It is thus simultaneously high-precision, volumetric, and amenable to learning-based neural architectures. We show that it can represent arbitrary, complex topology, is both memory and computationally efficient, and can produce high-fidelity reconstructions with a significantly smaller grid size than alternative volumetric approaches. The predicted surfaces are also inherently defined as tetrahedral meshes, thus do not require post-processing.