| dc.contributor.author | Vialard, François-Xavier | |
| dc.date.accessioned | 2011-10-05T13:45:33Z | |
| dc.date.available | 2011-10-05T13:45:33Z | |
| dc.date.issued | 2013 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/7120 | |
| dc.language.iso | en | en |
| dc.subject | medical imaging | en |
| dc.subject.ddc | 519 | en |
| dc.title | Extension to Infinite Dimensions of a Stochastic Second-Order Model associated with the Shape Splines | en |
| dc.type | Article accepté pour publication ou publié | |
| dc.description.abstracten | 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. | en |
| dc.relation.isversionofjnlname | Stochastic Processes and their Applications | |
| dc.relation.isversionofjnlvol | 123 | |
| dc.relation.isversionofjnlissue | 6 | |
| dc.relation.isversionofjnldate | 2013 | |
| dc.relation.isversionofjnlpages | 2110-2157 | |
| dc.relation.isversionofdoi | http://dx.doi.org/10.1016/j.spa.2013.01.012 | |
| dc.identifier.urlsite | http://arxiv.org/abs/1003.3957v1 | |
| dc.description.sponsorshipprivate | oui | en |
| dc.relation.isversionofjnlpublisher | Elsevier | |
| dc.subject.ddclabel | Probabilités et mathématiques appliquées | en |
