| 图像形态学中的拓扑结构 |
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| 引用本文： | 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. |
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| 作者姓名： | 高智民 汤建良 |
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| 作者单位： | 深圳大学数学科学学院,深圳,518060 |
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| 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.
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| 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 |
| 文章编号： | 1000-2618(2007)02-0217-04 |
| 修稿时间： | 2006-10-24 |
Topological structure for the space consisting of images |
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| GAO Zhi-min,TANG Jian-liang.Topological structure for the space consisting of images[J].Journal of Shenzhen University(Science &engineering),2007,24(2):217-220. |
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| Authors: | GAO Zhi-min TANG Jian-liang |
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| Affiliation: | GAO Zhi-min and TANG Jian-liangCollege of Mathe matics and Computing Science Shenzhen University Shenzhen 518060 P.R. China |
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| 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. |
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| Keywords: | pattern analysis erosion operation dilation operation opening operation closing operation compact sets upper closed limit lower closed limit topological structure |
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