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Multiple Subclass Pattern Recognition: A Maximin Correlation Approach
April 1995 (vol. 17 no. 4)
pp. 418-431

Abstract—This paper addresses a correlation based nearest neighbor pattern recognition problem where each class is given as a collection of subclass templates. The recognition is performed in two stages. In the first stage the class is determined. Templates for this stage are created using the subclass templates. Assignment into subclasses occurs in the second stage. This two stage approach may be used to accelerate template matching. In particular, the second stage may be omitted when only the class needs to be determined.

We present a method for optimal aggregation of subclass templates into class templates. For each class, the new template is optimal in that it maximizes the worst case (i.e., minimum) correlation with its subclass templates. An algorithm which solves this maximin optimization problem is presented and its correctness is proved. In addition, test results are provided, indicating that the algorithm’s execution time is polynomial in the number of subclass templates.

We show tight bounds on the maximin correlation. The bounds are functions only of the number of original subclass templates and the minimum element in their correlation matrix.

The algorithm is demonstrated on a multifont optical character recognition problem.

[1] L. Capodiferro,R. Cusani,G. Jacovitti,, and M. Vascotto,“Correlation-based technique for shift, scale, and rotation independent object classification,” Proc. IEEE Int’l Conf. Acoustics, Speech, and Signal Processing, Apr. 1987.
[2] T.M. Cover and P. Hart, "Nearest Neighbor Pattern Classification," Proc. IEEE Trans. Information Theory, pp. 21-27, 1967.
[3] R.W. Cottle and G.B. Dantzig,“Complementary pivot theory of mathematical programming,” Linear Algebra Applications, vol 1, pp. 103-105, 1968.
[4] G.B. Dantzig,Linear Programming and Extensions, Princeton Univ. Press, 1993.
[5] R.O. Duda and P.E. Hart,Pattern Classification and Scene Analysis. John Wiley and Sons, New York, 1973.
[6] K. Fukunaga and T.E. Flick,“An optimal global nearest neighbor metric,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, May 1984.
[7] P.E. Gill,W. Murray,, and M.H. Wright,Practical Optimization, Academic Press, United Kingdom, 1981.
[8] A. Goshtasby,S.H. Gage,, and J.F. Bartholic,“A two-stage cross-correlation approach to template matching,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 3, pp. 374-378, May 1984.
[9] M.S. Grewal and A.P. Andrews,Kalman Filtering : Theory and Practice, Prentice Hall, 1993.
[10] O. Hoessjer and M. Mettiji,“Robust multiple classification of known signals in additive noise,” IEEE Trans. Information Theory, vol. 39, no. 2, March 1993.
[11] S. Huang,“Criteria of template matching and image sensor noise analysis,” Proc. IEEE CS Workshop Computer Vision, pp. 315-317,Miami Beach, Fla., Nov. 1987.
[12] F. Jenkins,J. Kanai,, and T.A. Nartker,“Using ideal images to establish a baseline of OCR performance,” Symp. Document Analysis and Information Retrieval,Las Vegas, Nev., 1993.
[13] S. Kahan,T. Pavlidis,, and H. S. Baird,“On the Recognition of Printed Characters of Any Font and Size,” IEEE-PAMI, vol. 9, no. 2, pp. 274-288, 1987.
[14] S. Kumar,Recent Developments in Mathematical Programming, Gordon and Breach Science Publishers, 1991.
[15] J.C. Lee and E. Milios,“Matching range images of human faces,” Proc. IEEE CS Third Int’l Conf. Computer Vision, pp. 722-726, 1990.
[16] K. Li,M. Ferdousi,M. Chen,, and T.T. Nguyen,“Image matching with multiple templates,” Proc. CS Workshop Computer Vision and Pattern Recognition Conf., pp. 610-613,Miami Beach, Fla., June 1986.
[17] D. Luenberger,Linear and Nonlinear Programming, Addison-Wesley, Reading, Mass., 1989.
[18] MATLAB, High-Performance Numeric Computation and Visualization Software Reference Guide, The MathWorks, Inc., Natick, Mass., 1992.
[19] S. Mori, C.Y. Suen, and K. Yamamoto, “Historical Review of OCR Research and Development,” Proc. IEEE, vol. 80, no. 7, pp. 1,029-1,058, 1992.
[20] M. Nakashima,T. Koezuka,N. Hiraoka,, and T. Inagaki,“Automatic pattern recognition system with self-learning algorithm based on feature template matching,” Proc. SPIE, vol. 635, pp. 480-486, 1986.
[21] H.K. Ramapriyan,“A multilevel approach to sequential detection of pictorial features,” IEEE Trans. Computers, vol. 25, no. 1, pp. 66-78, Jan. 1976.
[22] S.V. Rice,J. Kanai,, and T.A. Nartker,“A report on the accuracy of OCR devices,” Symp. Document Analysis and Information Retrieval,Las Vegas, Nev., 1992.
[23] A. Rosenfeld and A.C. Kak,Digital Picture Processing. Academic Press, 2nd ed., 1982
[24] A. Rosenfeld and G.J. Vanderburg,“Coarse-fine template matching,” IEEE Trans. Systems, Man and Cybernetics, vol. 7, pp. 104-107, 1977.
[25] M. Svedlow,C.D. McGillem,, and P.E. Anuta,“Experimental examination of similarity measures and preprocessing methods used for image registration,” Symp. Machine Processing Remotely Sensed Data, 1976.
[26] J.T. Tou and R.C. Gonzalez,Pattern Recognition Principles. Addison-Wesley, Reading, Mass., 1974.
[27] G.J. Vanderburg and A. Rosenfeld,“Two-stage template matching,” IEEE Trans. Computers, vol. 26, pp. 384-393, Apr. 1977.

Index Terms:
Pattern recognition, nearest neighbor, template matching, correlation, maximin, minimax, clustering, multifont optical character recognition.
Hadar I. Avi-Itzhak, Jan A. Van Mieghem, Leonardo Rub, "Multiple Subclass Pattern Recognition: A Maximin Correlation Approach," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 4, pp. 418-431, April 1995, doi:10.1109/34.385977
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