Extension to Infinite Dimensions of a Stochastic Second-Order Model associated with the Shape Splines
Vialard, François-Xavier (2013), Extension to Infinite Dimensions of a Stochastic Second-Order Model associated with the Shape Splines, Stochastic Processes and their Applications, 123, 6, p. 2110-2157. http://dx.doi.org/10.1016/j.spa.2013.01.012
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1003.3957v1
Journal nameStochastic Processes and their Applications
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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.
Subjects / Keywordsmedical imaging
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Benamou, Jean-David; Gallouët, Thomas; Vialard, François-Xavier (2019) Article accepté pour publication ou publié