臺灣博碩士論文加值系統

根據以往的研究顯示，將碎形編碼（fractal coding）應用於資料壓縮方面，可以得到很高的壓縮比（compression ratio），而達到節省記憶體空間、提升傳輸效率的目的。但是本篇論文的研究重點不在於資料壓縮方面，而是將碎形編碼應用在邊緣偵測方面。
當碎形編碼用於壓縮時，在平滑（smooth）的區域測得的誤差值（MSE）很小，而含有邊緣（edge）或對比強烈的區域測得的誤差值很大。我們就利用這個特性，將屬於邊緣的部分偵測出來。
碎形編碼至今仍未被廣泛的使用主要是因為它的壓縮過程過於複雜，因而造成執行時花費太多的時間。當它應用在邊緣偵測時，也會有相同的困擾，所以本論文中提出了一個新的方法，來降低其複雜度，以減少運算及分析所需的時間。同時，此方法之抗雜訊能力優於大多數之邊緣偵測方法。

According to the previous researches, fractal coding applied to data compression achieves high compression ratio, which accordingly results in reduction in memory capacity and improvement on transmission efficiency. This research work does not aim at the data compression aspect. Instead the fractal coding approach is applied to edge detection.
When applying fractal coding to image compression, a smaller mean square error（MSE）between the original and decompressed images is usually obtained in the smoothing region; a larger MSE is observed for the region containing edge or strong contrast attribute. Hence, we utilize this property to identify and extract the edges.
The reason that fractal coding has not been widely used is because of the complexity of the compression process, which requires a large amount of operating time. It is the same problem encountered in our research study. This thesis presents a new method to reduce the arithmetic complexity and operating time. Moreover, the method has better noise immunization ability compared with some widely used methods.

中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
圖目錄 VI
表目錄 VII
一、簡介 1
1.1 背景 1
1.2 動機 2
1.3 章節安排 3
二、碎形編碼之基本理論及方法 4
2.1 IFS 4
2.2 Collage Theorem 6
2.3 基本的理論及定義 7
2.3.1 名詞定義 7
2.3.2 誤差測量 8
2.3.3 基本的轉換函式 8
2.4 碎形編碼的方法 14
2.4.1 影像分割 16
2.4.2 分類 16
2.4.3 搜尋過程 17
三、以碎形編碼為基礎的邊緣偵 23
3.1 原理 23
3.2 演算法一 23
3.3 演算法二 28
3.4 討論與觀察 31
四、快速邊緣偵測 34
4.1 原理 34
4.2 演算法三 36
4.3 討論與觀察 39
五、實驗結果與分析 40
5.1 實驗結果與分析―搜尋範圍的改變 40
5.2 實驗結果與分析―Scaling Factor 41
5.3 實驗結果與分析―取消Edge類別 42
5.4 實驗結果與分析―直接使用分類器來偵測邊緣 44
5.5 實驗結果與分析―對雜訊的影響 45
5.6 實驗結果與分析―區塊（Block）大小的影響 48
六、結論與未來方向 50
6.1 結論50
6.2 未來方向 50
參考文獻 52
附錄一 分類器 54

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