A NEW DERIVATIVE-FREE ALGORITHM FOR THE MEDICAL IMAGE REGISTRATION PROBLEM

R. Oeuvray and M. Bierlaire

References

  1. [1] J.E. Dennis & R.B. Schnabel, Numerical methods for unconstrained optimization and nonlinear equations (Englewood Cliffs, USA: Prentice-Hall, 1983).
  2. [2] J.B.A. Maintz & M.A. Viergever, A survey of medical image registration, Medical Image Analysis, 2, 1998, 1–36.
  3. [3] D.L.G. Hill, P.G. Batchelor, M. Holden, & D.J. Hawkes,Medical image registration, Physics in Medicine and Biology, 46, 2001, R1–R45. doi:10.1088/0031-9155/46/3/201
  4. [4] A. Collignon, F. Maes, D. Delaere, D. Vandermeulen et al., Automated multi-modality image registration based on information theory, in Y. Bizais, C. Barillot & R. Di Paola (Eds.), Information processing in medical imaging (Dordrecht: Kluwer Academic Publishers), 1995, 265–274.
  5. [5] P.A. Viola, Alignment by maximisation of mutual information, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1995.
  6. [6] J.P.W. Pluim, Mutual information based registration of medical images, Ph.D. Thesis, Utrecht University, Utrecht, The Netherlands, 2001.
  7. [7] C. Studholme, D.L.G. Hill, & D.J. Hawkes, An overlap invariant entropy measure of 3D medical image alignment, Pattern Recognition, 32(1), 1999, 71–86. doi:10.1016/S0031-3203(98)00091-0
  8. [8] Ph. Thévenaz & M. Unser, Optimization of mutual information for multiresolution image registration, IEEE Trans. on Image Processing, 9(12), 2000, 2083–2098. doi:10.1109/83.887976
  9. [9] F. Maes, A. Collignon, D. Vandermeulen, G. Marchal et al., Multimodality image registration by maximization of mutual information, IEEE Trans. on Medical Imaging, 16, 1997, 187–198. doi:10.1109/42.563664
  10. [10] R. Oeuvray, Trust-region methods based on radial basis functions with application to biomedical imaging, Ph.D. Thesis, Ecole Polytechnique Fédérale de Lausanne, Switzerland, 2005.
  11. [11] S.D. Chatterji, Cours d’analyse (Volume 1): Analyse vectorielle (Presse polytechniques et Universitaires Romandes, 1997), Lausanne, Switzerland.
  12. [12] N.Z. Shor, Minimization methods for non-differentiable functions (Berlin, Germany: Springer-Verlag, 1985).
  13. [13] A.V. Kuntsevich & F. Kappel, The solver for local nonlinear optimization problems, Institute for Mathematics, Karl-Franzens University of Graz, Heinrichstr. 36, A-8010 Graz (Austria), version 1.1 edition, June 1997.
  14. [14] M.J.D. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives, Computer Journal, 17, 1964, 155–162. doi:10.1093/comjnl/7.2.155
  15. [15] A. Collignon, Multi-modality medical image registration by maximization of mutual information, Ph.D. Thesis, Catholic University of Leuven, Belgium, 1998.
  16. [16] A.R. Conn & Ph.L. Toint, An algorithm using quadratic interpolation for unconstrained derivative free optimization, in G. Di Pillo & F. Gianessi (Eds.), Nonlinear optimization and applications (New-York, USA: Plenum Publishing, 1995).Also available as Report 95/6, Department of Mathematics,FUNDP, Namur, Belgium.
  17. [17] M.J.D. Powell, Uobyqa: Unconstrained optimization by quadratic approximation, Technical Report DAMTP NA14, Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, UK, 2000.
  18. [18] M.J.D. Powell, On the use of quadratic models in unconstrained minimization without derivatives, Technical Report DAMTP NA03, Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, UK, 2003.
  19. [19] M.J.D. Powell, A new algorithm for unconstrained minimization without derivatives, ISMP, Copenhagen, 2003.
  20. [20] R. Oeuvray & M. Bierlaire, Boosters: A derivative-free algorithm based on radial basis functions, Technical Report RO 2003.0918, EPFL-SB-IMA-ROSO, 2003.
  21. [21] A. Conn, N. Gould, & Ph. Toint, Trust region methods, MPS-SIAM Series on Optimization (SIAM, 2000), Philadelphia, USA.
  22. [22] E.D. Dolan & J.J. Moré, Benchmarking optimization software with performance profiles, Mathematical Programming, Serie A, 91(22), 2002, 201–213. doi:10.1007/s101070100263
  23. [23] R. Oeuvray & M. Bierlaire, On the differentiability of the Mi estimator for medical image registration, Technical Report RO-020403, EPFL, 2002.

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