Hamiltonian Systems

In this talk, we will present a new framework for image registration that allows for discontinuous deformations, such as the discontinuous sliding motion observed between lung tissues and surrounding structures during breathing. Traditional approaches, like Large Deformation Diffeomorphic Metric Mapping (LDDMM), rely on Lie group structures and assume smooth velocity fields, which makes them unsuitable for problems with discontinuities.

To address this limitation, we extend the setting from Lie groups to diffeomorphism groupoids and algebroids, enabling discontinuous flows while preserving diffeomorphic structure within each region. We will introduce the mathematical background, present the associated Euler–Arnold equations, and share some numerical results.

This talk is based on joint work with Stefan Sommer, Shihui Ying, and Bin Xiao.