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Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
TLDR
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.
Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
TLDR
This paper studies the Sinkhorn Divergences, a family of geometric divergences that interpolates between MMD and OT, and provides theoretical guarantees for positivity, convexity and metrization of the convergence in law.
Diffeomorphisms Groups and Pattern Matching in Image Analysis
  • A. Trouvé
  • Mathematics
    International Journal of Computer Vision
  • 1 July 1998
TLDR
This paper constructs a distance between deformations defined through a metric given the cost of infinitesimal deformations, and proposes a numerical scheme to solve a variational problem involving this distance and leading to a sub-optimal gradient pattern matching.
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.
Towards a coherent statistical framework for dense deformable template estimation
TLDR
A rigorous Bayesian framework is proposed for which it is proved asymptotic consistency of the maximum a posteriori estimate and which leads to an effective iterative estimation algorithm of the geometric and photometric parameters in the small sample setting.
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.
Local Geometry of Deformable Templates
TLDR
This paper provides a rigorous and general construction of this infinite dimensional "shape manifold" on which a Riemannian metric is placed and uses this to provide a geometrically founded linear approximation of the deformations of shapes in the neighborhood of a given template.
Metamorphoses Through Lie Group Action
TLDR
A modification of the metric is introduced by partly expressing displacements on M as an effect of the action of some group element, called metamorphoses, which can and has been applied to image processing problems, providing in particular diffeomorphic matching algorithms for pattern recognition.
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