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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 704567, 8 pages
http://dx.doi.org/10.1155/2012/704567
Research Article

Efficient Variational Approaches for Deformable Registration of Images

1Department of Mathematics, Bilecik Seyh Edebali University, 11210 Bilecik, Turkey
2Department of Mathematics, Yildiz Technical University, 34220 Istanbul, Turkey

Received 15 March 2012; Revised 14 April 2012; Accepted 10 May 2012

Academic Editor: Allaberen Ashyralyev

Copyright © 2012 Mehmet Ali Akinlar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 6 5 × 6 5 . Computational results indicate that the presented method is quite fast and efficient in the registration of deformable medical images.