The k-homotopic thinning and a torus-like digital image in Zn supercript stop
The k-homotopic thinning and a torus-like digital image in Zn supercript stop
复制标题
DOI：
10.1007/s10851-007-0061-2
复制
发表时间：
2008-05-01
影响因子：
2
通讯作者：
Han, Sang-Eon
中科院分区：
文献类型：
--
作者：
Han, Sang-Eon
为了讨论数字图像（X，k）的数字拓扑性质，最近的许多文献都使用了数字基本群和一些数字拓扑不变量，如k-连接数、k-拓扑数等。由于建立数字基本群的乘法性质存在一定的困难，因此k-同伦细化方法可用于计算具有k-邻接的数字积的数字基本群。更精确地说，设SC（ki）（ni，li）是一个简单的k（i）-闭曲线，l（i）个元素在Z（ni）中，i <${1，2}。对于Z（n1 + n2）的类环面集的数字积Sc（k1）（n1，l1）× Sc（k2）（n2，l2）子集的某个k-邻接，从Sc（k1）（n1，l1）× Sc（k2）（n2，l2）的k-同伦稀疏出发，得到了它的k-同伦稀疏集DT（k）.给出了一个计算Sc（k1）（n1，l1）xSc（k2）（n2，l2）的数字基本群的算法，利用数字覆盖（ZxZ，p（1）xp（2），DT（k））的各种性质，强k-变形收缩和代数拓扑工具，研究了（Sc（k1）（n1，l1）xSc（k2）（n2，l2），k）的k-基本群.最后，我们发现了数字基本群的伪乘性（与乘性相反）。这一性质可用于从数字k-同伦理论和数学形态学的角度对数字图像进行分类。
In order to discuss digital topological properties of a digital image ( X, k), many recent papers have used the digital fundamental group and several digital topological invariants such as the k-linking number, the k-topological number, and so forth. Owing to some difficulties of an establishment of the multiplicative property of the digital fundamental group, a k-homotopic thinning method can be essentially used in calculating the digital fundamental group of a digital product with k-adjacency. More precisely, let SC(ki)(ni,li) be a simple closed k(i)-curve with l(i) elements in Z(ni), i epsilon {1,2}. For some k-adjacency of the digital product Sc(k1)(n1,l1) x Sc(k2)(n2,l2) subset of Z(n1 + n2) which is a torus-like set, proceeding with the k-homotopic thinning of Sc(k1)(n1,l1) x Sc(k2)(n2,l2) ,we obtain its k-homotopic thinning set denoted by DT(k). Writing an algorithm for calculating the digital fundamental group of Sc(k1)(n1,l1) x Sc(k2)(n2,l2) ,we investigate the k-fundamental group of (Sc(k1)(n1,l1) x Sc(k2)(n2,l2), k) by the use of various properties of a digital covering (Zx Z,p(1) x p(2),DT(k)), a strong k-deformation retract, and algebraic topological tools. Finally, we find the pseudo-multiplicative property ( contrary to the multiplicative property) of the digital fundamental group. This property can be used in classifying digital images from the view points of both digital k-homotopy theory and mathematical morphology.