U. Clarenz, M. Droske, S. Henn, M. Rumpf, and K. Witsch.
Computational methods for nonlinear image registration.
In O. Scherzer, editor, Mathematical Models for Registration and
Applications to Medical Imaging, Mathematics in Industry, volume 10, 2006.
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Image registration is the process of the alignment of two or more data sets recorded with the same or different imaging machineries. Especially nonlinear image registration techniques allow the alignment of data sets that are mismatched in a nonuniform manner. Mathematically, this yields a nonlinear ill-conditioned inverse problem. In this presentation, we introduce several computational methods based on variational PDE approaches to obtain an approximate solution of the nonlinear registration problem. In each approach we have to solve a sequence of subproblems. Each subproblem has to be well-posed and should be efficiently solvable.