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Mathematical Problems in Engineering
Volume 2015, Article ID 235314, 16 pages
Research Article

A Combination of the Total Variation Filter and a Fourth-Order Filter for Image Registration

1Department of Mathematics, East China Normal University, Shanghai 200241, China
2Joint Laboratory for Imaging Science Technology and Department of Computer Science, East China Normal University, Shanghai 200241, China

Received 9 December 2014; Revised 31 March 2015; Accepted 31 March 2015

Academic Editor: Giuseppe Vairo

Copyright © 2015 Xiaomei Yang 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.


We introduce a novel method for nonrigid image registration which combines the total variation filter and a fourth-order filter. We decompose the deformation field into two components, that is, a piecewise constant component and a smooth component. The total variation filter is used for the first component and the fourth-order filter is used for the second one. Then, we present a new PDE-based image registration model suitable for both smooth and nonsmooth deformation problem. Meanwhile, the local-global similarity measure is used in our method to improve the accuracy and robustness for image matching. By applying the split Bregman algorithm and dual algorithm, we present a fast and stable numerical scheme. The numerical experiments and comparisons on both synthetic images and real images demonstrate the effectiveness of our method in nonrigid image registration.