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Handbook of Mathematical Methods in Imaging pp 125–155Cite as

Distance Measures and Applications to Multimodal Variational Imaging

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Abstract

Today imaging is rapidly improving by increased specificity and sensitivity of measurement devices. However, even more diagnostic information can be gained by combination of data recorded with different imaging systems.

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References

  1. Ali, S.M., Silvey, S.D.: A general class of coefficients of divergence of one distribution from another. J. R. Stat. Soc. B 28, 131–142 (1966)

    MATH  MathSciNet  Google Scholar 

  2. Bajcsy, R., Kovačič, S.: Multiresolution elastic matching. Comput. Vis. Graph. 46, 1–21 (1989)

    Article  Google Scholar 

  3. Christensen, G.: Deformable shape models for anatomy. PhD thesis, Washington University, Department of Electrical Engineering (1994)

    Google Scholar 

  4. Chung, A.C.S., Wells, W.M., Norbash, A., Grimson, W.E.L.: Multi modal image registration by minimizing Kullback-Leibler distance. In: MICCAI’02: Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part II, pp. 525–532. Springer, London (2002)

    Google Scholar 

  5. Csiszár, I.: Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten. Magyar Tud Akad Mat Kutató Int Közl 8, 85–108 (1963)

    MATH  Google Scholar 

  6. Dragomir, S.S.: Some general divergence measures for probability distributions. Acta Math. Hung. 109(4), 331–345 (2005)

    Article  MATH  Google Scholar 

  7. Droske, M., Rumpf, M.: A variational approach to nonrigid morphological image registration. SIAM J. Appl. Math. 64(2), 668–687 (2003/2004) (electronic)

    Article  MathSciNet  Google Scholar 

  8. Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Mathematics and Its Applications, vol. 375. Kluwer, Dordrecht (1996)

    Book  Google Scholar 

  9. Ens, K., Schumacher, H., Franz, A., Fischer, B.: Improved elastic medical image registration using mutual information. In: Pluim, J.P.W., Reinhardt, J.M. (eds.) Medical Imaging 2007: Image Processing, vol. 6512, p 65122C. SPIE (2007)

    Chapter  Google Scholar 

  10. Fahrmeir, L., Künstler, R., Pigeot, I., Tutz, G.: Statistik, 5th edn. Springer, Berlin (2004)

    MATH  Google Scholar 

  11. Faugeras, O., Hermosillo, G.: Well-posedness of two nonrigid multi modal image registrational methods. SIAM J. Appl. Math. 64(5), 1550–1587 (2004). (electronic)

    Article  MATH  MathSciNet  Google Scholar 

  12. Feldman, D., Österreicher, F.: A note on f-divergences. Stud. Sci. Math. Hung. 24(2–3), 191–200 (1989)

    MATH  Google Scholar 

  13. Gee, J., Haynor, D., Le Briquer, L., Bajcsyand, R.: Advances in elastic matching theory and its implementation. In: CVRMed-MRCAS’97, Grenoble, pp 63–72, 1997

    Google Scholar 

  14. Guetter, C., Xu, C., Sauer, F., Hornegger, J.: Learning based non-rigid multi modal image registration using Kullback-Leibler divergence. In: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2005, Palm Springs. Lecture Notes in Computer Science, vol. 3750, pp. 255–262. Springer (2005)

    Chapter  Google Scholar 

  15. Haber, E., Modersitzki, J.: Intensity gradient based registration and fusion of multi modal images. In: Methods of Information in Medicine, pp. 726–733. Schattauer Verlag, Stuttgart (2006)

    Google Scholar 

  16. Henn, S., Witsch, K.: Multi modal image registration using a variational approach. SIAM J. Sci. Comput. 25(4), 1429–1447 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hermosillo, G.: Variational methods for multi modal image matching. PhD thesis, Université de Nice, France (2002)

    Google Scholar 

  18. Hömke, L.: A multigrid method for elastic image registration with additional structural constraints. PhD thesis, Heinrich-Heine Universität, Düsseldorf (2006)

    Google Scholar 

  19. Ivanov, V.K., Vasin, V.V., Tanana, V.P.: Theory of Linear Ill-Posed Problems and Its Applications. Inverse and Ill-Posed Problems Series, 2nd edn. VSP, Utrecht (2002). (Translated and revised from the 1978 Russian original)

    Google Scholar 

  20. Kaneko, S., Satoh, Y., Igarashi, S.: Using selective correlation coefficient for robust image registration. Pattern Recognit. 36(5), 1165–1173 (2003)

    Article  Google Scholar 

  21. Kim, J., Fessler, J.A.: Intensity-based image registration using robust correlation coefficients. IEEE Trans. Med. Imaging 23(11), 1430–1444 (2004)

    Article  Google Scholar 

  22. Lee, D., Hofmann, M., Steinke, F., Altun, Y., Cahill, N.D., Scholkopf, B.: Learning similarity measure for multi modal 3d image registration. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Miami, pp 186–193. IEEE Service Center, Piscataway (2009)

    Google Scholar 

  23. Leventon, M.E., Grimson, W.E.L.: Multi modal volume registration using joint intensity distributions. In: MICCAI’98: Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention, Cambridge, pp. 1057–1066. Springer, London (1998)

    Google Scholar 

  24. Likar, B., Pernus, F.: A hierarchical approach to elastic registration based on mutual information. Image Vis. Comput. 19, 33–44 (2001)

