本研究提出一個方法用來擷取維度降低且具翻轉不變性之SIFT特徵，此方法將SIFT特徵描述符重新排列以達到翻轉不變性，並將排列後的特徵進行Log-Polar轉換，產生LPT特徵，以便將特徵維度降至72維，減少比對的時間。
所提出的方法分為特徵擷取及特徵匹配兩個階段，前者包含以下步驟：首先將原始影像預處理，產生預處理影像，接著抽取預處理影像的LPT特徵，最後將特徵存放至資料庫；後者則是抽取待比對影像的特徵，其方式與前者相同，然後逐一與資料庫的影像特徵進行比對。
實驗數據顯示，利用本方法所抽取的特徵擁有翻轉不變性且比對時間縮短許多，因為本方法的特徵維度只有72維，且本方法較其他方法能正確且有效的搜尋複製影像與近似複製影像。

This thesis presents a method used to extract SIFT features with flip-invariance and reduced dimensionality. This method is based on SIFT descriptor. First, features are rearranged to achieve flip-invariance. Second, the features after the arrangement are converted by Log-Polar transform, which generates LPT features. Finally, the feature dimensions are reduced to 72 dimensions to decrease the matching time.
The method contains the feature extraction phase and the feature matching phase. The former phase extracts LPT features from the image after the preprocessing stage. The latter phase extracts LPT features from the query image, and compares them with those in the database.
The experimental results show the features are flip-invariant. In addition, the matching time is also shorter because the dimension of the extracted feature is 72. The experimental results also show the proposed method can not only effectively discover duplicate images and near-duplicate images, but also can achieve high precision rates.

誌謝 i
中文摘要 ii
ABSTRACT iii
目錄 iv
圖目錄 vi
表目錄 viii
第1章 概論 1
1.1 研究背景與動機 1
1.2 研究目標 3
1.3 論文架構 3
第2章 相關知識 4
2.1 Log-Polar Transform 4
2.2 SIFT(Scale-Invariant Feature Transform) 6
2.2.1 方向定位 6
2.2.2 特徵點描述 7
2.3 翻轉影像 8
2.4 Y. W. Chen’s Method 8
2.5 F-SIFT 9
2.6 FIND 10
2.7 MI-SIFT 12
第3章 抗翻轉的SIFT特徵擷取 13
3.1 SIFT特徵點分析 13
3.2 特徵擷取 14
3.2.1 影像預處理 15
3.2.2 SIFT特徵抽取且特徵維度增加 16
3.2.3 特徵重新排列 17
3.2.4 特徵Log-Polar轉換 18
3.2.5 產生LPT特徵 20
3.2.6 特徵維度降低 21
3.3 特徵比對 23
第4章 實驗結果與分析 24
4.1 效能評價指標 24
4.2 實驗環境與資料庫 24
4.3 複製影像實驗結果與分析 28
4.4 近似複製影像實驗結果與分析 29
第5章 結論與未來展望 34
5.1 結論 34
5.2 未來研究方向 35
參考文獻 36

參考文獻
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