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研究生:王子松
研究生(外文):Tzu-sung Wang
論文名稱:基於分數微分遮罩之數位影像銳化技術
論文名稱(外文):Digital Image Sharpening Based on Fractional Differential Masks
指導教授:曾建誠曾建誠引用關係
指導教授(外文):Chien-Cheng Tseng
學位類別:碩士
校院名稱:國立高雄第一科技大學
系所名稱:電腦與通訊工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:中文
論文頁數:125
中文關鍵詞:分數微分遮罩影像銳化
外文關鍵詞:Fractional Differential MasksImage Sharpening
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在傳統的數位影像銳化方法中,通常使用整數次微分運算來達成目的。為了
增加銳化方法的彈性,本論文將探討如何使用分數微分運算來建構影像銳化遮罩。
首先,我們使用克朗沃德-雷特尼可夫分數微分的定義,來分別建構出一維和二維
的分數微分遮罩以及其對應的影像銳化方法。接著,本論文推導基於萊斯位勢的
分數微分萊斯遮罩,並應用在數位影像銳化上。最後,使用實驗將分數微分遮罩、
萊斯遮罩的銳化結果影像與傳統的拉普拉斯法和去銳化遮罩法之銳化結果影像
相比較,以證實所提影像銳化方法的有效性。
In the traditional digital image sharpening methods,integer-order differentiation operators are often used. To improve the flexibilities of sharpening methods, we study how to use fractional differentiation to construct the image sharpening masks in this thesis. First, we use the Grunwald-Letnikov fractional derivative to construct onedimensional and two-dimensional fractional differential masks, and apply both of them to develop image sharpening methods. Next, a digital image sharpening mask based on Riesz potential is also presented. Finally, the comparisons with conventional Laplacian and un-sharp masking methods are made to show the effectiveness of the proposed image sharpening methods based on fractional differentiation masks.
中文摘要 .................................................I
英文摘要 .................................................II
誌謝 .................................................III
目錄 .................................................IV
圖目錄 .................................................VI
壹、緒論 ..................................................1
1.1 研究動機 ..........................................1
1.2 相關研究 ..........................................1
1.3 論文架構 ..........................................4
貳、分數微積分 ..........................................5
2.1 分數微積分簡介 ..................................5
2.2 分數微分定義 ..................................5
2.2.1 Grunwald-Letnikov導數(Derivative) ..........6
2.2.2 各種函數之分數微分 .........................10
參、傳統影像銳化方法 .................................14
3.1 拉普拉斯(Laplacian) .........................14
3.2 去銳化遮罩法(Unsharp Masking) .................22
肆、基於分數微分遮罩影像銳化方法 .........................28
4.1 一維分數微分遮罩 .........................28
4.1.1 一維分數階微分器 .........................28
4.1.2 一維分數階微分器影像銳化方法 .................30
4.2 二維(2-D)分數微分遮罩(Fractional Differential Mask).37
4.2.1 2-D分數微分遮罩 .............................37
4.2.2 遮罩建構與影像銳化方法 .........................41
伍、基於萊斯位勢影像銳化方法 .................................48
5.1 萊斯位勢 .........................................48
5.1.1 靜電場 .................................48
5.1.2 電位勢 .................................52
5.1.3 N度空間之電位勢 .........................57
5.1.4 萊斯位勢 .................................61
5.2 萊斯位勢的性質 .................................62
5.2.1 萊斯位勢的傅立葉分析 .................62
5.2.2 萊斯位勢和分數微積分之關係 .................69
5.3 萊斯位勢影像銳化方法 .........................71
5.3.1 萊斯位勢影像銳化之演算法 .................71
5.3.2 萊斯位勢影像銳化之步驟 .................73
陸、實驗結果討論 .........................................76
6.1 實驗結果- 1-D分數微分遮罩 .........................76
6.2 實驗結果- 2-D分數微分遮罩 .........................85
6.3 實驗結果-萊斯位勢 .................................94
6.4 實驗結果 ........................................104
柒、結論與未來展望 ........................................112
7.1 結論 ........................................112
7.2 未來展望 ........................................112
參考文獻 ................................................113
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