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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Generalization of Deformable Registration in Riemannian Sobolev Spaces
verfasst von : Darko Zikic, Maximilian Baust, Ali Kamen, Nassir Navab
Erschienen in: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010
Verlag: Springer Berlin Heidelberg
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In this work we discuss the generalized treatment of the deformable registration problem in Sobolev spaces. We extend previous approaches in two points: 1) by employing a general energy model which includes a regularization term, and 2) by changing the notion of distance in the Sobolev space by problem-dependent Riemannian metrics. The actual choice of the metric is such that it has a preconditioning effect on the problem, it is applicable to arbitrary similarity measures, and features a simple implementation. The experiments demonstrate an improvement in convergence and runtime by several orders of magnitude in comparison to semi-implicit gradient flows in
L
2
. This translates to increased accuracy in practical scenarios. Furthermore, the proposed generalization establishes a theoretical link between gradient flow in Sobolev spaces and elastic registration methods.