Numerical optimization for constrained image registration

Eldad Haber*, Raya Horesh, Jan Modersitzki

*Corresponding author for this work
22 Citations (Scopus)


Image registration or image matching is a technique to establish meaningful correspondences between points in different scenes. It is a mandatory tool for various applications in medicine, geoscience, and other disciplines. However, obtaining plausible deformations is a complex task. For example, many applications require the transformations to be locally invertible, or even harder, keep volume changes within a reasonable bandwidth. In this work, solutions to the registration problem are obtained by direct imposition of a volume constraint on each voxel in a discretized domain. In contrast to previous work, the focus here is on development of an efficient and robust numerical algorithm and in particular, the study of an augmented Lagrangian method with a multigrid solver. The paper demonstrates that this combination yields an almost optimal solver (i.e. linear time) for the problem.

Original languageEnglish
JournalNumerical Linear Algebra with Applications
Issue number2-3
Pages (from-to)343-359
Number of pages17
Publication statusPublished - 01.04.2010


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