Estimation Of Differential Quantities On Point Clouds And Applications

Recently,with the development of 3D digital scanners and technology, point clouds have received a growing amount of attention as an alternative surface representation both in academic domain and industry. Point clouds models have widespread applications in computer-aided medical diagnosis, digital entertainment, industrial design, aviation simulation, cultural relic's protection and so on. Estimation of differential properties of point clouds is a fundamental task in digital geometric processing, computer graphics and computer vision, and it is also a prerequisite step for many applications. Both the domestic and overseas scholars have done much research in this aspect and gained pleasing effect.This paper presents algorithms for estimating the normal and curvature of point clouds with outliers, respectively. The presented algorithm for estimating the normal of point clouds is based on the least square projection method and M-estimation in robust statistics. The proposed scheme for estimating curvature of each sample point on point clouds is based on a local sphere fitting technique and a forward search approach. The presented curvature estimation method constructs working point clouds firstly, and then uses the least median square method to construct the initial point clouds subset excluding outliers based on the working point clouds. We estimate the curvature based on the initial point clouds and make sure the outliers will not be added into the succeeding computation, thus our scheme is robust.Experimental results show that traditional least square projection cannot compute the projection point correctly if the point clouds have outliers; as a result, it gives a wrong normal estimation. The same problem exists in estimating the curvature of point clouds by sphere fitting technique. However, our proposed algorithms attain robust estimation of normal and curvature as adopting M-estimation and forward search approaches.