Algorithms for Computing Curvatures from Range Data

This article presents a comparison of several methods for local estimation of normal direction, principal curvatures and principal directions, given a range image as input. Here we take a range image to be a set of points in 3D space; we also need a definition for neighbourhoods. All methods we compare are based on local approximation of the range image by an analytic surface or curves. Other approaches to computing curvatures also exist, and some of these are briefly described at the start of this paper. Results of using each algorithm to estimate normal direction and principle curvature on four simulated surfaces (plane, sphere, cylinder and a trigonometric surface) are presented. In particular, we discuss stability of the estimates when the data is noisy.