Soliton dynamics in computational anatomy

@article{Holm2004SolitonDI,
  title={Soliton dynamics in computational anatomy},
  author={Darryl D. Holm and J. Tilak Ratnanather and Alain Trouv{\'e} and Laurent Younes},
  journal={NeuroImage},
  year={2004},
  volume={23},
  pages={S170-S178}
}
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References

SHOWING 1-10 OF 109 REFERENCES
The metric spaces, Euler equations, and normal geodesic image motions of computational anatomy
TLDR
The purpose of this paper is to examine the generation of the geodesics associated with the metric from several points of view, the first the Euler equation describing the Geodesic diffeomorphic flow, and the second the variational formulation of theGeodesic in terms of the minimizing flow of vector fields which generate them.
On the metrics and euler-lagrange equations of computational anatomy.
TLDR
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.
Geodesic Shooting for Computational Anatomy
TLDR
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.
Statistics on diffeomorphisms via tangent space representations
Computational anatomy: an emerging discipline
This paper studies mathematical methods in the emerging new discipline of Computational Anatomy. Herein we formalize the Brown/Washington University model of anatomy following the global pattern…
Integrable vs. nonintegrable geodesic soliton behavior
Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation
This paper is concerned with the dynamics of measure-valued solutions of the EPDiff equations, standing for the Euler-Poincare equations associated with the diffeomorphism group (of ℝn or of an…
Landmark Matching via Large Deformation Diffeomorphisms on the Sphere
TLDR
A methodology and algorithm for generating diffeomorphisms of the sphere onto itself, given the displacements of a finite set of template landmarks, has application in brain mapping, where surface data is typically mapped to the sphere as a common coordinate system.
Topological methods in hydrodynamics
A group theoretical approach to hydrodynamics considers hydrodynamics to be the differential geometry of diffeomorphism groups. The principle of least action implies that the motion of a fluid is…
Group Actions, Homeomorphisms, and Matching: A General Framework
TLDR
Left-invariant metrics are defined on the product G × I thus allowing the generation of transformations of the background geometry as well as the image values, and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another.
...
...