透鏡是光學影像系統中最重要的元件,然而,透鏡容易受到污染而變成有缺陷使影像品質變差。本論文的目的就是要還原此種不完美的影像,針對此污染透鏡我們可等效成是一個隨機的污染薄膜緊貼著一個乾淨的透鏡,假設污點是呈波松分佈(Poisson distribution),具重疊的性質,且其透射率效應是乘積性(multiplicative)的,可藉由污點的濃度、半徑、透射率來決定出污染薄膜的自相關函數。利用光學轉移函數(optical transfer function)及污染薄膜的自相關函數的統計特性可還原出近似完美的影像。

本論文共包含電腦模擬、實驗並與其他模式及還原方法做比較首先,建立一個適當的實驗模型是非常重要的。實驗中我們所用到儀器包括數位攝影機、影像擷取卡、個人電腦。我們會藉由實驗所得之實際的自相關函數去估測出理論的自相關函數, 可利用此函數估測出三個參數並且將其運用在影像還原上,我們提出兩種不同的還原方式,其中一種是利用理論的自相關函數來還原,另外一種是利用光學轉移函數之二階統計,在計算的過程之中牽涉到四重積分,藉由變數變換及幾何分析的幫助可將四重積分簡化成二重積分。最後利用此二種方法來還原影像,
我們所用的這兩種方法都比Tamas Daboczi所提供的方法還要好。

The lenses are important elements in optical imaging systems. However, lenses are liable to defects such as dusts and thus deteriorate their imaging quality. These kinds of imaging systems are investigated in this thesis .The polluted lens can be verified equivalent to a polluted random screen set against a clean lens .In our model ,the defects on random screen are assumed poisson-distribution ,overlapped and the transmittance effect of each defect is multiplicative .The autocorrelation function of screen is obtained by defects' density ,radius ,and transmittance. The evaluation of the optical transfer function for this imaging system can be achieved by the autocorrelation of the above random screen.

This thesis includes computer simulation, experiments and comparison with other model and restoration method. The experiments are set up by the instruments including the video camera , capture card ,and personal computer. We may estimate the key parameters of our theoretical autocorrelation function by the real optical transfer function obtained from experiment. Accordingly, two methods are applied to image restoration in this thesis. One is to use the theoretical autocorrelation, the other is to use a second-order statistics of optical transfer function. The computation of second-order statistics involves a fourfold integration .By the help of changing variables and geometric analysis, we simplify the fourfold integration to double integration. Both of our methods are better for image restoration in RMS value than the method proposed by Tamas Daboczi

第一章 引言 ...........................................1
第二章 光學影像系統之基礎...............................8
2.1同調之影像系統.......................................8
2.2非同調之影像系統 ....................................10
2.3同調轉移函數與OTF之間的關係 .........................12
第三章 污染透鏡之影像系統理論.........................13
3.1 透射雜訊...........................................13
3.2 OTF之一階統計..................................... 14
3.2-1 統計自相關函數之公式推導.....................14
3.2-2波松分佈之自相關函數之公式推導................19
3.2-3自相關數值分析的結果......................... 20
3.2-4 otf數值分析的結果............................24

3.3 OTF之二階統計.......................................25
3.3-1公式計算.......................................25
3.3-2數值分析的結果.................................28
3.4計算的困難性.....................................30
3.4-1相交集三個圓面積之計算.................30
3.4-2四個交集圓面積的計算...................32
第四章 實驗及分析......................................34
4.1 實驗的模型.........................................34
4.2 幾何轉換...........................................36
4.2-1空間轉換......................................36
4.2-2灰階插值......................................39
4.2-3 電子影像數值分析.............................40
4.3 自相關函數之估測...................................41
4.3-1 數值分析............................44
第五章 影像還原........................................59
5.1方法一:自相關的方法..................................59
5.2方法二:二階統計的方法................................60
5.3方法三:Wiener 濾波器還原法...........................63
5.4 比較及分析..........................................64
5.4數值分析.............................................66
第六章 結論............................................105
參考文獻................................................107

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