本文關(guān)鍵詞： 數(shù)字圖像 數(shù)字拓?fù)?連續(xù)映射 圖像分類 圖像約化　出處：《河北師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：本文立足于數(shù)字空間Z3上的拓?fù)淅碚?對3D數(shù)字圖像進行理論分析和研究.首先,在數(shù)字空間Z3上建立一種拓?fù)浣Y(jié)構(gòu):二維格點拓?fù)?GP2-拓?fù)?與Khalimsky線拓?fù)?K1-拓?fù)?的乘積拓?fù)?簡稱GK-拓?fù)?分析了在此種拓?fù)湎旅恳稽c的最小開鄰域的結(jié)構(gòu),根據(jù)最小開鄰域結(jié)構(gòu)的不同把數(shù)字空間Z3上的點進行了分類.其次,討論了基于此種拓?fù)湎碌倪B續(xù)映射(稱為GK-連續(xù)映射)和同胚(稱為GK-同胚),并發(fā)現(xiàn)其在研究數(shù)字圖像的旋轉(zhuǎn)和分類等問題時存在局限性.為了克服此種局限性,引入了拓?fù)溧徑余徲蚝屯負(fù)溧徑蛹母拍?從而建立了像素之間一種新的鄰接關(guān)系.在此基礎(chǔ)上定義了 GK-鄰接映射和GK-A-映射,并給出了GK-A-映射保持連通性的證明.之后,通過具體例子分析了GK-鄰接映射和GK-A-映射分別與GK-連續(xù)映射的異同并總結(jié)了上述三種映射在某些特定變換(旋轉(zhuǎn)、平移等)下比較的結(jié)果.證明了 GK-連續(xù)映射一定是GK-A-映射,但反之未必.基于GK-A-映射是GK-連續(xù)映射的推廣,在GK-拓?fù)湎陆⒘藘蓚�新范疇GKAC和GKTC.論文也建立了GK-A-同構(gòu)的概念,并證明了GK-同胚一定是GK-A-同構(gòu),但反之未必.通過GK-A-同構(gòu)實現(xiàn)了對3D數(shù)字圖像更廣的一種等價分類.最后,基于GK-拓?fù)浣Y(jié)構(gòu),本文提供了一種通過利用GK-A-收縮映射來細化或約化數(shù)字圖像的方法,從而對計算機科學(xué)中的圖像分析、圖像處理提供幫助.
[Abstract]:Based on the topological theory of digital space Z3, this paper makes theoretical analysis and research on 3D digital image. A product topology is established on the digital space Z3: 2-D lattice topology (GP2- topology) and Khalimsky line topology (K1-topology). In this paper, the structure of the minimum open neighborhood of each point in this topology is analyzed, and the points on the digital space Z3 are classified according to the structure of the minimum open neighborhood. The continuous mapping (called GK-continuous mapping) and homeomorphism (called GK-homeomorphism) based on this topology are discussed. In order to overcome this limitation, the concepts of topological neighborhood and topological adjacency set are introduced. On the basis of this, we define GK-adjacent mapping and GK-A- map, and prove that GK-A- map maintains connectivity. The similarities and differences between GK-adjacent mapping and GK-A- mapping and GK-continuous mapping are analyzed through concrete examples, and the above three kinds of mappings are summarized in some special transformations (rotation). It is proved that GK-continuous mapping must be GK-A- mapping, but not necessarily vice versa. GK-A- mapping is a generalization of GK-continuous mapping based on GK-A- mapping. Two new categories of GKAC and GKTCare established under GK-topology. The concept of GK-A- isomorphism is also established and it is proved that GK-A- homomorphism must be GK-A- isomorphism. But not necessarily. Through GK-A- isomorphism to realize a more extensive equivalent classification of 3D digital images. Finally, based on GK- topology. In this paper, a method of thinning or reducing digital images by using GK-A-shrinkage mapping is provided, which can be helpful to image analysis and image processing in computer science.
【學(xué)位授予單位】：河北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O189;TP391.41

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