title: Generalization of deformable registration in Riemannian Sobolev spaces.
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 L2. 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.
authors.affiliation: Computer Aided Medical Procedures (CAMP), TU München, Germany.
authors.forename: Darko
authors.initials: D
authors.lastname: Zikic
authors.forename: Maximilian
authors.initials: M
authors.lastname: Baust
authors.forename: Ali
authors.initials: A
authors.lastname: Kamen
authors.forename: Nassir
authors.initials: N
authors.lastname: Navab
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique