Diffusion Bridges for Stochastic Hamiltonian Systems and Shape Evolutions
Journal article, 2022

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 sto-chastic 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 appli-cability of such models. We exemplify these methods by estimating template shapes from observed shape configurations while simultaneously learning model parameters.

hypoelliptic diffusion

landmark dynamics

shape analysis

guided proposals

words

shape matching

conditional diffusion

bridge simulation

Author

Alexis Arnaudon

Imperial College London

Frank van der Meulen

Delft University of Technology

Moritz Schauer

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Stefan Sommer

University of Copenhagen

SIAM Journal on Imaging Sciences

19364954 (eISSN)

Vol. 15 1 293-323

Subject Categories

Bioinformatics (Computational Biology)

Probability Theory and Statistics

Control Engineering

DOI

10.1137/21M1406283

More information

Latest update

12/16/2022