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. © 2010 Springer-Verlag.
CITATION STYLE
Zikic, D., Baust, M., Kamen, A., & Navab, N. (2010). Generalization of deformable registration in Riemannian Sobolev spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6362 LNCS, pp. 586–593). https://doi.org/10.1007/978-3-642-15745-5_72
Mendeley helps you to discover research relevant for your work.