[1]高智民,汤建良.图像形态学中的拓扑结构[J].深圳大学学报理工版,2007,24(2):217-220.
 GAO Zhi-min and TANG Jian-liang.Topological structure for the space consisting of images[J].Journal of Shenzhen University Science and Engineering,2007,24(2):217-220.
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图像形态学中的拓扑结构()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第24卷
期数:
2007年2期
页码:
217-220
栏目:
数学与应用数学
出版日期:
2007-04-30

文章信息/Info

Title:
Topological structure for the space consisting of images
文章编号:
1000-2618(2007)02-0217-04
作者:
高智民汤建良
深圳大学数学科学学院,深圳 518060
Author(s):
GAO Zhi-min and TANG Jian-liang
College of Mathe matics and Computing Science,Shenzhen University,Shenzhen 518060,P.R. China
关键词:
图像分析腐蚀运算膨胀运算开运算闭运算紧集上闭极限下闭极限拓扑结构
Keywords:
pattern analysiserosion operationdilation operationopening operationclosing operationcompact setsupper closed limitlower closed limittopological structure
分类号:
O 189.1
文献标志码:
A
摘要:
精确描述和论证了图像空间的拓扑结构.证明由欧氏空间的紧集所组成的拓扑空间不是紧拓扑空间,且在这种空间上没有豪斯道夫度量,当这些紧集取自某个固定的有界集时,所构成的空间是紧空间,且有豪斯道夫度量.
Abstract:
A perfect topological Structure for the space consisting of images was given. It is proved that the topological space consisting of compact sets of the n-dimensional Euclidean space is not compact and has no Hausdorff metric. But the topological space consisting of compact sets of a fixed bounded closed set of the n-dimensional Euclidean space is a compact space and has the Hausdorff metric.

参考文献/References:

[1]Serra J.图像分析与数学形态学[M].伦敦:科学出版社,1982(英文版).
[2]吴敏金. 图像形态学[M].上海:上海科学文献出版社,1991.
[3]龚 伟,石青云, 程民德. 数字空间中数学形态学理论与应用[M].北京:科学出版社,1995.
[4]豪斯道夫 F. 集合论[M].张义良,顔家驹译.北京:科学出版社,1960.
[1]Serra J. Image Analysis and Mathematical Morphology[M]. London:Academic Press,1982.
[2] WU Min-jin. Imagical Morphology[M]. Shanghai:Shanghai Science Document Publishing House,1991(in Chinese).
[3] GONG Wei,SHI Qing-yun,CHENG Min-de. Digital Spaces Mathematical Morphology-Theory and its Applications[M].Beijing:Science Publisher,1995(in Chinese).
[4]Hausdorff F. Set Theory[M]. ZHANG Yi-liang,YAN Jia-ju,Tran.Beijing:Science Publisher.1960(in Chinese).

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备注/Memo

备注/Memo:
收稿日期:2006-10-24
基金项目:国家自然科学基金资助项目(10571151,60603028)
作者简介:高智民 (1952-),男(汉族),陕西省西安市人,深圳大学教授、博士生导师.E-mail:zhimin@szu.edu.cn
更新日期/Last Update: 2007-12-09