Smooth Mesh Estimation from Depth Data using Non-Smooth Convex Optimization

Meshes are commonly used as 3D maps since they encode the topology of the scene while being lightweight. Unfortunately, 3D meshes are mathematically difficult to handle directly because of their combinatorial and discrete nature. Therefore, most approaches generate 3D meshes of a scene after fusing depth data using volumetric or other representations. Nevertheless, volumetric fusion remains computationally expensive both in terms of speed and memory. In this paper, we leapfrog these intermediate representations and build a 3D mesh directly from a depth map and the sparse landmarks triangulated with visual odometry. To this end, we formulate a non-smooth convex optimization problem that we solve using a primal-dual method. Our approach generates a smooth and accurate 3D mesh that substantially improves the state-of-the-art on direct mesh reconstruction while running in real-time.