Diffeomorphisms Groups and Pattern Matching in Image Analysis
International Journal of Computer Vision
Variational Methods for Multimodal Image Matching
International Journal of Computer Vision
Understanding the "Demon's Algorithm": 3D Non-rigid Registration by Gradient Descent
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
A Multilevel Method for Image Registration
SIAM Journal on Scientific Computing
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
Non-local shape descriptor: a new similarity metric for deformable multi-modal registration
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Random walks for deformable image registration
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
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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 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.