nips nips2007 nips2007-193 nips2007-193-reference knowledge-graph by maker-knowledge-mining

193 nips-2007-The Distribution Family of Similarity Distances


Source: pdf

Author: Gertjan Burghouts, Arnold Smeulders, Jan-mark Geusebroek

Abstract: Assessing similarity between features is a key step in object recognition and scene categorization tasks. We argue that knowledge on the distribution of distances generated by similarity functions is crucial in deciding whether features are similar or not. Intuitively one would expect that similarities between features could arise from any distribution. In this paper, we will derive the contrary, and report the theoretical result that Lp -norms –a class of commonly applied distance metrics– from one feature vector to other vectors are Weibull-distributed if the feature values are correlated and non-identically distributed. Besides these assumptions being realistic for images, we experimentally show them to hold for various popular feature extraction algorithms, for a diverse range of images. This fundamental insight opens new directions in the assessment of feature similarity, with projected improvements in object and scene recognition algorithms. 1


reference text

[1] B. G. Batchelor. Pattern Recognition: Ideas in Practice. Plenum Press, New York, 1995.

[2] E. Bertin. Global fluctuations and Gumbel statistics. Physical Review Letters, 95(170601):1–4, 2005.

[3] E. Bertin and M. Clusel. Generalised extreme value statistics and sum of correlated variables. Journal of Physics A, 39:7607, 2006.

[4] W. J. Conover. Practical nonparametric statistics. Wiley, New York, 1971.

[5] Corel Gallery. www.corel.com.

[6] L. Fei-Fei and P. Perona. A bayesian hierarchical model for learning natural scene categories. In CVPR, 2005.

[7] A. Ferencz, E.G. Learned-Miller, and J. Malik. Building a classification cascade for visual identification from one example. In Proceedings of the International Conference Computer Vision, pages 286–293. IEEE Computer Society, 2003.

[8] R. Fergus, P. Perona, and A. Zisserman. A sparse object category model for efficient learning and exhaustive recognition. In Proceedings of the Computer Vision and Pattern Recognition. IEEE, 2005.

[9] J. M. Geusebroek, R. van den Boomgaard, A. W. M. Smeulders, and H. Geerts. Color invariance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(12):1338–1350, 2001.

[10] E. J. Gumbel. Statistics of Extremes. Columbia University Press, New York, 1958.

[11] C. Harris and M. Stephans. A combined corner and edge detector. In Proceedings of the 4th Alvey Vision Conference, pages 189–192, Manchester, 1988.

[12] F. Jurie and B. Triggs. Creating efficient codebooks for visual recognition. In ICCV, pages 604–610, 2005.

[13] D. G. Lowe. Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision, 60(2):91–110, 2004.

[14] J. M. Marin, M. T. Rodriquez-Bernal, and M. P. Wiper. Using weibull mixture distributions to model heterogeneous survival data. Communications in statistics, 34(3):673–684, 2005.

[15] R. S. Michalski, R. E. Stepp, and E. Diday. A recent advance in data analysis: Clustering objects into classes characterized by conjunctive concepts. In L. N. Kanal and A. Rosenfeld, editors, Progress in Pattern Recognition, pages 33–56. North-Holland Publishing Co., Amsterdam, 1981.

[16] K. Mikolajczyk, B. Leibe, and B. Schiele. Multiple object class detection with a generative model. In CVPR, 2006.

[17] K. Mikolajczyk and C. Schmid. A performance evaluation of local descriptors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(10):1615–1630, 2005.

[18] K. Mikolajczyk, T. Tuytelaars, C. Schmid, A. Zisserman, J. Matas, F. Schaffalitzky, T. Kadir, and L. Van Gool. A comparison of affine region detectors. International Journal of Computer Vision, 65(1/2):43–72, 2005.

[19] K. Mosler. Mixture models in econometric duration analysis. Applied Stochastic Models in Business and Industry, 19(2):91–104, 2003.

[20] NIST/SEMATECH. e-Handbook of Statistical Methods. NIST, http://www.itl.nist.gov/div898/handbook/, 2006.

[21] E. Nowak and F. Jurie. Learning visual similarity measures for comparing never seen objects. In CVPR, 2007.

[22] A. Papoulis and S. U. Pillai. Probability, Random Variables and Stochastic Processes. McGraw-Hill, New York, 4 edition, 2002.

[23] E. Pekalska and R. P. W. Duin. Classifiers for dissimilarity-based pattern recognition. In Proceedings of the International Conference on Pattern Recognition, volume 2, page 2012, 2000.

[24] C. Schmid and R. Mohr. Local grayvalue invariants for image retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(5):530–535, 1997.

[25] J.C. van Gemert, J.M. Geusebroek, C.J. Veenman, C.G.M. Snoek, and Arnold W.M. Smeulders. Robust scene categorization by learning image statistics in context. In CVPR Workshop on Semantic Learning Applications in Multimedia (SLAM), 2006. 8