Image Retrieval Based on Fractal Signatures John Y. Chiang Z. Z. Tsai 蔣依吾 國立中山大學 資訊工程學系 E-mail: chiang@cse.nsysu.edu.tw Web: http://image.cse.nsysu.edu.tw

Block Diagram of Image retrieval System

Feature used for querying Text, color, shape, texture , spatial relations Image Retrieval Systems： IBM QBIC： color , texture, shape Berkeley BlobWorld： color, texture, location and shape of region (blobs) Columbia VisualSEEK: text, color , texture, shape, spatial relations

Ideal image retrieval 相似之影像有相似之索引檔 不相似之影像有不相似之索引檔 (a) 高相關度影像資訊有高相關索引檔 (b) 索引檔相關度高，其影像資訊相關度高 不相似之影像有不相似之索引檔 (c) 索引檔相關度低，其影像資訊相關度低 (d) 影像資訊相關度低，其索引檔相關度低 Based on Fractal Orthogonal Basis, image index satisfy the four properties.

Fractal Orthogonal Basis Vines, Nonlinear address maps in a one-dimensional fractal model, IEEE Trans. Signal Processing,1993. Training Orthonormal basis vectors. Gram-Schmidt method Compression: each image range block (R) decomposed into a linear combination, Using linear combination coefficient as a feature vector。

Proof of Theorem theorem 1： Let f , g is distance space（K，d）functions， Range block length k，f= , g= , i,j 1.. xi‧xj=0 and | xi |=1 , S={s1s2.. } f has fixed point a，S: query image a’s index, T={t1t2… }, g has fixed point b , T: database image b’s index, if a , b is close, then S , T is close； if S , T is close, then a , b is close。

(a) Proof : a , b is close , S , T is close Proof of Theorem 1 (a) Proof : a , b is close , S , T is close a , b is close , then ||a－b|| thus a , b is close , S , T is close

(b) Proof: S , T is close , a , b is close Proof of Theorem 1 (b) Proof: S , T is close , a , b is close S , T is close , then thus S , T is close , a , b is close

Proof of Theorem theorem 2： Let f , g is distance space（K，d）functions， Range block length k，f= , g= , i,j 1.. xi‧xj=0 and | xi |=1 , S={s1s2.. } f has fixed point a，S: query image a’s index, T={t1t2… }, g has fixed point b , T: database image b’s index, if a , b is not close, then S , T is not close； if S , T is not close, then a , b is not close。

(c) Proof : a , b is not close , S , T is not close Proof of Theorem 2 (c) Proof : a , b is not close , S , T is not close by theorem 1, a , b is close S , T is close thus a , b is not close , S , T is not close (d) Proof: S , T is not close , a , b is not close by theorem 1, a , b is close S , T is close thus S , T is not close , a , b is not close

Advantages based on Fractal Orthogonal Basis Compressed data can be used directly as indices for query. Image index satisfy the four properties. Similarity measurement is easy.

Orthonormal Basis Vectors (a) (b) (c) Figure 3. The 64 fractal orthonormal basis vectors of (a) R, (b) G, and (c) B color components, respectively, derived from an ensemble of 100 butterfly database images. The size of each vector is enlarged by two for ease of observation..

Fourier transform vs Fractal Orthonormal basis

Original image Compressed image

Experimental Results Image database The source of images: http://www.thais.it/entomologia/ http://turing.csie.ntu.edu.tw/ncnudlm/index.html http://www.ogphoto.com/index.html http://yuri.owes.tnc.edu.tw/gallery/butterfly http://www.mesc.usgs.gov/resources/education/butterfly/ http://mamba.bio.uci.edu/~pjbryant/biodiv/bflyplnt.htm Image size:320x240 Total of images:1013 Range block size:8x8 Domain block size:8x8 Domain block set: 64 domain blocks in each color plane

Figure 4. An image retrieval example Figure 4. An image retrieval example. The features from R, G, B color components and brightness level of the query image are all selected. The rectangular area in the upper right-hand corner provides an enlarged viewing window for the image retrieved.

Figure 6. Retrieval results based on a sub-region of a query image with scaling factors 0.8 through 1.2 and rotation angles every 30 degrees.

Future work 1. With Multiple Instance Learning, finding “ideal” feature vector, as query feature. 2. Considering spatial relations of sub-regions. 3. Increasing performance.