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International Journal of Biomedical Imaging
Volume 2008, Article ID 686875, 9 pages
Research Article

Symmetric and Transitive Registration of Image Sequences

1Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
2School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
3Departments of Electrical Engineering and Diagnostic Radiology, Yale University, New Haven, CT 06511, USA

Received 7 July 2008; Revised 18 November 2008; Accepted 31 December 2008

Academic Editor: Yue Wang

Copyright © 2008 Oskar Škrinjar 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.


This paper presents a method for constructing symmetric and transitive algorithms for registration of image sequences from image registration algorithms that do not have these two properties. The method is applicable to both rigid and nonrigid registration and it can be used with linear or periodic image sequences. The symmetry and transitivity properties are satisfied exactly (up to the machine precision), that is, they always hold regardless of the image type, quality, and the registration algorithm as long as the computed transformations are invertable. These two properties are especially important in motion tracking applications since physically incorrect deformations might be obtained if the registration algorithm is not symmetric and transitive. The method was tested on two sequences of cardiac magnetic resonance images using two different nonrigid image registration algorithms. It was demonstrated that the transitivity and symmetry errors of the symmetric and transitive modification of the algorithms could be made arbitrary small when the computed transformations are invertable, whereas the corresponding errors for the nonmodified algorithms were on the order of the pixel size. Furthermore, the symmetric and transitive modification of the algorithms had higher registration accuracy than the nonmodified algorithms for both image sequences.