Diffusion Bridges for Stochastic Hamiltonian Systems and Shape Evolutions
Abstract
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modeling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a natural generalization as diffusion bridges in a stochastic setting. Simulation of such bridges is key to solving inference and registration problems in shape analysis. We demonstrate how to apply state-of-the-art diffusion bridge simulation methods to recently introduced stochastic shape deformation models, thereby substantially expanding the applicability of such models. We exemplify these methods by estimating template shapes from observed shape configurations while simultaneously learning model parameters.
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© 2022, Society for Industrial and Applied Mathematics.
History
Submitted: 19 March 2021
Accepted: 29 November 2021
Published online: 14 March 2022
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University of Copenhagen
Novo Nordisk Fonden https://doi.org/10.13039/501100009708 : NNF18OC0052000
Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 : EP/N014529/1
Villum Fonden https://doi.org/10.13039/100008398 : 00022924
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