Mathematical theory of medial axis transform
Mathematical theory of medial axis transform
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DOI：
10.2140/pjm.1997.181.57
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发表时间：
1997-11-01
影响因子：
0.6
通讯作者：
Moon, HP
中科院分区：
文献类型：
--
作者：
Choi, HI;Choi, SW;Moon, HP
平面域的中轴定义为最大内接圆盘的中心的集合。它本质上是边界的向内单位法丛的割轨迹。本文证明了：如果平面区域有有限条边界曲线，每条边界曲线由有限个真实的解析片组成，则其中轴是R-2中一个顶点和边数均为1/2的连通几何图.每条边都是一条真实的解析曲线，在端点处可以C-1方式延拓。我们阐明了顶点度与整环的局部几何之间的关系。我们还详细分析了各种连续性和正则性结果，并证明了中轴是区域的一个强变形收缩核，这意味着在实际意义上它保留了区域的所有拓扑信息。我们还获得了平行的中轴变换的结果。
The medial axis of a plane domain is defined to be the set of the centers of the maximal inscribed disks. It is essentially the cut loci of the inward unit normal bundle of the boundary. We prove that if a plane domain has finite number of boundary curves each of which consists of finite number of real analytic pieces, then the medial axis is a connected geometric graph in R-2 with finitely many vertices and edges. And each edge is a real analytic curve which can be extended in the C-1 manner at the end vertices. We clarify the relation between the vertex degree and the local geometry of the domain. We also analyze various continuity and regularity results in detail, and show that the medial axis is a strong deformation retract of the domain which means in the practical sense that it retains all the topological informations of the domain. We also obtain parallel results for the medial axis transform.