Estimating differential quantities from point cloud based on a linear fitting of normal vectors

作     者：CHENG ZhangLin ZHANG XiaoPeng 

作者机构：Sino-French Laboratory LLAMA National Laboratory of Pattern Recognition Institute of Automation Chinese Academy of SciencesBeijing 100080 China 

出 版 物：《Science in China(Series F)》 (中国科学（F辑英文版）)

年 卷 期：2009年第52卷第3期

页      面：431-444页

核心收录：

学科分类：07[理学] 08[工学] 0701[理学-数学] 070101[理学-基础数学] 081202[工学-计算机软件与理论] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Supported in part by the National Natural Science Foundation of China (Grant Nos. 60672148, 60872120) the National High-Tech Research & Development Program of China (Grant Nos. 2006AA01Z301, 2008AA01Z301) Beijing Municipal Natural Science Foundation (Grant No.4062033) 

主　　题：differential geometric properties point cloud normal fitting Weingarten matrix 

摘      要：Estimation of differential geometric properties on a discrete surface is a fundamental work in computer graphics and computer vision. In this paper, we present an accurate and robust method for estimating differential quantities from unorganized point cloud. The principal curvatures and principal directions at each point are computed with the help of partial derivatives of the unit normal vector at that point, where the normal derivatives are estimated by fitting a linear function to each component of the normal vectors in a neighborhood. This method takes into account the normal information of all neighboring points and computes curvatures directly from the variation of unit normal vectors, which improves the accuracy and robustness of curvature estimation on irregular sampled noisy data. The main advantage of our approach is that the estimation of curvatures at a point does not rely on the accuracy of the normal vector at that point, and the normal vectors can be refined in the process of curvature estimation. Compared with the state of the art methods for estimating curvatures and Darboux frames on both synthetic and real point clouds, the approach is shown to be more accurate and robust for noisy and unorganized point cloud data.