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Efficient Color Histogram Indexing for Quadratic Form Distance Functions
July 1995 (vol. 17 no. 7)
pp. 729-736

Abstract—In image retrieval based on color, the weighted distance between color histograms of two images, represented as a quadratic form, may be defined as a match measure. However, this distance measure is computationally expensive (naively O(N2) and at best O(N) in the number N of histogram bins) and it operates on high dimensional features (O(N)). We propose the use of low-dimensional, simple to compute distance measures between the color distributions, and show that these are lower bounds on the histogram distance measure. Results on color histogram matching in large image databases show that prefiltering with the simpler distance measures leads to significantly less time complexity because the quadratic histogram distance is now computed on a smaller set of images. The low-dimensional distance measure can also be used for indexing into the database.

[1] R. Agrawal, C. Faloutsos, and A. Swami, “Efficient Similarity Search in Sequence Databases,” Proc. Fourth Int'l Conf. Foundations of Data Organization and Algorithms, pp. 69-84, Oct. 1993.
[2] E. Binaghi,I. Gagliardi,, and R. Schettini,“Indexing and fuzzy logic-based retrieval of color images,” Visual Database Systems, II, IFIP Trans. A-7, pp. 79-92, Elsevier Science Publishers, 1992.
[3] T.M. Cover and J.A. Thomas, Elements of Information Theory. John Wiley&Sons, 1991.
[4] P. Dewilde and E.F. Deprettere,“Singular value decomposition, an introduction,” SVD and Signal Processing: Algorithms, Applications, and Architectures, E.F. Deprettere, ed., pp. 3-42.New York: Elsevier Science Publishing Co., 1988.
[5] T. Feder,“On a quadratic form for points in space,” IBM Internal Note, 1993.
[6] G.H. Golub and C.F. van Loan,Matrix Computations. The Johns Hopkins Univ. Press, 1989.
[7] J. Hasegawa,N. Okada,, and J. Toriwaki,“Intelligent retrieval of chest x-ray database using sketches,” Systems and Computers in Japan, vol. 20, no. 7, pp. 29-42, 1989.
[8] K. Hirata and T. Kato, “Query by Visual Example,” Advances in Database Technology EDBT '92, Third Int'l Conf. Extending Database Technology, 1992.
[9] IMSL, Inc.,User’s Manual MATH/Library.Texas: IMSL, Inc., 1991.
[10] M. Ioka,“A method of defining the similarity of images on the basis of color information,” Technical report RT-0030, IBM Tokyo Research Lab, 1989.
[11] M.A. Ireton and C.S. Xydeas,“Classification of shape for content retrieval of images in a multimedia database,” Sixth Int’l Conf. on Dig. Proc. of Signals in Comm., pp. 111-116,Loughborough, U.K., Sept.2-6, 1990.
[12] H.V. Jagadish, “A Retrieval Technique for Similar Shapes,” Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 208-217, 1991.
[13] D.G. Luenberger,Linear and Nonlinear Optimization. Mass.: Addison-Wesley, 1984.
[14] M. Miyahara and Y. Yoshida,“Mathematical transform of (R, G, B) color data to Munsell (H, V, C) color data,” Visual Communication and Image Processing, vol. 1,001, pp. 650-657, SPIE, 1988.
[15] A. Mood,F. Graybill,, and D. Boes,Introduction to the Theory of Statistics. McGraw-Hill series in probability and statistics, McGraw-Hill, third edition, 1963.
[16] W. Niblack,R. Berber,W. Equitz,M. Flickner,E. Glasman,D. Petkovic,, and P. Yanker,“The QBIC project: Querying ims. by content using color, texture, and shape,” SPIE 1908, Storage and Retrieval for Image and Video Dbases, Feb. 1993.
[17] C.L. Novak and S.A. Shafer,“Color vision,” Physics-Based Vision COLOR, pp. 1-10, Jones and Bartlett, 1992.
[18] M. Otterman,“Approximate matching with high dimensionality R-trees,” MSc scholarly paper, Dept. of Computer Science, Univ. of Maryland, College Park, Md., supervised by C. Faloutsos, 1992.
[19] A. Pentland,R. Picard,G. Davenport,, and B. Welsh,“The BT/MIT project on advanced image tools for telecommunications: An overview,” Technical report 212, MIT Media Lab. Perceptual Comp. Group TR, 1992.
[20] M.J. Swain and B.H. Ballard, “Color Indexing,” Int'l J. Computer Vision, vol. 7, no. 1, pp. 11-32, 1991.

Index Terms:
Color histogram matching, image querying, image databases, efficient multidimensional feature matching, histogram indexing.
Citation:
James Hafner, Harpreet S. Sawhney, Will Equitz, Myron Flickner, Wayne Niblack, "Efficient Color Histogram Indexing for Quadratic Form Distance Functions," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 7, pp. 729-736, July 1995, doi:10.1109/34.391417
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