本論文將探討基因演算法在碎形影像壓縮及動態輪廓模型上的應用。關於在碎形影像壓縮上的研究，傳統碎形影像壓縮的最大缺點為編碼速率太慢，因此吾人提出兩種方法來解決這類問題。首先我們提出schema genetic algorithm (SGA)以解決編碼速率太慢的問題。此演算法乃將基因演算法中的一個重要定理–Schema定理嵌入GA裡面以便加速這編碼器。在GA的進化過程中，每一個要被編碼的range block，其基因運算子都依據schema定理來做改造。依據此策略，編碼所需的時間將可大幅的減少，且可維持不錯的重建影像品質。接著根據自然影像的自我相似性，吾人提出一SC-GA演算法以便更進一步降低編碼的時間。此方法分成兩個步驟，首先利用每一個欲編碼的range block與它相鄰blocks之間的空間相關性來找出區域最佳解。假如此解不夠理想的話，則第二階段才會被啟動以便嘗試發現更佳的解。在此階段中，GA將作用在整張影像中以便找出更相似的domain block。如此不僅編碼的時間會被更進一步地減少。由於在第一階段所發現的解只需記錄和相鄰range block的解之偏移量來代替完整的位置，因此壓縮比將更進一步被提高。上述兩種方法將和full search、傳統的 GA及其它的GA搜尋方法做比較以證明它們確實能大幅的提升編碼的速率。緊接著是關於動態輪廓模型的研究(以下簡稱為ACM)。首先針對傳統ACM的缺點之一–蛇輪廓無法收斂於物件凹陷的邊界，吾人提出一改良的ACM演算法來克服此類問題。此方法分成兩個階段。第一階段為執行傳統的ACM演算法以便擷取除了凹陷區域以外的物件輪廓。接著於第二階段中，對於那些停留在凹陷區域外的控制點，分別將適當的能量模板加入它們的外部能量。如此利用此修正過後的蛇能量將這些控制點導引進入凹陷區域來完整地擷取物件的輪廓。實驗的結果將發現吾人所提出的方法確實能完整擷取所需的物件輪廓，且在第二階段中額外再付出的計算量非常地少。另外，在有限數量的控制點之下，蛇輪廓通常無法精確擷取到物件的邊界，因此吾人進一步提出一以GA為基礎的ACM演算法來處理此問題。首先利用先前所提出的改良式ACM演算法初步擷取物件輪廓後，接著利用GA的進化策略，嘗試著在兩兩相鄰的控制點之間額外加入少量的控制點以便進一步擷取更精確的物件輪廓。同樣地，一些實驗也將被執行以便說明此方法的可行性。

In this dissertation, several GA-based approaches for fractal image compression and active contour model are proposed. The main drawback of the classical fractal image compression is the long encoding time. Two methods are proposed in this dissertation to solve this problem. First, a schema genetic algorithm (SGA), in which the Schema Theorem is embedded in GA, is proposed to reduce the encoding time. In SGA, the genetic operators are adapted according to the Schema Theorem in the evolutionary process performed on the range blocks. We find that such a method can indeed speedup the encoder and also preserve the image quality. Moreover, based on the self-similarity characteristic of the natural image, a spatial correlation genetic algorithm (SC-GA) is proposed to further reduce the encoding time. There are two stages in the SC-GA method. The first stage makes use of spatial correlations in images for both the domain pool and the range pool to exploit local optima. The second stage is operated on the whole image to explore more adequate similarities if the local optima are not satisfactory. Thus not only the encoding speed is accelerated further, but also the higher compression ratio is achieved, because the search space is limited relative to the positions of the previously matched blocks, fewer bits are required to record the offset of the domain block instead of the absolute position. The experimental results of comparing the two methods with the full search, traditional GA, and other GA search methods are provided to demonstrate that they can indeed reduce the encoding time substantially. The main drawback of the traditional active contour model (ACM) for extracting the contour of a given object is that the snake cannot converge to the concave region of the object under consideration. An improved ACM algorithm is proposed in this dissertation to solve this problem. The algorithm is composed of two stages. In the first stage, the ACM with traditional energy function guides the snake to converge to the object boundary except the concave regions. In the second stage, for the control points which stay outside the concave regions, a proper energy template are chosen and are added in the external energy. The modified energy function is applied so as to move the snake toward the concave regions. Therefore, the object of interest can be completely extracted. The experimental results show that, by using this method, the snake can indeed completely extract the boundary of the given object, while the extra cost is very low. In addition, for the problem that the snake cannot precisely extract the object contour when the number of the control points on the snake is not enough, a GA-based ACM algorithm is presented to deal with such a problem. First the improved ACM algorithm is used to guide the snake to approximately extract the object boundary. By utilizing the evolutionary strategy of GA, we attempt to extract precisely the object boundary by adding a few control points into the snake. Similarly, some experimental results are provided to show the performance of the method.

誌謝 i
摘要 ii
ABSTRACT iv
LIST OF FIGURES vi
LIST OF TABLES xii
GLOSSARY OF SYMBOLS xiii
CHAPTER 1 INTRODUCTION……………………………………………………… 1
1.1 Motivation………………………………………………………...……….. 1
1.2 Brief Sketch of the Contents……………………………………………..... 5
CHAPTER 2 GENETIC ALGORITHM………………………………………………. 8
2.1 Evolutionary Computation of Genetic Algorithm…………………………. 9
2.2 Schema Theorem…………………………………………………………. 11
CHAPTER 3 FRACTAL IMAGE COMPRESSION………………………………… 13
3.1 Some Definitions and Theorems………………………………..…….….. 14
3.2 Introduction to Fractal Image Compression…………………………...…. 15
CHAPTER 4 SCHEMA GENETIC ALGORITHM FOR FRACTAL IMAGE
COMPRESSION………………………………………………..……….. 19
4.1 Introduction………………………………………………………………. 19
4.2 Fractal Image Compression using SGA Method…………………………. 20
4.3 Experimental Result……………………………………………………… 25
CHAPTER 5 SPATIAL CORRELATION GENETIC ALGORITHM FOR
FRACTAL IMAGE COMPRESSION…………………………………… 36
5.1 Introduction………………………………………………………………. 36
5.2 Fractal Image Compression using SC-GA Method……………………… 37
5.3 Experimental Result………………………………………….................... 46
CHAPTER 6 ACTIVE CONTOUR MODEL………………………………………... 59
6.1 Introduction to Conventional ACM……………………………………… 60
6.2 Drawbacks and Remedial Methods……………………………………… 62
CHAPTER 7 GENETIC ALGORITHM APPROACH FOR ACTIVE CONTOUR
MODEL………………………………………………………………….. 64
7.1 An Improved ACM for Extracting Objects with Concavities…………… 64
7.2 GA-based ACM………………………………………………………….. 67
7.3 Experimental Results…………………………………………………….. 71
CHAPTER 8 CONCLUSIONS AND DISCUSSIONS……………………………… 78
REFERENCES………………………………………………………………………… 82

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