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We introduce a second-order stochastic model to explore the variability ingrowth of biological shapes with applications to medical imaging. Our model isa perturbation with a random force of the Hamiltonian formulation of thegeodesics. Starting with the finite-dimensional case of landmarks, we provethat the random solutions do not blow up in finite time. We then prove theconsistency of the model by demonstrating a strong convergence result from thefinite-dimensional approximations to the infinite-dimensional setting ofshapes. To this end we introduce a suitable Hilbert space close to a Besovspace that leads to our result being valid in any dimension of the ambientspace and for a wide range of shapes.

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