Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Deformations incorporating rigid structures
Computer Vision and Image Understanding
Journal of Mathematical Imaging and Vision
Multigrid
Image Registration, Optical Flow and Local Rigidity
Journal of Mathematical Imaging and Vision
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Optimal Control Formulation for Determining Optical Flow
SIAM Journal on Scientific Computing
Curvature Based Image Registration
Journal of Mathematical Imaging and Vision
Mass Preserving Mappings and Image Registration
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
Image Similarity Based on Intensity Scaling
Journal of Mathematical Imaging and Vision
Generalized Rigid and Generalized Affine Image Registration and Interpolation by Geometric Multigrid
Journal of Mathematical Imaging and Vision
FLIRT with Rigidity--Image Registration with a Local Non-rigidity Penalty
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
Resolution of the Transport equation subject to constraint
Journal of Computational and Applied Mathematics
Shape Metrics Based on Elastic Deformations
Journal of Mathematical Imaging and Vision
Optimal extended optical flow subject to a statistical constraint
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
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In this paper a variational method for registering or mapping like points in medical images is proposed and analyzed. The proposed variational principle penalizes a departure from rigidity and thereby provides a natural generalization of strictly rigid registration techniques used widely in medical contexts. Difficulties with finite displacements are elucidated, and alternative infinitesimal displacements are developed for an optical flow formulation which also permits image interpolation. The variational penalty against non-rigid flows provides sufficient regularization for a well-posed minimization and yet does not rule out irregular registrations corresponding to an object excision. Image similarity is measured by penalizing the variation of intensity along optical flow trajectories. The approach proposed here is also independent of the order in which images are taken. For computations, a lumped finite element Eulerian discretization is used to solve for the optical flow. Also, a Lagrangian integration of the intensity along optical flow trajectories has the advantage of prohibiting diffusion among trajectories which would otherwise blur interpolated images. The subtle aspects of the methods developed are illustrated in terms of simple examples, and the approach is finally applied to the registration of magnetic resonance images.