儲存於資料庫之資料，以往多僅限於文字，由於資訊多樣化，現今多轉變為多媒體資料，如何由數量龐大影像資料符合使用者條件，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致為根據影像中顏色、形狀、紋理、物體、結構等特徵建立影像資料庫索引檔，雖可適用特定處理領域CBIR(Content-Based Image Retrieval)，但均無法保證所擷取特徵能符合(a) 高相關度影像資訊具高相關索引檔；(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，此四項基本特質。
本論文使用碎形正交基底編碼(Fractal orthonormal bases)技術結合Multiple-Instance Learning，建立熱帶魚影像資料庫，每張資料庫內影像之特徵均由對碎形正交基底之投影向量值表示。正交基底是由碎形迭代函數透過target及domain blocks比對所訓練導出，可證明相似影像具相似碎形函數，而且不相似影像具相異碎形特徵向量；換言之，特徵點相距越遠，保證其對應影像內容一定不相似，然而特徵點較靠近，則保證其影像內容相似。因此，使用碎形正交基底函數線性組合所得係數為搜尋資料庫索引鍵值，可取得相似影像，並避免找出不相似影像。
由於欲搜尋之影像很難根據單一張搜尋影像(query image)代表所有可能之形狀、大小或方位，為使搜尋條件更為明確，藉由輸入多張與目標影像正、負相關搜尋影像，透過Multiple-Instance learning 法則自動地找出與正相關影像(positive examples) 相似且與負相關(negative examples)不相似之碎形正交基底投影向量特徵，使搜尋條件更為明確，將使用者最有興趣之部分，結合具有良好索引檔之碎形正交基底之技術。
影像比對時，方法是依據MIL所擷取之特徵，找尋資料庫哪些影像具有相似特徵，計算相似度，依此作排名輸出。詳細比對時，將資料庫中有著搜尋特徵之影像，找出該所屬區域，將擷取之特徵群正規化，求得每個特徵群佔所有搜尋特徵群之比例關係，再以依正相關特徵群之比例和資料庫影像特徵群比例，類似計算histogram之方式求得特徵比例相似度之外；另外還加入計算所求得特徵群之間結構關係，與正相關範例影像之特徵群結構關係亦計算特徵結構相似度；在加入每個特徵群區域之分散程度，及簡單計算其區域變異數亦和正相關範例做比較，於上述三者加入相似性量測中。
最後本論文將實作和此三種方法VQ, thumbnail fractal, multiscale entropy 為基礎，依其上述之影像特徵和碎形正交基底投影量之特徵，觀察這些影像特徵經MIL擷取共同之特徵群，再進行相同之比對依特徵群之分散程度、比例、結構關係量測，其搜尋結果之效能如何。

The objective of the present work is to propose a novel method to extract a stable feature set representative of image content. Each image is represented by a linear combination of fractal orthonormal basis vectors. The mapping coefficients of an image projected onto each orthonormal basis constitute the feature vector. The set of orthonormal basis vectors are generated by utilizing fractal iterative function through target and domain blocks mapping. The distance measure remains consistent, i.e., isometric embedded, between any image pairs before and after the projection onto orthonormal axes. Not only similar images generate points close to each other in the feature space, but also dissimilar ones produce feature points far apart. The above statements are logically equivalent to that distant feature points are guaranteed to map to images with dissimilar contents, while close feature points correspond to similar images.
In this paper, we adapt the Multiple Instance Learning paradigm using the Diverse Density algorithm as a way of modeling the ambiguity in images in order to learning concepts used to classify images. A user labels an image as positive if the image contains the concepts, as negative if the image far from the concepts. Each example image is a bag of blocks where only the bag is labeled. The User selects positive and negative image examples to train the concepts in feature space.
From a small collection of positive and negative examples, the system learns the concepts using them to retrieve images that contain the concepts from database. Each concept having similar blocks becomes the group in each image. According groups’ location distribution, variation and spatial relations computes positive examples and database images similarity.

