Abstract

A 3D mesh offers a rich yet lightweight representation of geometry and topology for the metric and semantic understanding of a robot’s scene. Noisy features are often used to generate the mesh which furthers the need for accurate regularisation. Current approaches tightly couple front-end optimisation with regularisation making it difficult to evaluate the choice of discretisation and regularisation on mesh accuracy. In this work, we aim to explicitly query the performance of a set of well-known convex and non-convex regularisers on the mesh optimisation problem. We then apply these norms to dense depth estimation from a mesh representation and evaluate their performance in indoor and outdoor environments.While we show that the use of exotic, non-convex regularisers such as logTV and logTGV can result in more faithful structural reconstruction under noise, this comes at the cost of stronger outlier persistence…