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 在數位影像處理的相關領域中，影像表示法是一個很重要的課題，廣泛被運用在影像辨認，電腦繪圖及影像壓縮等方面。數位影像一般可以三種方式表示：樹狀結構、數碼字串與數碼集合。此三種表示法相較之下，數碼集合表示法的資料量較少，並且可以有效率的運用在影像處理的演算法。本研究主要目的在於發展運算速度快，又能產生最少數碼資料的資料表示法。在前人提出的相關研究論文中，產生代表影像的數碼集合有三種方法：線性四元樹演算法、內插式線性二元樹演算法、布林化簡函數演算法。前兩個演算法產生數碼集合的運算速度較快，但是數碼資料量較多，浪費儲存空間。而最後一個演算法則可以產生最少的數碼資料量，需要的儲存空間較少，缺點是運算速度較慢。我們綜合前述三種方法的優點，提出新的演算法。實驗證明新的演算法可以產生最少的數碼資料量，並且大幅降低運算時間。另外我們採用影像切割的技術作為前處理，可以將運算效能更進一步提昇。最後，以數碼集合為基礎，我們提出影像的降取樣之影像表示法的轉換技術。我們可以選擇產生較佳影像品質的轉換演算法，或者犧牲少許的影像品質，獲得較快的運算速度的轉換演算法。
 In the related fields of digital image processing, image representation is a very important issue. It is widely performed in pattern recognition, computer graphics, and image compression. Digital images may be represented as a tree structure, strings, or set-of-codes. The set-of-codes representation generates the fewest data as compared with the others, and it can be effectively manipulated by the image processing algorithms. The purpose of our study is to develop two image representation algorithms with quicker operation speed and fewer codes.Many set-of-codes techniques have been devised and can be classified into three categories: linear quadtree, interpolation-based bintree, and boolean switching function. The linear tree structure has faster operation speed, but it has more data of set-of-codes. However the boolean function may generate fewer data, but it has slower operation speed. Our proposed algorithm of image representation has faster operation speed and fewer data of set-of-codes. Experiments show that the improved methods have outstanding effect in saving storage space and reducing operation time. Besides, we apply image partition technique to further improve the performance.Finally, we devise the transformation of image representation based on set-of-codes when the image is downsampled. We can choose proper algorithms to acquire better image quality or quicker operation speed at the sacrifice of little image quality.
 Chapter 1 Introduction 11.1Motivation 11.2Related researches 31.3Thesis organizations 4Chapter 2 Region-Based Representation of Bi-level Image 62.1Introduction 62.2Tree-structured representation 72.2.1Quadtree 72.2.2Binary tree 92.3Set-of-codes Techniques 102.3.1Linear quadtree representation 122.3.2Interpolation-based bintree 132.3.3Boolean switching function 15Chapter 3 Image Processing Based on Logic Minimization 223.1Introduction 223.2Enhanced boolean function-based encoding 243.2.1Block decomposition 243.2.1.1Quadtree-type 253.2.1.2Bintree-type 253.2.1.3Hybrid-type 283.2.2Symbol string encoding 293.2.2.1Binary code of decimal 303.2.2.2Gray code 313.2.3Symbol string minimization 343.3Image partition 363.4Image compression 383.5Downsampling 40Chapter 4 Simulation Results and Comparisons 444.1Introduction 444.2Enhanced boolean function-based encoding 454.3Image partition 544.4Image compression 604.5Downsampling 60Chapter 5 Conclusions and Future Studies 745.1Conclusions 745.2Future Studies 75References 76Vita 80
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