点采样曲面的曲率估计  

Estimating curvatures for point-sampled surfaces

作　　者：吴剑煌[1] 刘伟军[1] 王天然[1] 王华兵[1] 

机构地区：[1]中国科学院沈阳自动化所

出　　处：《仪器仪表学报》2006年第12期1557-1562,共6页Chinese Journal of Scientific Instrument

基　　金：国家"863"计划(2001AA421160)资助项目

摘　　要：本文提出一种直接在点采样曲面上计算曲面的高斯曲率、平均曲率及主曲率等局部微分性质的方法。首先,为了去除测量产生的噪声和误差,引入高斯核函数为每个采样点加权;接着计算每个采样点的最近邻域点集;然后用双三次B样条曲面最小二乘拟合邻域点集,构造局部参数曲面来逼近原始曲面,以局部参数曲面的曲率估计点采样曲面的曲率;最后给出曲率估计的应用。实验结果表明,该方法能有效地反映曲面的基本特征。An approach is proposed to estimate several differential properties, including Gaussian curvature, mean curvature and main curvature on point-sampled surfaces in presence of noise. To filter out the noise and error arising out of various physical measurement processes and limitations of the acquisition technology, a Gaussian weight is assigned to each point acquired. Moving local bicubic B-spline surface is obtained by applying the least square fitting method to the nearest neighbors of the points. Then the local differential geometric properties of point-sampled surface are approximated by analyzing the bicubic B-spline surface. Applications of curvature estimation are given and experimental results are also provided.

关 键 词：曲率估计 点采样曲面 双三次B样条曲面 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]