一种带约束限制的三次B样条曲线矢量数据压缩算法  

A CUBIC B-SPLINE-BASED VECTOR DATA COMPRESSION ALGORITHM WITH BOUNDARY CONSTRAINTS

作　　者：冯峰 蒋维 FENG Feng;JIANG Wei(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2021年第3期247-256,共10页Journal of Mathematics

基　　金：湖北省自然科学基金面上项目资助(2018CFB466).

摘　　要：为了便于大型矢量数据高效的检索分析,存储和传输,事先对矢量数据进行压缩是极为必要的.本文基于B样条良好的局部性和光滑性,利用带约束条件限制的三次B样条拟合方法对曲线矢量数据进行压缩.为了验证所提出算法的高效性,本文给出了9种不同的曲线矢量数据压缩算例,并同时与传统的Douglas-Peucker矢量压缩算法进行对比.数值算例表明,本文所提出的曲线矢量数据压缩算法明显优于传统的Douglas-Peucker压缩算法.该算法不仅能够保证曲线整体的二阶光滑性,还能够显著地降低数据的压缩率,因而具有广泛的应用前景(例如自动驾驶).In order to efficiently retrieve,analyze,store and transmit large amount of vector data,it is extremely necessary to compress these vector data in advance.Based on elegant properties of the B-spline(e.g.,locality and smoothness),we propose a cubic B-spline-based algorithm to compress the vector data with boundary constraints.The proposed cubic B-spline vector data compression algorithm is tested on nine examples with curve vector data.We also compare numerical results produced by the proposed algorithm with these of the classical DouglasPeucker compression algorithm.Numerical results show that the proposed cubic B-spline-based vector compression algorithm not only can significantly reduce the compression rate,but also can produce highly accurate compression curve with C^(2)-smoothness.Therefore,the algorithm has many important potential applications(e.g.,automatic drive).

关 键 词：曲线矢量数据压缩 三次B样条 整体C^(2)-连续 DOUGLAS-PEUCKER算法 约束条件 

分 类 号：O241.5[理学—计算数学]