Invariant surface segmentation through energy minimization with discontinuities

摘要

The computational problems in segmenting range data into surface patches based on the invariant surface properties, i.e., mean curvature H and Gaussian curvature K, are investigated. The goal is to obtain reliable HK surface maps. Two commonly encountered problems are: firstly the noise effect in computing derivative estimates, and secondly the smoothing across discontinuities. Here, the segmentation is formulated as finding minimization solutions of energy functionals involving discontinuities. A two-stage approach to the goal is presented: stage (1) from a range image to curvature images and stage (2) from the curvature images to the HK maps. In both stages, solutions are found through minimizing energy functionals that measure the degree of bias of a solution from two constraints: the closeness of the solution to the data, and the smoothness of the solution controlled by predetermined discontinuities. Propagation across discontinuities is prevented during minimization, which preserves the original surface shapes. Experimental results are given for a variety of test images.