【摘要】：拓?fù)鋵W(xué)方法是數(shù)字圖像分析中重要的方法之一,本文研究基于格點拓?fù)?簡稱M-拓?fù)?的三維數(shù)字圖像分析.出于實現(xiàn)圖像變換的需要,自然考慮與格點拓?fù)渎?lián)系的M-連續(xù)映射和M-同胚,然而這些映射在數(shù)字圖像分析中明顯有些剛性,常見的一些旋轉(zhuǎn)變換和平移變換甚至都不是M-連續(xù)映射.為了實現(xiàn)對數(shù)字圖像更有效地分析,本文引入了MA-映射和MA-同構(gòu)的概念,在此基礎(chǔ)上定義了M-鄰接范疇,并同另兩個范疇進行了比較,討論了這些范疇中幾種數(shù)字簡單閉曲線的等價分類.本文證明了 Z3上的M-鄰接關(guān)系等價于數(shù)字6-鄰接關(guān)系;Z3上的MA-映射等價于數(shù)字6-連續(xù)映射,它也是保持多種連通性的一種映射,亦是M-連續(xù)映射的推廣;MA-同構(gòu)是M-同胚的推廣.本文還證明了SC_M~(3,l_1)和SC_M~(3,l_2)是M-同胚的當(dāng)且僅當(dāng)l_1=l_2,這里SC_M~(3,l)代表Z~3上具有l(wèi)個元素的簡單閉M-曲線;SC_(MA)~(3,l_1)和SC_(MA)~(3,l2)是MA-同構(gòu)的當(dāng)且僅當(dāng)l1=l2,這里SC_(MA)~(3,l)代表Z~3上具有l(wèi)個元素的簡單閉MA-曲線.最后,本文針對三維數(shù)字圖像的約化定義了MA-收縮映射,與拓?fù)湟饬x下的收縮映射相比較,MA-收縮映射在約化三維數(shù)字圖像時顯得更有效.
[Abstract]:Topology is one of the most important methods in digital image analysis. In this paper, 3D digital image analysis based on lattice topology (M- topology) is studied. In order to realize the image transformation, we naturally consider the M-continuous mapping and M-homeomorphism associated with the lattice topology. However, these mappings are obviously somewhat rigid in digital image analysis. Some of the common rotation and translation transformations are not even M-continuous mapping. In order to analyze digital image more effectively, the concepts of MA-mapping and MA-isomorphism are introduced in this paper. On this basis, M-adjacency category is defined and compared with the other two categories. The equivalent classification of several simple closed digital curves in these categories is discussed. In this paper, we prove that the M-adjacency relation on Z3 is equivalent to the MA-mapping on the digital 6-adjacency relation, and that MA-mapping is equivalent to the digital 6-continuous mapping. It is also a kind of mapping that preserves many kinds of connectedness. It is also a generalization of M- continuous mappings. MA-isomorphism is a generalization of M- homeomorphism. It is also proved that SCS _ M ~ (3s) and SCS _ S _ M ~ (3N ~ 2) are M- homomorphisms if and only if L _ 1 / L ~ (3L) represents a simple closed M- (MA) ~ (3L) curve with one element on ZT _ 3 and SC_ (MA) ~ (3L ~ 2) is MA-isomorphism if and only if L _ 1L ~ (3L) represents a simple closed MA-curve with one element on Zi _ 3. Finally, the MA-contraction mapping is defined for the reduction of 3D digital images, which is more effective than the contractive mapping in topological sense.
【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】：O189.11

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