Abstract
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.
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Zikic, D., Baust, M., Kamen, A., Navab, N. (2010). Generalization of Deformable Registration in Riemannian Sobolev Spaces. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010. MICCAI 2010. Lecture Notes in Computer Science, vol 6362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15745-5_72
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DOI: https://doi.org/10.1007/978-3-642-15745-5_72
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