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

2010/03/20 by Vialard, François-Xavier · 1 citation
#FOS: Biological sciences #FOS: Mathematics #Probability (math.PR) #Quantitative Methods (q-bio.QM)

paper · doi:10.48550/arxiv.1003.3957

Abstract

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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