    Article  Google Scholar 

  25. Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., Suetens, P.: Multi modality image registration by maximization of mutual information. IEEE Trans. Med. Imaging 16(2), 187–198 (1997)

    Article  Google Scholar 

  26. Mattes, D., Haynor, D.R., Vesselle, H., Lewellen, T.K., Eubank, W.: PET-CT image registration in the chest using free-form deformations. IEEE Trans. Med. Imaging 22(1), 120–128 (2003)

    Article  Google Scholar 

  27. Modersitzki, J.: Numerical Methods for Image Registration. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford (2004)

    MATH  Google Scholar 

  28. Pluim, J.P.W., Maintz, J.B.A., Viergever, M.A.: f-information measures in medical image registration. IEEE Trans. Med. Imaging 23(12), 1508–1516 (2004)

    Article  Google Scholar 

  29. Peckar, W., Schnörr, C., Rohr, K., Stiehl, H.S.: Non-rigid image registration using a parameter-free elastic model. In: British Machine Vision Conference, Southampton (1998)

    Book  Google Scholar 

  30. Pöschl, C.: Tikhonov regularization with general residual term. PhD thesis, Leopold Franzens Universität, Innsbruck (2008)

    Google Scholar 

  31. Rachev, S.T.: Probability Metrics and the Stability of Stochastic Models. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Wiley, Chichester (1991)

    Google Scholar 

  32. Roche, A.: Recalage d’images médicales par inférence statistique. PhD thesis, Université de Nice, Sophia-Antipolis, France (2001)

    Google Scholar 

  33. Roche, A., Malandain, G., Pennec, X., Ayache, N.: The correlation ratio as a new similarity measure for multi modal image registration. In: Medical Image Computing and Computer-Assisted Interventation – MICCAI’98, Cambridge. Lecture Notes in Computer Science, vol. 1496, pp. 1115–1124. Springer (1998)

    Chapter  Google Scholar 

  34. Roche, A., Pennec, X., Ayache, N.: The correlation ratio as a new similarity measure for multi modal image registration. In: Medical Image Computing and Computer-Assisted Intervention MICCAI98, Cambridge. Lecture Notes in Computer Science, vol. 1496, pp. 1115–1124. Springer (1998)

    Chapter  Google Scholar 

  35. Studholme, C.: Measures of 3D medical image alignment. PhD thesis, University of London, London (1997)

    Google Scholar 

  36. Vajda, I.: Theory of Statistical Inference and Information. Kluwer, Dordrecht (1989)

    MATH  Google Scholar 

  37. van den Elsen, P., Maintz, J.B.A., Viergever, M.A.: Automatic registration of CT and MR brain images using correlation of geometrical features. IEEE Trans. Med. Imaging. 14(2), 384–396 (1995)

    Article  Google Scholar 

  38. Viola, P.A.: Alignment by maximization of mutual information. PhD thesis, Massachusetts Institute of Technology, Massachusetts (1995)

    Book  Google Scholar 

  39. Viola, P.A., Wells, W.M.: Alignment by maximization of mutual information. In: ICCV’95: Proceedings of the Fifth International Conference on Computer Vision, Boston, p. 16. IEEE Computer Society (1995)

    Google Scholar 

  40. Wang, X.Y., Feng, D.D.: Automatic elastic medical image registration based on image intensity. Int. J. Image Graph. 5(2), 351–369 (2005)

    Article  Google Scholar 

  41. West, J., Fitzpatrick, J.M., Wang, M.Y., Dawant, B.M., Maurer, C.R., Kessler, R.M., Maciunas, R.J., Barillot, C., Lemoine, D., Collignon, A., Maes, F., Suetens, P., Vandermeulen, D., van den Elsen, P., Napel, S., Sumanaweera, T.S., Harkness, B., Hemler, P.F., Hill, D.L.G., Hawkes, D.J., Studholme, C., Maintz, J.B.A., Viergever, M.A., Malandain, G., Pennec, X., Noz, M.E., Maguire, G.Q., Pollack, M., Pelizzari, C.A., Robb, R.A., Hanson, D., Woods, R.P.: Comparison and evaluation of retrospective intermodality brain image registration techniques. J. Comput. Assist. Tomogr. 21, 554–566 (1997)

    Article  Google Scholar 

  42. Woods, R.P., Cherry, S.R., Mazziotta, J.C.: Rapid automated algorithm for aligning and reslicing PET images. J. Comput. Assist. Tomogr. 16, 620–633 (1992)

    Article  Google Scholar 

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Acknowledgements

The work of OS has been supported by the Austrian Science Fund(FWF) within the national research networks Industrial Geometry, project9203-N12, and Photoacoustic Imaging in Biology and Medicine, projectS10505-N20.The work of CP has been supported by the Austrian Science Fund (FWF) via the Erwin Schrödinger Scholarship J2970.

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Authors and Affiliations

  1. Institute of Mathematics, Alpen Adria Universität Klagenfurt, Universitätsstr. 65-67, Klagenfurt, Austria

    Christiane Pöschl

  2. Computational Science Center, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Otmar Scherzer

  3. RICAM, Austrian Academy of Sciences, Altenbergerstraße 69, 4040, Linz, Austria

    Otmar Scherzer

Authors
  1. Christiane Pöschl
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  2. Otmar Scherzer
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Corresponding author

Correspondence to Christiane Pöschl .

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Editors and Affiliations

  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

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Pöschl, C., Scherzer, O. (2015). Distance Measures and Applications to Multimodal Variational Imaging. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_4

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