Computing surface-based representations from range images

The authors present a system which computes a qualitative surface-based description of a scene from a range image. They consider patches belonging to a qualitative shape catalog suggested by differential geometry as the main features of the representation. The surface is segmented and the patches classified by estimating the sign of the mean and Gaussian curvature at each nonsingular point. The parameters of the local differential structure of the surface are also estimated. Shape distortion effects introduced by Gaussian smoothing, modeled according to the diffusion paradigm, are discussed. A shape-preserving boundary condition for the diffusion equation is proposed. The authors precompute depth and orientation discontinuities maps and use them to restrict the diffusion process to nondiscontinuity points, avoiding the creation of spurious curved regions around discontinuity contours. Some experimental and quantitative test results are given