Refining Surface Curvature with Relaxation Labeling

Our main contributions in this paper are twofold. In the first instance, we demonstrate how H K surface labelling can be realised using dictionary-based probabilistic relaxation. To facilitate this implementation we have developed a dictionary of feasible surface-label configurations. These configurations observe certain constraints on the contiguity of elliptic and hyperbolic regions, and, on the continuity and thinness of parabolic lines. The second contribution is to develop a statistical model which allows the relaxation scheme to be initialised using the probabilities of the different H K labels. These probabilities model the assignment of curvature classes using surface normal information. They also capture uncertainties in the computation of surface curvature through the propagation of variance in the surface normal measurements.