The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.11 - November (2011 vol.33)
pp: 2321-2329
Bernhard A. Moser , Software Competence Center Hagenberg, Hagenberg
ABSTRACT
The paper focuses on similarity measures for translationally misaligned image and volumetric patterns. For measures based on standard concepts such as cross-correlation, L_p-norm, and mutual information, monotonicity with respect to the extent of misalignment cannot be guaranteed. In this paper, we introduce a novel distance measure based on Hermann Weyl's discrepancy concept that relies on the evaluation of partial sums. In contrast to standard concepts, in this case, monotonicity, positive-definiteness, and a homogenously linear upper bound with respect to the extent of misalignment can be proven. We show that this monotonicity property is not influenced by the image's frequencies or other characteristics, which makes this new similarity measure useful for similarity-based registration, tracking, and segmentation.
INDEX TERMS
Similarity of images, normalized cross correlation, autocorrelation, mutual information, discrepancy norm, registration, tracking, image processing, similarity measure.
CITATION
Bernhard A. Moser, "A Similarity Measure for Image and Volumetric Data Based on Hermann Weyl's Discrepancy", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.33, no. 11, pp. 2321-2329, November 2011, doi:10.1109/TPAMI.2009.50
REFERENCES
[1] H. Krim, A. Hamza, and Y. He, "An Information Divergence Measure for Isar Image Registration," Proc. IEEE Workshop Statistical Signal Processing, pp. 130-133, 2001.
[2] P. Bauer, U. Bodenhofer, and E.P. Klement, "A Fuzzy Algorithm for Pixel Classification Based on the Discrepancy Norm," Proc. Fifth IEEE Int'l Conf. Fuzzy Systems, vol. III, pp. 2007-2012, Sept. 1996.
[3] J.F. Bercher, "On Some Entropy Functionals Derived from Rényi Information Divergence," Information Sciences, vol. 178, no. 12, pp. 2489-2506, 2008.
[4] A. Bhattacharyya, "On a Measure of Divergence Between Two Statistical Populations Defined by Probability Distributions," Bull. Calcutta Math., vol. 35, pp. 99-109, 1943.
[5] B. Chazelle, The Discrepancy Method: Randomness and Complexity. Cambridge Univ. Press, 2000.
[6] R. Jain, S.N.J. Murthy, P.L.J. Chen, and S. Chatterjee, "Similarity Measures for Image Databases," Proc. IEEE Int'l Conf. Fuzzy Systems, vol. 3, pp. 1247-1254, 1995.
[7] W. Jiang, G. Er, Q. Dai, and J. Gu, "Similarity-Based Online Feature Selection in Content-Based Image Retrieval," IEEE Trans. Image Processing, vol. 15, no. 3, pp. 702-712, Mar. 2006.
[8] M.S. Khalid and M.B. Malik, "Biased Nature of Bhattacharyya Coefficient in Correlation of Gray-Scale Objects," Proc. Fourth Int'l Symp. Image and Signal Processing and Analysis, pp. 209-214, 2005.
[9] S. Kullback, Information Theory and Statistics. Wiley, 1959.
[10] O. Michailovich, Y. Rathi, and A. Tannenbaum, "Image Segmentation Using Active Contours Driven by the Bhattacharyya Gradient Flow," IEEE Trans. on Image Processing, vol. 16, no. 11, pp. 2787-2801, Nov. 2007.
[11] B. Moser and T. Hoch, "Misalignment Measure Based on Hermann Weyl's Discrepancy," Proc. 32nd Workshop of the Austrian Assoc. on Pattern Recognition, Challenges in the Biosciences: Image Analysis and Pattern Recognition Aspects, A. Kuijper, B. Heise, and L. Muresan, eds., pp. 187-198, May 2008.
[12] H. Neunzert and B. Wetton, "Pattern Recognition Using Measure Space Metrics," Technical Report 28, Dept. of Math., Univ. of Kaiserslautern, Nov. 1987.
[13] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods. SIAM, 1992.
[14] S. Peng, J. Yang, and K. Zhou, "Study on Bhattacharyya Coefficients within Mean-Shift Framework and Its Application," Soft Computing, vol. 10, no. 12, pp. 1127-1134, 2006.
[15] A. Pérez-García, V. Ayala-Ramírez, R.E. Sánchez-Yáñez, and J.G. Aviña-Cervantes, "Monte Carlo Evaluation of the Hausdorff Distance for Shape Matching," J.F.M. Trinidad, J.A. Carrasco-Ochoa, and J. Kittler, eds., Progress in Pattern Recognition, Image Analysis and Applications, pp. 686-695, Springer, 2006.
[16] J.P.W. Pluim, J.B.A. Maintz, and M.A. Viergever, "Mutual Information-Based Registration of Medical Images: A Survey," IEEE Trans. Medical Imaging, vol. 22, no. 8, pp. 986-1004, Aug. 2003.
[17] J.P.W. Pluim, J.B.A. Maintz, and M.A. Viergever, "f-Information Measures in Medical Image Registration," IEEE Trans. Medical Imaging, vol. 23, no. 12, pp. 1506-1518, Dec. 2004.
[18] A. Rényi, "On Measures of Entropy and Information," Proc. Fourth Berkeley Symp. Math. Statistics and Probability, vol. 1, pp. 547-561, 1961.
[19] I. Vajda, Theory of Statistical Inference and Information. Kluwer Academic, 1989.
[20] N. Vasconcelos and A. Lippman, "A Unifying View of Image Similarity," Proc. 15th Int'l Conf. Pattern Recognition, vol. 1, pp. 38-41, Aug. 2001.
[21] H. Weyl, "Über die Gleichverteilung von Zahlen Mod. Eins," Math. Ann., vol. 77, pp. 313-352, 1916.
[22] B. Zitová and J. Flusser, "Image Registration Methods: A Survey," Image and Vision Computing, vol. 21, no. 11, pp. 977-1000, 2003.
46 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool