Diffusion Bridges for Stochastic Hamiltonian Systems and Shape Evolutions

Alexis Arnaudon, Frank van der Meulen, Moritz Schauer, Stefan Sommer

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
44 Downloads (Pure)

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

Original languageEnglish
Pages (from-to)293-323
Number of pages31
JournalSIAM Journal on Imaging Sciences
Volume15
Issue number1
DOIs
Publication statusPublished - 2022

Keywords

  • bridge simulation
  • conditional diffusion
  • guided proposals
  • hypoelliptic diffusion
  • landmark dynamics
  • shape analysis
  • shape matching

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