Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation
@article{Vialard2011Diffeomorphic3I, title={Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation}, author={François-Xavier Vialard and Laurent Risser and Daniel Rueckert and Colin J. Cotter}, journal={International Journal of Computer Vision}, year={2011}, volume={97}, pages={229-241} }
In the context of large deformations by diffeomorphisms, we propose a new diffeomorphic registration algorithm for 3D images that performs the optimization directly on the set of geodesic flows. The key contribution of this work is to provide an accurate estimation of the so-called initial momentum, which is a scalar function encoding the optimal deformation between two images through the Hamiltonian equations of geodesics. Since the initial momentum has proven to be a key tool for statistics…
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References
SHOWING 1-10 OF 63 REFERENCES
Whole brain diffeomorphic metric mapping via integration of sulcal and gyral curves, cortical surfaces, and images
- MathematicsNeuroImage
- 2011
Diffeomorphic demons: Efficient non-parametric image registration
- Computer ScienceNeuroImage
- 2009
Geodesic Shooting for Computational Anatomy
- MathematicsJournal of Mathematical Imaging and Vision
- 2005
It is shown that this momentum can be also used for describing a deformation of given visual structures, like points, contours or images, and that, it has the same dimension as the described object, as a consequence of the normal momentum constraint the authors introduce.
Geodesic Shooting and Diffeomorphic Matching Via Textured Meshes
- Mathematics, Computer ScienceEMMCVPR
- 2005
Two optimization methods formulated in terms of the initial momentum are analyzed and compared: direct optimization by gradient descent, or root-finding for the transversality equation, enhanced by a preconditioning of the Jacobian.
Simultaneous Multi-scale Registration Using Large Deformation Diffeomorphic Metric Mapping
- MathematicsIEEE Transactions on Medical Imaging
- 2011
The goal is to perform rich anatomical shape comparisons from volumetric images with the mathematical properties offered by the LDDMM framework, and proposes a strategy to quantitatively measure the feature differences observed at each characteristic scale separately.
On the metrics and euler-lagrange equations of computational anatomy.
- MathematicsAnnual review of biomedical engineering
- 2002
Current experimental results from the Toga & Thompson group in growth, the Van Essen group in macaque and human cortex mapping, and the Csernansky group in hippocampus mapping for neuropsychiatric studies in aging and schizophrenia are shown.
An optimal control approach for deformable registration
- Mathematics2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops
- 2009
This paper proposes a novel formulation for unbiased image registration, which naturally extends to the case of time-series of images, and discusses numerical implementation details and carefully evaluates the properties of the alternative algorithms.
A Hamiltonian Particle Method for Diffeomorphic Image Registration
- MathematicsIPMI
- 2007
A novel algorithm for computing diffeomorphic warps that solves the Euler equations on the diffeomorphism group explicitly, based on a discretisation of the Hamiltonian, rather than using an optimiser.