Abstract and Applied Analysis

Efficient Variational Approaches for Deformable Registration of Images

Mehmet Ali Akinlar, Muhammet Kurulay, Aydin Secer, and Mustafa Bayram

Full-text: Open access

Abstract

Dirichlet, anisotropic, and Huber regularization terms are presented for efficient registration of deformable images. Image registration, an ill-posed optimization problem, is solved using a gradient-descent-based method and some fundamental theorems in calculus of variations. Euler-Lagrange equations with homogeneous Neumann boundary conditions are obtained. These equations are discretized by multigrid and finite difference numerical techniques. The method is applied to the registration of brain MR images of size 65 × 65 . Computational results indicate that the presented method is quite fast and efficient in the registration of deformable medical images.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 704567, 8 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365174051

Digital Object Identifier
doi:10.1155/2012/704567

Mathematical Reviews number (MathSciNet)
MR2947711

Zentralblatt MATH identifier
1246.94011

Citation

Akinlar, Mehmet Ali; Kurulay, Muhammet; Secer, Aydin; Bayram, Mustafa. Efficient Variational Approaches for Deformable Registration of Images. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 704567, 8 pages. doi:10.1155/2012/704567. https://projecteuclid.org/euclid.aaa/1365174051


Export citation

References

  • J. Modersitzki, Numerical Methods for Image Registration, Oxford University Press, New York, NY, USA, 2004.
  • J. Modersitzki, FAIR: Flexible Algorithms for Image Registration, SIAM, Philadelphia, Pa, USA, 2009.
  • M. A. Akinlar, A new method for non-rigid registration of 3D images [Ph.D. thesis], The University of Texas at Arlington, 2009.
  • M. A. Akinlar and R. N. Ibragimov, “Application of an image registration method to noisy images,” Sarajevo Journal of Mathematics, vol. 7, no. 1, pp. 135–144, 2011.
  • J. Kuangk, “Variational approach to quasi-periodic solution of nonautonomous second-order hamiltonian systems,” Abstract and Applied Analysis, vol. 2012, Article ID 271616, 14 pages, 2012.
  • A. B. Hamza and H. Krim, “A variational approach to maximum a posteriori estimation for image denoising,” in Proceedings of the 6th International Conference: EMMCVPR, pp. 27–29, Ezhou, China, 2007.
  • A. B. Hamza, H. Krim, and G. B. Unal, “Towards a unified estimation theme: probabilistic versus variational,” IEEE Signal Processing Magazine, pp. 37–47, 2002.
  • M. A. Akinlar and M. Celenk, “Quality assessment for an image registration method,” International Journal of Contemporary Mathematical Sciences, vol. 6, no. 30, pp. 1483–1489, 2011.
  • S. Gramsch and E. Schock, “Ill-posed equations with transformed argument,” Abstract and Applied Analysis, vol. 2003, no. 13, pp. 785–791, 2003.
  • H. Köstler, A multigrid framework for variational approaches in medical image processing and computer vision [Diplom-Informatiker, Diplom-Kaufmann], Universität Erlangen-Nürnberg, 2008.
  • I. M. Gelfand and S. V. Fomin, Calculus of Variations, Dover, 2000.
  • Y. L. You, W. Xu, A. Tannenbaum, and M. Kaveh, “Behavioral analysis of anisotropic diffusion in image processing,” IEEE Transactions on Image Processing, vol. 5, no. 11, pp. 1539–1553, 1996.
  • P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629–639, 1990.