資訊多樣化，使得儲存於資料庫中資料，由以往多僅限於文字轉變為多媒體，如何由數量龐大影像資料庫取出使用者欲搜尋影像，為使用者所殷切需求。目前以影像為鍵值進行影像資料庫索引之技術大至可區分為根據影像中顏色、形狀、內容建立影像資料庫索引檔。上述研究方向雖有特定擅長處理條件，但無法保證其使用之方式能符合(a) 高相關度影像資訊有高相關索引檔；(b) 索引檔相關度高，其影像資訊相關度亦高；(c) 索引檔相關度低，其影像資訊相關度亦低；
(d) 影像資訊相關度低，其索引檔相關度亦低；
本研究提出一個新方法來處理影像搜尋，碎形（Fractal）使用在影像壓縮上，已被證實有良好效果，其壓縮方法是先將原影像分割成數個方塊，對於每一個方塊，在事先訓練出之方塊集中找出數個方塊及一個轉換函數，使得這數個方塊經過轉換函數線性組合後，會與較小方塊相似，結合所有方塊轉換函數成為一個函數集，將每張影像轉換函數集之係數伴隨影像存入資料庫中，成為該影像之索引檔，日後對資料庫進行搜尋時，將針對此索引檔比對，找出與使用者選定鍵值影像相似之影像。
並非所有方法建立之索引檔能具前述性質(a) 高相關度影像資訊有高相關索引檔；(b) 索引檔相關度高，其影像資訊相關度亦高；(c) 索引檔相關度低，其影像資訊相關度亦低；(d) 影像資訊相關度低，其索引檔相關度亦低。在本研究中，證明使用碎形編碼技術建立之索引檔將具(a) 相似影像有相似碎形函數，(b)相似碎形迭代函數能產生相似影像，(c) 不相似影像有不相似碎形函數，(d) 不相似碎形函數產生不相似影像，反觀使用其它方法建立影像資料庫，無法證明其建立之索引檔，具相似影像產生相似索引檔，相似索引檔取回相似影像兩性質，找回不相似影像，是可預期地。
影像比對時可分為兩種模式，一種是以整張圖之轉換函數集當作索引檔，因為以整張圖形比對相當費時，所以在整張圖形比對時，利用Nona-tree來增進比對時之效率；另一種則為以圖中之部分影像之轉換函數集當作索引影像，這部份就不以Nona-tree來切割圖片，因為使用者所選擇之區域比原圖小，在比對時效率會比較好，所以不用Nona-tree以求做出更精確之比對，部分影像比對可以提供使用者更彈性之選擇方式，讓使用者能將有興趣之影像部分進行搜尋，也可以避免圖中不相關之資訊影響整個比對結果，可以得到更合乎人眼直覺之結果。系統實作上，本研究選擇蝴蝶之影像建立影像資料庫，由於蝴蝶是色彩豐富之昆蟲，故將有助於本研究結果之驗證。

With the advent of multimedia computer, the voice and images could be stored in database. How to retrieve the information user want is a heard question. To query the large numbers of digital images which human desired is not a simple task. The studies of traditional image database retrieval use color, shape, and content to analyze a digital image, and create the index file. But they cannot promise that use the similar index files will find the similar images, and the similar images can get the similar index files.
In this thesis, we propose a new method to analyze a digital image by fractal code. Fractal coding is an effective method to compress digital image. In fractal code, the image is partitioned into a set of non-overlapping range blocks, and a set of overlapping domain blocks is chosen from the same image. For all range blocks, we need to find one domain block and one iteration function such that the mapping from the domain block is similar to the range block. Two similar images have similar iterated functions, and two similar iterated functions have similar attractors. In these two reasons, we use the iteration function to create index file. We have proved fractal code can be a good index file in chapter 2.
In chapter 3, we implement the fractal-based image database. In this system, we used fractal code to create index file, and used Fisher discriminate function, color, complexity, and illumination to decide the output order.

中文摘要 i
第一章 相關研究 5
1.1以顏色為特徵 6
1.2以形狀為特徵 9
1.3以內容進行分析 12
1.4影像尺寸不變 14
1.5影像位移不變 17
1.6影像旋轉不變 19
1.7IBM QBIC(TM)系統 20
1.7.1使用顏色搜尋 21
1.7.2使用配置搜尋 22
1.7.3商標搜尋系統 24
1.7.4郵票搜尋系統 28
1.8Blobworld 30
1.9碎形在影像搜尋的應用 33
1.10良好資料搜尋系統 35
第二章 基本理論 37
2.1資料庫搜尋 37
2.2碎形 40
2.2.1 轉換之收歛性 43
2.2.2 迭代函數系統 ( iterative function system) 44
2.2.3 影像分割 45
2.2.4 迭代函數 46
2.2.5 Orthogonal Basis IFS 49
2.3定理證明 54
2.4 Nona-tree分解 60
第三章 研究方法步驟及結果 64
3.1研究方法 65
3.2 步驟 66
3.2.1 資料庫建立 66
3.2.2 碎形編碼（Orthonormal IFS） 67
3.2.3 整張圖形進行索引 74
3.2.4 部分圖形進行索引 78
3.2.5 影像搜尋結果 86
第四章 結論 89
第五章 參考資料 91
目錄A 97

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