在本論文中，我們針對著名的複合高斯馬可夫影像場做廣泛的研究。在此影像模型之中，像素場中的像素點是由其周圍的鄰近點配合邊緣場的資訊來決定的。此模型在影像還原上面是很有幫助的，它利用兩個遞迴的步驟：用假定的影像場來還原邊緣場以及在計算完邊緣場之後還原影像場。
CGM(複合高斯馬可夫)影像模式具有邊緣場與生成雜訊這兩個特徵。在本篇論文中，我們利用像是改變處理的順序、及時更新、機率判別這些技巧的結合來找出最佳化的影像模型。此外，這個影像模型的效果將由其能量、視覺品質以及抗雜訊能力來驗證。最後，利用非線性方成組的解決，我們把CGM模型應用在光學污染透鏡的影像還原上面。

In this thesis, we have a comprehensive study of the famous compound Gauss-Markov image model. In this model, a pixel in the image random field is determined by the surrounding pixels according to a predetermined line field. This model is useful in image restoration by applying two steps iteratively: restoring the line field by the assumed image field and restoring the image field by the just computed line field.
CGM (Compound Gauss-Markov) image modeling is characterized by the line fields and the generating noise. In this thesis we apply combinations of techniques such as changing processing order, immediate updating, probability determination and different methods to find the best modeling. Furthermore, the effects of the above modeling are demonstrated by its energy, visual quality, and error resistance. Finally, by solving a set of nonlinear equations we apply the CGM model to an image restoration problem for image corrupted by a dusted lens.

第一章 緒論 1

第二章 高斯馬可夫隨機場理論之回顧
2.1 簡介 5
2.1.1 影像模式的介紹 5
2.1.2 像素間的一些基本關係 6
2.2 複合高斯馬可夫隨機場 7
2.2.1 高斯馬可夫隨機場 7
2.2.2 複合高斯馬可夫隨機場 9
2.3 聯合最大後置機率（MAP）的估測 11
2.3.1 決策搜尋法（Deterministic Search） 15
2.4 複合高斯馬可夫模型之參數 16

第三章 複合高斯馬可夫影像場之觀察
3.1 簡介 19
3.1.1 如何找最佳化的影像模式 19
3.1.2 如何檢驗最佳化的影像模式 19
3.2 利用技巧以遞迴的方式找出最佳化的影像模式 20
3.2.1 複合高斯馬可夫影像場的特徵 20
3.2.2 七大技巧：方法、更新、同不同類的限制、格局、交替、順序以及機率 21
3.2.3 三種技巧:順序、機率、更新 24
3.3 以能量的觀點來檢驗最佳化的影像模式 32
3.3.1 如何計算一張影像的能量 32
3.3.2 以生成雜訊的觀點求邊緣場 34
3.3.3 計算像素點的能量和邊緣場的能量 34
3.3.4 計算生程雜訊的能量和邊緣場的能量 36
3.3.5 分別以兩種能量的方式檢驗影像模式 36
3.4 以圖的好壞來檢驗最佳化的影像模式 39
3.4.1 如何用圖來判別影像模式的好壞 39
3.4.2 製做人工圖的方式 39
3.5 以抗雜訊的能力來檢驗最佳化的影像模式 43
3.5.1 在影像還原上面抗雜訊能力的比較 43
3.5.2 人工圖抗雜訊能力的比較 43

第四章 複合高斯馬可夫影像場之探討
4.1 簡介 46
4.2 污染透鏡之影像系統簡介 46
4.3 數值分析 47
4.3.1 求解非線性方程式 47
4.3.2 如何從模擬的曲線得到一條近似的理論曲線 52
4.4 污染透鏡結合複合高斯馬可夫影像場的應用 58

第五章 實驗結果與分析
5.1 簡介 60
5.2 影像模式最佳化的結果 60
5.3 能量的分析比較 80
5.4 以圖來檢驗影像模式 108
5.4.1 參數c的調整 109
5.4.2 比較最佳化影像模式下各個人工圖的好壞 110
5.5 以抗雜訊能力檢驗影像模式 115
5.6 光學結合馬可夫還原的結果與分析 118

第六章 結論 122

參考文獻 125

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