Smoothing Away From The Edge For Mesh Estimation in Urban Outdoor Environments

3D meshes offer a computationally efficient but still quite accurate path to the understanding of a robot's environment. While mesh reconstructions are often employed in indoor regions where regular planar surfaces dominate the scene, their use in urban outdoor environments has been under-explored. This is as outdoor urban environments produce a significant contrast between preserving discontinuities between different objects and maintaining smoothness in the solution. When coupled with the natural sparse nature of meshes this presents a significant challenge to their optimisation. Motivated by these challenges and leveraging insights from computer graphics, we firstly balance previously introduced real-time definitions of variational smoothing on meshes with their ‘canonical’ definitions. In doing so we introduce a novel Delaunay-Voronoi formulation for real-time mesh smoothing that allows for the accumulation of information away from the triangular edges. This allows for the use of more powerful non-convex regularisers that are able to more finely balance smoothness and object discontinuities and showcase more faithful reconstructions of the urban outdoor scene. In doing so the benefits of non-convex regularisers promised in the ‘every-pixel’ scenarios can now be inherited by sparse mesh formulations.