Consistent topographic surface labelling

This paper describes work aimed at consistently labelling surface facets using topographic classes derived from mean and Gaussian curvature measurements. There are two distinct contributions. Firstly, we develop a statistical model which allows label probabilities to be assigned to the different topographic classes. These probabilities capture uncertainties in the computation of surface curvature from raw surface normal information. The probabilities are computed using propagation of variance from the surface normal measurements. The second contribution is to demonstrate how topographic surface labelling can be realised using probabilistic relaxation. The key ingredient is to develop a constraint dictionary for the feasible configurations of the topographic labels that can occur on neighbouring faces of the surface mesh. These constraints relate to the legal adjacency of different topographic structures together with the smoothness and continuity of uniform regions.