【摘要】：拓撲學(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撲(簡稱M-拓撲)的三維數(shù)字圖像分析.出于實現(xiàn)圖像變換的需要,自然考慮與格點拓撲聯(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,與拓撲意義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

【相似文獻】

相關(guān)期刊論文 前7條

1 張永林;綜合地學(xué)數(shù)據(jù)微機數(shù)字圖像分析軟件獲全國地質(zhì)遙感圖像處理軟件評比二等獎[J];礦產(chǎn)與地質(zhì);1991年01期

2 顧磊;吳晟;李寶鋒;孫東懷;王飛;王鑫;張月寶;李再軍;;基于數(shù)字圖像分析的沉積物色度測量方法及其古環(huán)境應(yīng)用[J];蘭州大學(xué)學(xué)報(自然科學(xué)版);2010年S1期

3 于起峰,孫祥一;關(guān)于“光測力學(xué)數(shù)字圖像分析技術(shù)”課程的建設(shè)[J];力學(xué)與實踐;1997年06期

4 張遠飛,劉齊躍,邵孟林,植起漢,朱谷昌;綜合地學(xué)數(shù)據(jù)微機數(shù)字圖像分析軟件GDIIA系統(tǒng)及其應(yīng)用[J];礦產(chǎn)與地質(zhì);1990年S1期

5 張遠飛,劉齊躍,邵孟林,植起漢,朱谷昌,鄭獻華,安萍,謝瑞娟,李曉蓮;綜合地學(xué)數(shù)據(jù)微機數(shù)字圖像分析軟件GDIIA系統(tǒng)及其應(yīng)用[J];國土資源遙感;1990年03期

6 李志強;王元;張洋;;躍移沙粒運動參數(shù)的數(shù)字圖像分析[J];西安交通大學(xué)學(xué)報;2010年07期

7 孫東懷,劉禹,譚明;古環(huán)境記錄的數(shù)字圖像分析及應(yīng)用[J];科學(xué)通報;2002年21期

相關(guān)會議論文 前3條

1 劉伊麗;;心血管數(shù)字圖像分析在臨床的應(yīng)用[A];第四屆全國心功能學(xué)術(shù)研討會論文摘要集[C];1994年

2 沈國良;;數(shù)字圖像分析技術(shù)在涂漆前后表面評估中的應(yīng)用[A];第十屆全國內(nèi)河船舶與航運技術(shù)學(xué)術(shù)會議論文集[C];2006年

3 陳力;李德聰;鄭波;劉學(xué)柱;楊世弘;丁雁生;;炸藥近地空爆近區(qū)現(xiàn)象的數(shù)字圖像分析[A];第八屆全國爆炸力學(xué)學(xué)術(shù)會議論文集[C];2007年

相關(guān)碩士學(xué)位論文 前2條

1 國維潔;基于格點拓撲的數(shù)字圖像分析[D];河北師范大學(xué);2017年

2 王俊;離焦數(shù)字圖像分析與恢復(fù)[D];浙江大學(xué);2006年

，

本文編號：2189562