在現今這個網路發達的時代，傳送電子文件的機會成倍數增加，可想而知，要將電子檔輸出成文件檔的機會也是日趨上升。但是在我們要將電子檔案轉成紙張的文件檔案時，不免會有失真的情況產生，像是文字模糊、文字傾斜、文字扭曲等等，這些都會造成閱讀時的不便與困擾，本論文提供了一個將扭曲文字更正還原的方法，可以在短時間內得到不錯的更正結果。
本篇論文主要是以特徵子空間的概念[6]，將旋轉扭曲的文字從文件檔中更正。首先我們會先產生26個特徵子空間(Eigen Sub-Space)分別對應26個英文字母，接著逐一的將英文字母旋轉不同角度並向對應的特徵子空間做投影，如此我們可以得到在特徵子空間的投影點，將這些點串連起來，可以得一曲線。所以當一個未知的樣本進來時，先把這個樣本對這26個特徵子空間再分別做投影，經過計算與曲線的最小距離後可以更正為失真前的文字。在這篇論文中，使用的是小寫的英文字母(a,b,c,d,…..,z)。
這個方法有一個不錯的優點就是，可以讓我們同時更正失真的文字以及扭曲的角度。

The opportunity of using electronic documents are growing in a rapid rate at the day of internet, so is the chance of transferring the electronic documents to the paper documents. Distortions like characters blurred, characters on a slant, characters distortion bother us when reading paper documents. This thesis proposes a method for the 3-dimentional distortion in document images. It provides good results for the correction efficiently.
In this thesis, the distortion in document images is corrected by using the eigen sub-space[6]. First, 26 eigen sub-spaces for each character are constructed. Next, we obtain a locus by projecting their rotated characters onto the eigen sub-space. When an unknown sample is input, it is projected onto the 26 eigen sub-spaces and the minimum distances to the locus are calculated. After the calculation we can obtain the recognition results of the 26 small letters, which will then give the corrected results.
This method has the added advantage of obtaining the correction result and angle of distortion at the same time.

第一章 緒論……………………………………………...…………….1
1.1 旋轉文字的概念…………………………………………….1
1.2 研究方向…………………………………………………….2
1.3 簡介………………………………………………………….3
第二章 影像處理之背景與流程………………………………………4
2.1 簡介………………………………………………………….4
2.2 影像處理之背景…………………………………………….4
2.3 影像處理之流程……………………………………….……7
第三章 辨識還原之方法………………………………………………9
3.1 簡介………………………………………………………….9
3.2 3-D旋轉文字的演算法……………………………………..9
3.3 投影………………………………………………………...13
3.4 未知影像的事前處理……………………………………..16
3.5 更正演算法………………………………………..………16
第四章 實驗結果…………………………………………………..…31
4.1 簡介………………………………………………………..31
4.2 實驗………………………………………………………..31
4.3 實驗改良…………………………………………………..34
4.3.1 四維實驗結果……………………………………..35
4.3.2 五維實驗結果……………………………………..38
4.3.3 六維實驗結果……………………………………..38
4.3.4 七維實驗結果……………………………………..39
4.3.5 八維與十維實驗結果……………………………..39
4.4 實際文件影像實驗…………………………………………63
第五章 結論…………………………………………………………..75
附錄……………………………………………………………………..78

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