第一章 影像搜尋之相關研究 1
1.1 良好影像搜尋系統 1
1.2現有影像搜尋系統 1
1.2.1 以顏色為特徵 2
1.2.2 以形狀為特徵 4
1.2.3 以內容物為特徵 6
1.3 研究概述 8
第二章 碎形基本理論 9
2.1 轉換之收歛性 11
2.2 迭代函數系統 (ITERATIVE FUNCTION SYSTEM) 11
2.3 影像分割 12
2.4 迭代函數 13
2.5 碎形在影像搜尋的應用 16
2.6 ORTHOGONAL BASIS IFS 17
定理證明 21
第三章 MULTIPLE-INSTANCE LEARNING 26
3.1 定義 26
3.2 MIL 應用於影像搜尋 26
3.2.1 應用實例 28
3.3 DIVERSE DENSITY ALGORITHM 33
3.3.1 Diverse Density definition: 34
3.3.2 計算 35
3.3.3計算 36
3.3.4 Finding the maximum 37
3.3.5 例子 38
第四章 研究方法步驟及結果 40
4.1研究方法 40
4.2步 驟 40
4.2.1 資料庫建立 41
4.2.2 碎形編碼（Orthonormal IFS） 43
4.2.3 使用MIL找出共有之特徵 46
4.2.4 比對方法 49
4.3 方法比較 52
4.4 實驗結果 53
第五章 結論 72
參考文獻 73

[1] B. Mandelbrot, “The Fractal Geometry of Nature,” San Francisco, CA: Freeman, 1982.
[2] M. F. Barnsley, “Fractals Everywhere,” Academic Press, San Diego, 1988.
[3] Arnaud E. Jacquin, “A Fractal Theory of Iterated Markov Operators with Applications to Digital Image Coding,” Ph.D. Thesis, Georgia Institute of Technology, 1989.
[4] Yuval Fisher, E. W. Jacobs, and R.D. Boss, “Iterated Transformation image compression,” NOSC Thec. Rep. TR-1408, Naval Oceans Systems Center, San Diego, CA, 1991.
[5] A.E. JACQUIN, “Image Coding based on a fractal theory of iterated contractive image transformation,” IEEE Trans. on Image Process. ,1992.
[6] G. Vines and M. H. Hayes, “Nonlinear interpolation in a one-dimensional fractal model,” In Proceedings of the fifth Digital Signal Processing Workshop, pp. 8.7.7-8.7.2, 1992.
[7] G. Vines and M.H. Hayes, “Nonlinear Address Maps in a One-Dimensional Fractal Model,” IEEE Trans. on Signal Processing, 1993.
[8] G. Vine, “Signal Modeling with Iterated Function System,” PhD thesis, Georgia Institute of Technology, Atlanat, GA, 1993.
[9] Yuval Fisher, “Fractal image compression: theory and application”, Springer, New York, 1996.
[10] Howard Anton, “Elementary Linear Algebra,” Wiley, 1994.
[11] QBIC Project, IBM Research, http://wwwqbic.almaden.ibm.com.
[12] The DMOZ Open Directory Project. http://dmoz.org.
[13] E. Remias, G. Sheikholeslmal, and A. ZHANG, “Block-oriented image decomposition and retrieval in image database systems,” Proceedings of 1996 International Workshop on Multimedia Database Management Systems, Aug. 1996.
[14] Smith, J.R., and Chang, S.F., “VisualSEEk: a fully automated content-based image query system,” in Proceedings ACM Multimedia, Boston MA, ACM Press, 87-98, 1996.
[15] WY. Ma and BS Manjunath, “NeTra: a Toolbox for Navigating Large Image Databases,” Multimedia Systems, Vol. 7, pp 184-198, 1999.
[16] Th. Gevers and AWM Smeulders, “PicToSeek: Combining Color and Shape Invariant Features for Image Retrieval pdf file,” IEEE Trans. on Image Processing, Vol. 9, No. 1, pp. 102-119, January, 2000.
[17] J. Guo, A. Zhang, E. Remias, and Sheikholeslami, G., “Image decomposition and representation in large image database systems,” J. Vis. Commun. Image Represent., 1997.
[18] X. Wanand, C.C.J Kuo, “A new approach to image retrieval with hierarchical color clustering,” IEEE Trans. on Circuits and Systems for Video Technology, vol. 8, no. 5, pp. 628-643, 1998.
[19] Hui Xu, Mengyang Liao, “Cluster-Based Texture Matching for Image Retrieval,” Image Processing ICIP 98. Proceedings International Conference on, Vol. 2, pp. 766-769, 1998.
[20] Chad Carson, “Blobworld: a system for region-based image indexing and retrieval,” International conference on visual information system, 1999.
[21] D. Androutsos, K.N. Plataniotis, and A.N. Ventsanopoulos, “A novel Vector-based approach to color image retrieval using a vector angular-based distanced measure,” Computer Vision and Image Understanding, vol. 75, no. 1/2, pp. 46-58, 1999.
[22] S.C. Pei and C.M. Cheng, “Extracting color features and dynamic matching for image data-base retrieval,” IEEE Trans. on Circuits and Systems for Video Technology, vol. 9, no. 3, pp. 501-512, 1999.
