Similarity/dissimilarity measures are at the core of image registration methods. In a comparative study  sponsored
by Image Registration and Fusion Systems various similarity/dissimilarity measures were compared for accuracy
under noise and change in modality. The results are summarized below. References to the original sources of the
measures are also provided.
Similarity/Dissimilarity Measures
for Image registration
Image Registration and Fusion Systems     
(Left) An image of a Martian Rock, courtesy of NASA. (Right) Noisy image of the Martian Rock. Gaussian noise of standard deviation
20 was added to the image.
(Left) Band 2 and (Right) band 4 of a Landsat TM image of a small desert city, courtesy of USGS.
Templates of radius 15 pixels were selected centered at each pixel in the left image. The templates were then
searched for in the right image. The number of correct matches obtained divided by the number of templates
selected for matching was multiplied by 100 to obtain percent correct matches for a number of similarity and
dissimilarity measures. The results are summarized below. The best similarit measure for the noisy image pair was
found to be Kendall's Tau, while the best dissimilarity measure was found to be the square L2 norm. For the
multimodality image pair, the best similarity measure was again found to be Kendall's Tau, while the best
dissimilarity measure was found to be incremental sign distance.
References

  1. K. Pearson, Contributions to the mathematical theory of evolution, III, Regression, heredity, and panmixia, Philosophical
    Transactions Royal Society London, Series A, vol. 187, 1896, 253–318.
  2. S. Theodoridis and K. Koutroumbas, Pattern Recognition, Fourth Edition, Academic Press, 2009, p. 606, 605.
  3. A. Venot, J. F. Lebruchec, J. L. Golmard, and J. C. Roucayrol, An automated method for the normalization of scintigraphic
    images, J. Nucl. Med., vol. 24, 1983, 529–531.
  4. A. Venot, J. Y. Devaux, M. Herbin, J. F. Lebruchec, L. Dubertret, Y. Raulo, and J. C. Roucayrol, An automated system for the
    registration and comparison of photographic images in medicine, IEEE Trans. Medical Imaging, vol. 7, no. 4, 1988, 298–
    303.
  5. C. Spearman, The proof and measurement of association between two things, The American Journal of Psychology, vol.
    15, no. 1, 1904, 72–101.
  6. M. G. Kendall, A new measure of rank correlation, Biometrika, vol. 30, 1938, 81–93.
  7. R. A. Gideon and R. A. Hollister, A rank correlation coefficient, Journal of the American Statistical Association, vol. 82, no.
    398, 1987, 656–666.
  8. N. Bhat and S. K. Nayar, Ordinal measures for image correspondence, IEEE Trans. Pattern Analysis and Machine
    Intelligence, vol. 20, no. 4, 1998, 415–423.
  9. K. Pearson, Mathematical contributions to the theory of evolution, XIV, On the general theory of skew correlation and non-
    linear regression, Drapers’ Company Research Memoirs, Biometric Series, II, London, Dulau and Co., 1905, 54 pages.
  10. A. Collignon, F. Maes, D. Delaere, D. Vandermeulen, P. Suetens, and A. Marchal, Automated multimodality image
    registration based on information theory, Proc. Information Processing in Medicine Conf., 1995, 263–174.
  11. A. R´enyi, On measures of entropy and information, Proc. Fourth Berkeley Symposium on Mathematical Statistics
    Probability, University of California Press, Berkeley, CA, vol. 1, 1961, 547–561; also available in Selected Papers of Alfr´ed
    R´enyi, vol. 2, 1976, 525–580.
  12. M. P. Wachowiak, R. Smolikova, G. D. Tourassi, and A. S. Elmaghraby, Similarity metrics based on nonadditive entropies
    for 2D-3D multimodal biomedical image registration, Medical Imaging Conf., Proc. SPIE, vol. 5032, San Diego, CA, 2003,
    1090–1100.
  13. 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, 2004, 1506–1518.
  14. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, Second Edition, Wiley-Interscience Publishing, New York,
    2001.
  15. G. D. Evangelidis and E. Z. Psarakis, Parametric image alignment using enhanced correlation coefficient maximization,
    IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 30, no. 10, 2008, 1858–1865.
  16. S. Kaneko, I. Murase, and S. Igarashi, Robust image registration by increment sign correlation, Pattern Recognition, vol. 35,
    no. 10, 2002, 2223–2234.
  17. R. P.Woods, S. R. Cherry, and J. C. Mazziotta, Rapid automatd algorithm for aligning and reslicing PET images, Journal of
    Computer Assisted Tomography, vol. 16, 1992, 620–633.
  18. R. P. Woods, J. C. Mazziotta, S. R. Cherry, MRI-PET registration with automated algorithm, Journal of Computer Assisted
    Tomography, vol. 17, no. 4, 1993, 536–546.
  19. D. L. G. Hill, D. J. Hawkes, N. A. Harrison, and C. F. Ruff, A strategy for automated multimodality image registration
    incorporating anatomical knowledge and imager characteristics, Proc. 13th Int’l Conf. Information Processing in Medical
    Imaging, 1993, 182–196.
  20. C. E. Shannon, The mathematical theory of Communication, in book with the same title by C. E. Shanno and W. Weaver,
    University of Illinois Press, Urbana, 1949, reprint 1998, 29–125.
  21. N. F. Rougon, C. Petitjean, and F. Preteux, Variational non rigid image registration using exclusive f -information, Proc. Int’l
    Conf. Image Processing, Los Alamitos, CA, 2003, 703–706.
Each similarity measure may be purchased separately as a library function. For more
information, please contact Image Registration and Fusion Systems: cs@imgfsr.com