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)相似影像能產生相似索引檔，(b)相似索引檔能取回相似影像。
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，在原影像中找到一個較大方塊及一轉換函數，使得較大方塊經此一函數處理後，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，根據固定點（Fixed Point）性質，使用此函數集不斷進行迭代轉換（Iterated Transformation），無論初始影像為何，終將得到同一歸結圖。由這樣結果可知，真正能影響結果因素是此函數集，或稱迭代函數系統（Iterated Function System，IFS），本研究運用這項重要特性，將影像經碎形編碼，得到每張影像迭代函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兩性質(a)相似影像能產生相似索引檔，(b)相似索引檔能取回相似影像。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。
影像經碎形編碼後，將得到相當大量資料，若以暴力法進行比對，需要O(n!)時間，因此，需要使用一更有效率方法。在多變量分析中，有一套理論－區別分析（Discriminant Analysis）可處理影像編碼後得到大量資料。區別分析可用來區別兩個或多個群體，在這，將每張影像碎形迭代函數視為一群體，群體中包含許多變數（每個方塊編碼後所得之碎形迭代函數），使用費雪（R. A. Fisher）區別函數區別兩張影像，依區別程度來判定影像相似度，再配合碎形函數中包含之資訊，決定資料庫中所有影像與輸入影像之相關度排名。
系統實作上，本研究選擇兩部電影建立影像資料庫，分別為臥虎藏龍及安娜與國王，由於電影為連續影像，短間隔時間內影像變化不大，要取得多樣化影像，需從較大差異時間取出，在第四章中提出了影像資料選取存入庫建立方法。

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 3.
In chapter 4, 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
Abstract i
章節目錄 iii
圖表目錄 v
1 簡介 1
1.1 資料庫搜尋 1
1.2 碎形 4
1.2.1 轉換之收歛性 7
1.2.2 迭代函數系統 ( iterative function system) 7
1.2.3 影像分割 8
1.2.4 迭代函數 9
1.2.5 改良方法 12
1.3 區別分析 14
2 相關研究 19
2.1 以顏色為特徵 19
2.2 以形狀為特徵 22
2.3 以內容進行分析 25
2.4 IBM QBIC(TM)系統 27
2.4.1 使用顏色搜尋 27
2.4.2 使用配置搜尋 29
2.4.3 商標搜尋系統 31
2.4.4 郵票搜尋系統 35
3 定理證明與應用 38
4 研究方法步驟及結果 53
4.1 研究方法 53
4.2 步驟 54
4.2.1 資料庫建立 54
4.2.2 碎形編碼 56
4.2.3 費雪區別函數 62
4.2.4 輸出排名 66
5 結論 72
6 參考資料 74
附錄 A 79
附錄 B 80

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