TY - JOUR

T1 - Diffusion Bridges for Stochastic Hamiltonian Systems and Shape Evolutions

AU - Arnaudon, Alexis

AU - Van Der Meulen, Frank

AU - Schauer, Moritz

AU - Sommer, Stefan

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

U2 - 10.1137/21M1406283

DO - 10.1137/21M1406283

M3 - Journal article

VL - 15

SP - 293

EP - 323

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 1

ER -