Accounting for changing overlap in variational image registration

Authors:
Nathan D. Cahill;J. Alison Noble;David J. Hawkes
Affiliations:
School of Mathematical Sciences, Rochester Institute of Technology;Institute of Biomedical Engineering, University of Oxford, UK;Centre for Medical Image Computing, University College London, UK
Venue:
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Year:
2010

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Abstract

Any similarity measure used for image registration depends in some way on the region Ω describing the overlap between the floating and reference images. In variational registration, where the Gâteaux derivative of the similarity measure drives the registration, most literature implicitly assumes that Ω remains constant. This assumption is valid if homogeneous Dirichlet or sliding boundary conditions are chosen for the displacement field; however, it is invalid if any other type of boundary conditions are chosen, or if the similarity measure is computed over some masked portion of the overlap region. This article illustrates how these more general situations of different boundary conditions and/or masked regions can be accommodated in variational registration by explicitly accounting for the varying Ω in the Gâteaux derivative of the similarity measure.