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Similarity Measures
September 1999 (vol. 21 no. 9)
pp. 871-883

Abstract—With complex multimedia data, we see the emergence of database systems in which the fundamental operation is similarity assessment. Before database issues can be addressed, it is necessary to give a definition of similarity as an operation. In this paper, we develop a similarity measure, based on fuzzy logic, that exhibits several features that match experimental findings in humans. The model is dubbed Fuzzy Feature Contrast (FFC) and is an extension to a more general domain of the Feature Contrast model due to Tversky. We show how the FFC model can be used to model similarity assessment from fuzzy judgment of properties, and we address the use of fuzzy measures to deal with dependencies among the properties.

[1] P. Aigrain, H.-J. Zhang, and D. Petkovic, “Content-Based Representation and Retrieval of Visual Media: A State-of-the-Art Review,” Multimedia Tools and Appliactions, vol. 3, pp. 179-202, 1996.
[2] F.G. Ashby and N.A. Perrin, “Toward a Unified Theory of Similarity and Recognition,” Psychological Review, vol. 95, no. 1, pp. 124-150, 1988.
[3] F. Attneave, “Dimensions of Similarity,” Am. J. Psychology, vol. 63, pp. 516-556, 1950.
[4] E. Brunswik, Perception and the Repreentative Design of Psychological Experiments. Univ. of California Press, 1956.
[5] G. Debreu, “Topological Methods in Cardinal Utility Theory,” Mathematical Models in the Social Sciences, K. Arrow, S. Karlin, and P. Suppes, eds. Stanford Univ. Press, 1960.
[6] D.A. Narasimhalu, M.S. Kankanhalli, and J. Wu, “Benchmarking Multimedia Databases,” Multimedia Tools and Applications, vol. 4, no. 3, pp. 333-355, 1997.
[7] D.M. Ennis, J.J. Palen, and K. Mullen, “A Multidimensional Stochastic Theory of Similarity,” J. Math. Psychology, vol. 32, pp. 449-465, 1988.
[8] A.K. Jain, Fundamentals of Digital Image Processing. Prentice Hall, 1989.
[9] R. Jain, R. Kasturi, and B.G. Schunck, Machine Vision. New York: McGraw-Hill, 1995.
[10] G. Keppel, Design and Analysis. A Researcher's Handbook. Upper Saddle River, N.J.: Prentice Hall, 1991.
[11] C.L. Krumhansl, “Concerning the Applicability of Geometric Models to Similarity Data: The Interrelationship between Similarity and Spatial Density,” Psychological Review, vol. 85, pp. 445-463, 1978.
[12] S.W. Link, The Wave Theory of Difference and Similarity. Lawrence Erlbaum Assoc., 1992.
[13] F. Liu and R.W. Picard, "Periodicity, Directionality, and Randomness: Wold Features for Perceptual Pattern Recognition," Proc. Int'l Conf. Pattern Recognition, vol. II, pp. 184-185,Jerusalem, Oct. 1994.
[14] B.S. Manjunath and W.Y. Ma, “Texture Features for Browsing and Retrieval of Image Data,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 8, pp. 837-842, Aug. 1996
[15] K. Miyajima and A. Ralescu, “Modeling of Natural Objects Including Fuzziness and Application to Image Understanding,” Proc. Second IEEE Int'l Conf. Fuzzy Systems, pp. 1,049-1,054, 1993.
[16] E. Rosh, “Cognitive Reference Points,” Cognitive Psychology, vol. 7, pp. 532-547, 1975.
[17] E.Z. Rothkopf, “A Measure of Stimulus Similarity and Errors in Some Paired-Associate Learning Tasks,” J. Experimental Psychology, vol. 53, pp. 94-101, 1957.
[18] S. Santini and R. Jain, “The Use of Psychological Similarity Measure for Queries in Image Databases,” technical report, Visual Computing Laboratory, Univ. of California, San Diego, 1996, available athttp://www.cfar.umd.edu/~kanungo/pubs/phdthesis.ps.Zhttp:/ /www-cse.ucsd.edu/users ssantini.
[19] S. Santini and R. Jain, “Similarity is a Geometer,” Multimedia Tools and Applications, vol. 5, no. 3, pp. 277-306, 1997.
[20] R.N. Shepard, “The Analysis of Proximities: Multidimensional Scaling with Unknown Distance Function, Part I,” Psychometrika, vol. 27, pp. 125-140, 1962.
[21] R.N. Shepard, “Toward a Universal Law of Generalization for Physical Science,” Science, vol. 237, pp. 1,317-1,323, 1987.
[22] M.J. Swain and B.H. Ballard, “Color Indexing,” Int'l J. Computer Vision, vol. 7, no. 1, pp. 11-32, 1991.
[23] L.L. Thurstone, “A Law of Comparative Judgement,” Psychological Review, vol. 34, pp. 273-286, 1927.
[24] W.S. Torgerson, “Multidimensional Scaling of Similarity,” Psychometrika, vol. 30, pp. 379-393, 1965.
[25] A. Tversky, “Features of Similarity,” Psychological Review, vol. 84, no. 4, pp. 327-352, July 1977.
[26] A. Tversky and I. Gati, “Similarity, Separability, and the Triangle Inequality,” Psychological Review, vol. 89, pp. 123-154, 1982.
[27] A. Tversky and D.H. Krantz, “The Dimensional Representation and the Metric Structure of Similarity Data,” J. Math. Psychology, vol. 7, pp. 572-597, 1970.
[28] Vision Texture, Web Page,http://www-white.media.mit.edu/vismod/imagery/ VisionTexturevistex.html.

Index Terms:
Similarity measures, content-based retrieval, image databases, perceptual similarity, image distances.
Citation:
Simone Santini, Ramesh Jain, "Similarity Measures," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 9, pp. 871-883, Sept. 1999, doi:10.1109/34.790428
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