平面有界闭区域图形的拓扑分类识别  

Closed Principle Curves Learning and Algorithm for Topological Recognition of Bounded Domains in Plane

作　　者：倪劲松[1] 

机构地区：[1]苏州大学数学科学学院,苏州215006

出　　处：《计算机科学》2007年第9期224-226,共3页Computer Science

基　　金：国家自然科学基金(10571129)资助

摘　　要：本文首先将具有简单封闭曲线特征的闭主曲线学习算法应用于平面有界闭区域图形的边界提取,给出相应的算法。结合拓扑度理论,本文还定义了有界闭区域的边界关联矩阵,引入了平面中图像的F-同胚概念,运用边界关联矩阵是F-同胚下的完全不变量原理,将F-同胚和边界关联矩阵概念有机结合起来,对平面有界区域图形进行拓扑粗分类,以达到缩小搜索范围、提高搜索速度的目的。最后,本文给出了平面有界闭区域图形的计算机拓扑识别的算法及其实现。By applying closed principal curve learning algorithm, we can obtain a simple polydragon as an approach for every simple closed curve in plane. So we can extract the boundary of every connect closed domain D in plane by simple polydragons. Thus we only need to consider the case of all domain which boundaries are simp[e polydragons . In this case, by topological degree theory, we can define conjunction index Ii,j= ind（Pi,Pj） for two un-joint simple closed curves Pi, Pj in plane, and conjunction matrix I（D）= （Ii,j） for every bounded closed domain D in lane. Then we in troduce the conception of F-homeomorphism for any two pictures in plane, and apply this conception to image recognition. In [5], combining the algebraic topology method, we have proven that conjunction matrix is complete topological invariant of bounded closed domain D in plane under F homeomorphism, so, for any two bounded closed domain in plane D1 and D2, we design several algorithms to pick-up their boundaries , computer their conjunction matrixes, and compare their conjunction matrixes when they will be the same. after all, we have satisfactorily resolved the problem of topological recognition of bounded closed domain in plane under F-homeomorphism.

关 键 词：闭主曲线 有界闭区域 边界关联矩阵 F-同胚 

分 类 号：TP317[自动化与计算机技术—计算机软件与理论]