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Stochastically evolving geometric systems are studied in shape analysis andcomputational anatomy for modelling random evolutions of human organ shapes.The notion of geodesic paths between shapes is central to shape analysis andhas a natural generalisation as diffusion bridges in a stochastic setting.Simulation of such bridges is key to solve inference and registration problemsin shape analysis. We demonstrate how to apply state-of-the-art diffusionbridge simulation methods to recently introduced stochastic shape deformationmodels thereby substantially expanding the applicability of such models. Weexemplify these methods by estimating template shapes from observed shapeconfigurations while simultaneously learning model parameters.

Diffusion bridges for stochastic Hamiltonian systems and shape evolutions