影像在隨機估測的訊號表示中通常被當成是一個隨機變數的陣列，稱為隨機場。為了要描述一影像的統計性質，我們採用自回歸模式當成我們要討論的影像模式。影像模式在影像處理上的應用很多，如影像壓縮、影像還原等等。因此影像模式的準確與否便便會影響到其應用在影像處理的表現。

自回歸模式主要是受生成雜訊功率和系統轉換矩陣這兩個參數所控制，影像模式的準確性便和這兩個參數息息相關。為了建立影像模式好壞的標準，我們從其應用之一影像還原來判定。在本篇論文中，我們利用卡門濾波器的等式來找出影像還原效果和影像模式中參數的關係。影像模式的系統轉換矩陣和生成雜訊功率越小，則表示該影像模式越好。藉助對參數的分析有助於我們對於這方面濾波器的瞭解，我們也可以知道影響參數的因素，進而找出這類問題的解決方法。

In stochastic representation an image is a sample function of an array of random variables which is called a random field. For characterizing an ensemble of images, we choose an autoregressive model as our image model. An image model often applies to image processing such as image data compression and image restoration. Therefore the validity of the image model affect it’s performance of image processing.

The output of the AR model depends on its parameters – system transition matrix and generating noise. Hence the validity of this model is related to these two parameters. How to seek the standard of the validity of the image model is a problem. We exploit performance of image model’s application – image restoration - to find a method of determining the validity of the image model. In our paper we find a relation between image restoration performance and image model’s parameters by the Kalman filtering equations. An image model with lower generating noise power and system transition matrix is better for image restoration and is considered a good image model. In the analysis of the parameters of the image model, we can meet the requirements of the parameters by image segmentation method, residual image method and normalized image method. In addition it also helps us understand the Kalman filter much more and know how to find the solution of similar problems.

Chapter 1 Introduction 1

Chapter 2 Gray-level Image Segmentation 4
2-1 Introduction 4
2-2 Image Segmentation Approaches 4
2-3 Practical Image Segmentation Method 5

Chapter 3 Kalman filter 8
3-1 Introduction 8
3-2 One-dimensional Kalman Filter 8
3-3 Two-dimensional Kalman Filter 10
3-4 Reduced Update Kalman Filter 11

Chapter 4 Influence of Parameters of Image
model on Image restoration 14
4-1 Relation of Parametersof Image
Model and Image Restoration 14

Chapter 5 Properties and Image Modeling of Residual and Normalized Images 18
5-1 Introduction 18
5-2 Residual Image 18
5-3 Normalized Image 22

Chapter 6 Simulation Results 26
6-1 Different Image Modeling Performance without Image Segmentation 26
6-2 Different Image Modeling Performance without Image Segmentation 29

Chapter 7 Conclusion 39

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