Variational problems on flows of diffeomorphisms for image matching
Quarterly of Applied Mathematics
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Geodesic Shooting for Computational Anatomy
Journal of Mathematical Imaging and Vision
Geodesic Matching with Free Extremities
Journal of Mathematical Imaging and Vision
Computational Anatomy to Assess Longitudinal Trajectory of Brain Growth
3DPVT '06 Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
A log-euclidean framework for statistics on diffeomorphisms
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
Large deformation diffeomorphic registration using fine and coarse strategies
WBIR'10 Proceedings of the 4th international conference on Biomedical image registration
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
International Journal of Computer Vision
Topology-preserving registration: a solution via graph cuts
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part I
A survey of shaped-based registration and segmentation techniques for cardiac images
Computer Vision and Image Understanding
Journal of Mathematical Imaging and Vision
Geodesics, Parallel Transport & One-Parameter Subgroups for Diffeomorphic Image Registration
International Journal of Computer Vision
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Computational Anatomy aims for the study of variability in anatomical structures from images. Variability is encoded by the spatial transformations existing between anatomical images and a template selected as reference. In the absence of a more justified model for inter-subject variability, transformations are considered to belong to a convenient family of diffeomorphisms which provides a suitable mathematical setting for the analysis of anatomical variability. One of the proposed paradigms for diffeomorphic registration is the Large Deformation Diffeomorphic Metric Mapping (LDDMM). In this framework, transformations are characterized as end points of paths parameterized by time-varying flows of vector fields defined on the tangent space of a Riemannian manifold of diffeomorphisms and computed from the solution of the non-stationary transport equation associated to these flows. With this characterization, optimization in LDDMM is performed on the space of non-stationary vector field flows resulting into a time and memory consuming algorithm. Recently, an alternative characterization of paths of diffeomorphisms based on constant-time flows of vector fields has been proposed in the literature. With this parameterization, diffeomorphisms constitute solutions of stationary ODEs. In this article, the stationary parameterization is included for diffeomorphic registration in the LDDMM framework. We formulate the variational problem related to this registration scenario and derive the associated Euler-Lagrange equations. Moreover, the performance of the non-stationary vs the stationary parameterizations in real and simulated 3D-MRI brain datasets is evaluated. Compared to the non-stationary parameterization, our proposal provides similar results in terms of image matching and local differences between the diffeomorphic transformations while drastically reducing memory and time requirements.