使用複合高斯馬可夫影像模型來更新還原影像已經被證明是有幫助的，在這樣一個影像隨機場下中心像素點的決定是與周遭像素相關程度有關。本論文所討論的就是基於此一複合高斯馬可夫影像場，除了介紹傳統的複合高斯馬可夫影像還原之外，還試著拋開傳統上論文參數的束縛，直接依照所接收到的雜訊影像求得這些模組參數。將一個受到污染的影像做影像還原主要可以分成兩個部分：計算更新邊緣場與像素場。
針對邊緣場的求法我們採用機率觀點法與向量內積法取代傳統做法。在率觀點法一方面我們求邊上擺脫了邊緣場的能量函數Vcl(L)數據上使用的限制，另一方面求系統參數Ckll(m,n)與σw2時不再採用傳統論文上神秘的數據資料。在向量內積法我們將得到一個比較合理的邊緣場。使用我們方法的影像還原可以得到一
個不錯的視覺效果，而且比傳統方法還好的數值效果。

This Compound Gauss-Markov image model has been proven helpful in image restoration. In this model, a pixel in the image random field is determined by the surrounding pixels according to a predetermined line field. In this thesis, we restored the noisy image based upon the traditional Compound Gauss-Markov image field without the constraint of the model parameters introduced in the original work. The image is restored in two steps iteratively: restoring the line field by the assumed image field and restoring the image field by the just computed line field.
Two methods are proposed to replace the traditional method in solving for the line field. They are probability method and vector method. In probability method, we break away from the limitation of the energy function Vcl(L) and the mystical system parameters Ckll(m,n) andσw2. In vector method, the line field appears more reasonable than the original method. The image restored by our methods has a similar visual quality but a better numerical value than the original method.

第一章 緒論 ………………………………………………………………1
第二章 複合高斯馬可夫隨機場理論之回顧…………………………...5
2.1 簡介……………………………………………………………5
2.2 像素間的一些基本關係 .…………………………………….6
2.3 複合高斯馬可夫隨機場……………………………………....7
2.3.1 高斯馬可夫隨機場……………………………………...7
2.3.2 複合高斯馬可夫隨機場………………………………...9
2.4 聯合最大後置機率(MAP)的估測 11
2.4.1決策搜尋法………………………………………………14
2.5 複合高斯馬可夫模型之參數………………………………..15
第三章 灰階影像分割……………………………………………………19
3.1 簡介…………………………………………………………..19
3.2 影像分割技術的分類………………………………………..19
3.3 複合高斯馬可夫邊緣場之影像分割………………………..20
第四章 複合高斯馬可夫影像場之探討……………………………….23
4.1 簡介………………………………………………………….23
4.2 機率觀點求邊緣場………………………………………….23
4.3 向量內積法………………………………………………….25
4.4 與影像分割的結合………………………………………….28
第五章 實驗結果與分析………………………………………………..32
5.1 簡介…………………………………………………………...32
5.2 實驗結果……………………………………………………...32
第六章 結論………………………………………………………………58
參考文獻……………………………………………………………….…...60

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