Injectivity conditions of 2D and 3D uniform cubic B-spline functions
Graphical Models - Pacific Graphics '99 in Graphical Models
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Diffeomorphic registration using b-splines
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
IEEE Transactions on Image Processing
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Recent advances in medical imaging technologies have made 4D image sequences available in clinical routine. As a consequence, image registration techniques are evolving from alignment of pairs of static volumetric images to spatio-temporal registration of dynamic (4D) images. Since the elastic image registration problem is ill-posed, additional prior information or constraints are usually required to regularize the problem. This work proposes to enforce local invertibility (diffeomorphism) of 4D deformations. A novel sufficient condition for local invertibility over continuous space and time is proposed and a practical regularization prior is designed from the theory. The method has been applied to an image registration (motion tracking) of a dynamic 4D CT image sequence. Results show that using proposed regularizer leads to deformations that are more plausible for respiratory motion than the standard approach without additional temporal regularization.