在影像研究與電腦視覺的領域上，距離轉換是一項重要的技術，利用距離轉換的計算，影像的重要特性得以被萃取出來，如形狀因數(shape factor)、骨幹(skeleton)和中軸(medial axis)等應用上。
查表法是基於4N的架構去遞迴演算。因此這個方法非常的快而且跟最快的4N法很接近。在我們實驗中，我們去跟全部的方法作比較。查表法能成功是基於去檢查幾何上錯誤的點。這些錯誤候選點的排列是根據他們對於關係點的距離作排列。另一種演算法，用一個局部陣列去儲存在工作列上離前景點最近的Y座標。因此我們可以從檢查局部陣列中找到正確的特徵點去取代檢查全部的特徵點。我們去比較全部在沒有錯誤的距離轉換演算法中濤選候選人點所花費的時間。

Euclidean Distance transformation is a fundamental technique for the application fields of image understanding and computer vision. Some important characteristics in image analysis such as shape factor, skeleton and medial axis are based upon the distance transformation computation.
The lookup table algorithm is based upon the recursive computation structure of the 4N method. Therefore, this algorithm is very fast and is close to the 4N method, which performs as the fastest one among all the comparing algorithms in our experiments. The success of the lookup table algorithm is based upon a checking strategy by error geometry. The error candidates are arranged in order according to their distances to the reference point. In addition, a Local_Array is used to store the y coordinates of the closest foreground pixels above the processing line. Therefore we can find the correct feature point by checking the ordered candidates with the information provided from the Local_Array instead of comparisons among the candidates. In contrast, all the comparing eror-free Euclidean algorithms select their feature points from candidates by time consuming distance comparison.

第1章 引言 3
第2章 距離轉換之一般概念 5
2.1 距離轉換之定義 5
2.2 距離轉換之整體性運算與局部性運算 7
2.3 歐氏距離轉換之特殊性 8
第3章 查表法 11
3.1 應用雜湊(hashing)觀念之查表法 11
3.1.1 查表之概念 11
3.1.2 查表與雜湊法(hashing) 13
第4章 實驗與討論 25
4.1 n-鄰居距離轉換 25
4.1.1 四鄰居向量式距離轉換之誤差 27
4.2 Ingemar Ragnemalm 29
4.3 David W.Paglieroni 30
4.4 Heinz Breu、Joseph Gil、David Kirkpatrick and Michael Werman 33
4.5 Weiguang Guan and Songde Ma 35
4.6 遮罩方式 38
4.7 Tomio Hirata 38
4.7.1 硬體演算法用軟體模擬 38
4.7.2 軟體演算法 39
4.8 二分法 41
第5章 實驗結果 42
5.1 實驗說明 42
5.2 實驗數據與結果 42
5.3 效能比較 47
第6章 結論 50
參考文獻 51

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