摘要
中轴是空间图形一种降维表达方法,能够保留图形的空间拓扑结构和几何特征信息,并去除冗余信息,它同时也是平移、旋转和尺度变换的不变量.中轴图广泛应用于科学和工程领域,包括地理信息系统、人脸识别、图像处理、计算机视觉和格网产生等.目前,中轴提取算法通常会由于形状轮廓上的噪音,产生冗余的中轴分枝.针对约束Delaunay三角网外心法构建中轴的算法,分析了约束Delaunay三角网外心法逼近中轴出现分枝的原因,给出了一种新的中轴剪枝方法.经多组复杂图形试验,该方法可以有效的剪除冗余的中轴分枝,并且具有良好的普适性.该方法也是对约束Delaunay三角网外心法构建中轴方法的一种优化,一方面使得外心法可以高精确性地逼近中轴,另一方面又可以消除去其副产物——中轴分枝.
The medial axis （or a topological skeleton） is a thinner version of a geometric object.The medial axis was first introduced by Blum as a description of shape.Its classical definitions include grass-fire model and maximal disk model.The grass-fire model means that an object＇s boundary is taken as an initial fire front that propagates within the object＇s interior region.Points where the fire front folds or interacts with itself are retained as the skeleton points.The maximal disk model means that the medial axis of a planar domain is the locus of the center of a maximal disc,which touches the boundary in at least two points.The medial axis has been used within various scientific and engineering areas,including geographical information systems,face recognition,path-finding,image processing,computer vision,collision detection,mesh-generation,and machining applications,etc.Usually,because of the noise on the boundary contours of a shape,the traditional algorithms of constructing medial axis produce the redundant branches of medial axis.This paper analyses the reason why the redundant branches of medial axis occur by using the circumcenter method based on constraint Delaunay triangulation,and then presents a new method to prune the redundant branches of medial axis.Several experiments demonstrate that the proposed method can remove the redundant medial axis branches effectively and efficiently and can be generalized.Obviously it is an optimization for the circumcenter method based on constraint Delaunay triangulation,making it more accuracy on the one hand,and eliminating its byproduct-medial axis branches on the other hand.
出处
《华中师范大学学报（自然科学版）》
CAS
北大核心
2014年第5期751-754,760,共5页
Journal of Central China Normal University：Natural Sciences
基金
国家自然科学基金项目(41071240)
关键词
复杂平面图形
约束Delaunay三角网
外心法
中轴
剪枝
planar free-form shape
constrained Delaunay triangulation
the circumcenter method
medial axis
pruning
