Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
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Summary
The Euler-Lagrange equations characterizing the minimizing vector fields vt, t∈[0, 1] assuming sufficient smoothness of the norm to guarantee existence of solutions in the space of diffeomorphisms are derived.
- Type
- article
- Published
- 2005-02-01
- Cited by
- 1,957
- References
- 18
- OpenAlex
- https://openalex.org/W2170167891
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:17772076
Keywords
Geodesic, Diffeomorphism, Mathematics, Vector field, Euler equations
References
- Group Actions, Homeomorphisms, and Matching: A General Framework
- Computational anatomy: an emerging discipline
- Variational problems on ows of di eomorphisms for image matching
- Optimal registration of deformed images
- Diffeomorphisms Groups and Pattern Matching in Image Analysis
- Biomedical Imaging, Visualization, and Analysis
- Differential Geometry of Curves and Surfaces
- A computerized system for the elastic matching of deformed radiographic images to idealized atlas images.
- A Nonlinear Variational Problem for Image Matching
- Optimal matching between shapes via elastic deformations
- Semi-Lagrangian integration schemes for atmospheric models - A review
- Deformable templates using large deformation kinematics
- On the metrics and euler-lagrange equations of computational anatomy.
- Image matching as a diffusion process: an analogy with Maxwell's demons
- Deformable Shape Models for Anatomy
- Riemannian Geometry
- THE NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS.
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- Cardiac Motion Estimation by Optimizing Transmural Homogeneity of the Myofiber Strain and Its Validation with Multimodal Sequences
- Semi-automated Basal Ganglia Segmentation Using Large Deformation Diffeomorphic Metric Mapping
- Patient Specific Dosimetry Phantoms Using Multichannel LDDMM of the Whole Body
- Evaluation of group-specific, whole-brain atlas generation using Volume-based Template Estimation (VTE): application to normal and Alzheimer's populations
- Detection of temporal lobe epilepsy using support vector machines in multi-parametric quantitative MR imaging
- Segmentation of brain magnetic resonance images based on multi-atlas likelihood fusion: testing using data with a broad range of anatomical and photometric profiles
- Multi-layer Deformation Estimation for Fluoroscopic Imaging
- Automated Methods for Hippocampus Segmentation: the Evolution and a Review of the State of the Art
- Integration of electro-anatomical and imaging data of the left ventricle: An evaluation framework
- Quicksilver: Fast Predictive Image Registration – a Deep Learning Approach
- Computational Anatomy and Diffeomorphometry: A Dynamical Systems Model of Neuroanatomy in the Soft Condensed Matter Continuum
- Novel methods for multi-modal MR image analysis with applications to Parkinson's
- Image-based physiological and statistical models of the heart: application to tetralogy of Fallot. (Modèles physiologiques et statistiques du cœur guidés par imagerie médicale : application à la tétralogie de Fallot)
- 4D MAP Image Reconstruction Incorporating Organ Motion
- Diffeomorphic Metric Mapping of Hybrid Diffusion Imaging Based on BFOR Signal Basis
- Fully Automated Medical Image Analysis Facilitating Subsequent User Analysis
- Interactive Medical Image Registration With Multigrid Methods And Bounded Biharmonic Functions
- 3D image reconstruction from serial sections
- CellOrganizer: Image-derived Models of Subcellular Organization and Protein Distribution
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