我們對於影像做取樣、儲存、傳輸時，可能因為環境的惡劣，會因為外來的因素干擾，例如雜訊，而污染了我們所要傳輸的影像。本論文的研究就是我們將已受到雜訊干擾之影像當作已知，配合影像分割技術和高斯馬可夫隨機場之機率模式，以最大後置機率（MAP）估測真實之影像。亦即，我們的真實影像是在給定雜訊干擾影像下，使條件機率為最大之最佳近似解。
在高斯馬可夫隨機場模式化之下，我們以條件機率最大化來探討問題。以最大後置機率為基礎，利用模擬降溫法以及非隨機搜尋法來還原影像。影像分割的目的在於求得區域參數 、 、 、 ，我們在做影像分割時，在分割出來的區域與區域之間會有邊界產生，此邊界是以像素來表示，而分割出來不同的區域，均有不同的區域參數與生成誤差，接著我們就把得到的區域參數與生成誤差帶入最大後置機率（MAP）得到最佳近似解。
所以，在本論文影像還原方法的程序上，就是先採用影像分割，求出區域參數，再利用最大後置機率來還原影像；最後，則再經過高斯馬可夫隨機場來作為影像還原過程中的最後一個程序。本論文影像還原方法之優點為減少雜訊，並且使還原影像的輪廓清楚，沒有模糊現象。

Images are liable to being corrupted by noise when they are processed for many applications such as sampling, storage and transmission. In this thesis, we propose a method of image restoration for image corrupted by a white Gaussian noise. This method is based upon Gauss-Markov random field model combined with a technique of image segmentation. As a result, the image can be restored by MAP estimation.
In the approach of Gauss-Markov random field model, the image is restored by MAP estimation implemented by simulated annealing or deterministic search methods. By image segmentation, the region parameters and the power of generating noise can be obtained for every region. The above parameters are important for MAP estimation of the Gauss-Markov Random field model.
As a summary, we first segment the image to find the important region parameters and then restore the image by MAP estimation with using the above region parameters. Finally, the intermediate image is restored again by the conventional Gauss-Markov random field model method. The advantage of our method is the clear edges by the first restoration and deblured images by the second restoration.

第一章 緒言 1

第二章 高斯馬可夫隨機場理論之回顧
2.1 簡介 5
2.2 複合高斯馬可夫隨機場 5
2.3 聯合最大後置機率的估測 11
2.3.1模擬降溫法 14
2.3.2非隨機搜尋法法 15
2.4 高斯馬可夫隨機場之影像還原技術 16

第三章 灰階影像分割
3.1 簡介 18
3.2 區域成長 19
3.2.1 重心連合 19
3.3 區域參數 20
3.4 影像分割技術 26

第四章 影像分割與複合高斯馬可夫之結合
4.1 簡介 30
4.2 系統之實現 31
4.2.1 分割後之影像還原技術 31
4.3 影像分割與高斯馬可夫隨機場組合之流程圖 33
4.4 組合之特色與比較 35
第五章 實驗結果與比較
5.1 簡介 37
5.2 影像還原結果 37
5.3 影像還原之比較 40

第六章 結論 53

參考文獻 55

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