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Mathematical Problems in Engineering
Volume 2009, Article ID 707026, 13 pages
Research Article

Fractional Regularization Term for Variational Image Registration

Department of Information Technologies and Communications, Technical University of Cartagena, Cartagena 30202, Spain

Received 3 December 2008; Revised 8 June 2009; Accepted 17 July 2009

Academic Editor: Victoria Vampa

Copyright © 2009 Rafael Verdú-Monedero 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.


Image registration is a widely used task of image analysis with applications in many fields. Its classical formulation and current improvements are given in the spatial domain. In this paper a regularization term based on fractional order derivatives is formulated. This term is defined and implemented in the frequency domain by translating the energy functional into the frequency domain and obtaining the Euler-Lagrange equations which minimize it. The new regularization term leads to a simple formulation and design, being applicable to higher dimensions by using the corresponding multidimensional Fourier transform. The proposed regularization term allows for a real gradual transition from a diffusion registration to a curvature registration which is best suited to some applications and it is not possible in the spatial domain. Results with 3D actual images show the validity of this approach.