[23] Euripides G.M. Petrakis, Evangelos Milios, “Efficient Retrieval by Shape Content,” Multimedia Computing and Systems, IEEE International Conference on, Vol. 2, pp. 616-621, 1999.
[24] Jim Z. C. Lai, Fu-Te Hsu, “Image Retrieval Using Semantic Classification and Partial Match,” The 13th IPPR Conference on Computer and Vision, Graphics and Image Processing, 1-6, 2000.
[25] Z.Wang, Z.Chi and D.Feng, “Content-based image retrieval using block-constrained fractal coding and nona-tree decomposition,” IEEE Signal Processing, 2000.
[26] S. Berretti, “Indexed retrieval by shape appearance,” IEE Proc.-Vis. Image Signal Processing, Vol. 147, No. 4,pp. 356-362, 2000.
[27] Elif Albuz, Erturk Kocalar, and Ashfaq A.Khokhar, “Scalable Color Image Indexing and Retrieval Using Vector Wavelets,” IEEE Trans. on Knowledge and Data Engineering, Vol. 13, No. 5, 2001.
[28] Gaurav Aggrwal, Ashwin T. V., ans Sugata Ghosal, “An Image Retrieval System With Automatic Query Modification,” IEEE Trans. on Multimedia, Vol. 4, NO. 2, JUNE 2002.
[29] Z. Wang, Z. Chi and D. Feng, “Shape based leaf image retrieval,” IEEE Trans. on Image Signal Progress, vol.150, no. 1, 2003.
[30] Khanh Vu, Kien A. Hua, “Image retrieval based on region of interest,” IEEE Trans. on knowledge and data engineering, vol. 15, no. 4, 2003.
[31] Young Deok Chum, “Image retrieval using BDIP and BVLC moments,” IEEE Trans. on circuits and systems for video technology, vol. 13, no. 9, 2003.
[32] John Y. Chiang, Z. Z. Tsai, “Image based on Fractal Signatures,” National Computer Symposium in Taichung, 2003.
[33] O. Maron, “Learning from Ambiguity,” Ph.D. dissertation, Massachusetts Institute of Technology, 1998.
[34] O. Maron and A. Lakshmi Ratan, “Multiple-instance learning for natural scene classification,” in Machine Learning: Proc. 15th International Conference, 1998.
[35] O. Maron and T. Lozano-P´erez, “A framework for multiple-instance learning,” in Advances in Neural Information Processing Systems, Vol. 10, pp. 570-576, 1997.
[36] C. Yang, “Image Database Retrieval With Multiple-Instance Learning Techniques,” M.S. thesis, Massachusetts Institute of Technology, 1998. http://www.ai.mit.edu/people/cheng/thesis/image-mi.ps.gz.
[37] Idris, F. and S. Panchanathan, “Image and video indexing using vector quantization”, Machine Vision and Applications, vol. 10, pp. 43-50.1997.
[38] Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizer design,” IEEE Trans. on Commun., vol. COM-28, pp. 84–95, Jan.1980.
[39] Sticker M, “Bounds for the discrimination power of color-indexing techniques,” SPIE Proc： Storage Retrieval Image Video Databases II 2185, pp. 15-24,1994.
[40] Harvey A. Cohen, “Fractal Image Coding for Thumbnail-based image Access,” Proc. Int'l Conf Signal Processing Applications, ISSPA'96, Gold Coast, Aug 26-28, vol. 1, pp. 158-161, 1996.
[41] Harvey A. Cohen, “Thumbnail-based Image Coding Utilising the Fractal Transform,” Proc.IEEE Int'l Conf Image Processing ICIP'96, Lausanne, Switzerland, Sept 16-19, Vol. 1, pp. 145-148,1996.
[42] Harvey A. Cohen, “Access and Retrieval from Image Databases Using Image Thumbnails,” Proc. Int'l Conf Signal Processing Applications, ISSPA, Gold Coast, August 26-28, vol. 1, pp. 427-8,1996.
[43] F. Murtagh, A. Alexander, A. Bouridane, D. Crookes, J.G. Campbell, J.-L. Starck, and Z. Geradts, "Fractal and Multiscale Methods for Content-Based Image Retrieval," CIR-2000: The Challenge of Image Retrieval, Third UK Conference on Image Retrieval, Brighton, United Kingdom, May 4-5, 2000.
[44] JL Starck, F. Murtagh, and F. Bonnarel., “Multiscale entropy for semantic description of images and signals”, submitted, 2000.
[45] Stepbane Mallat., “A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, July 1989.
[46]
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