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Extension to Infinite Dimensions of a Stochastic Second-Order Model associated with the Shape Splines

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Date
2013
Link to item file
http://arxiv.org/abs/1003.3957v1
Dewey
Probabilités et mathématiques appliquées
Sujet
medical imaging
Journal issue
Stochastic Processes and their Applications
Volume
123
Number
6
Publication date
2013
Article pages
2110-2157
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.spa.2013.01.012
URI
https://basepub.dauphine.fr/handle/123456789/7120
Collections
  • CEREMADE : Publications
Metadata
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Author
Vialard, François-Xavier
Type
Article accepté pour publication ou publié
Abstract (EN)
We introduce a second-order stochastic model to explore the variability in growth of biological shapes with applications to medical imaging. Our model is a perturbation with a random force of the Hamiltonian formulation of the geodesics. Starting with the finite-dimensional case of landmarks, we prove that the random solutions do not blow up in finite time. We then prove the consistency of the model by demonstrating a strong convergence result from the finite-dimensional approximations to the infinite-dimensional setting of shapes. To this end we introduce a suitable Hilbert space close to a Besov space that leads to our result being valid in any dimension of the ambient space and for a wide range of shapes.

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