A new gradient flow approach for image registration

17.5.2022
Tracey Balehowsky (University of Calgary), 17.05.2022, Exactum B121 (hybrid via zoom), 2pm-4pm

For zoom access, please contact Bjørn Jensen

Abstract
The problem of image registration is the following. We model an object (say human organs or tissues as in the case of medical imaging) as a compact Riemannian manifold without boundary $(M,g)$. Given a template image $I_0:M\to \mathbb R$ of $(M,g)$ of the object and another image $I:M\to \mathbb R$ (perhaps taken at a later time or at a different viewing angle), we seek to find a diffeomorphism $\phi: M\to M$ such that we can match the image to the template: $I= I_0 \circ \phi^{-1}$.  In this talk, I will introduce a gradient flow problem whose solution is a diffeomorphism which solves a related image registration problem. I will then discuss the well-posedness of the gradient flow problem. The key innovation of the gradient flow approach to image registration that I will introduce is that the flow takes into account the distortion effects of the diffeomorphism on both the template image $I_0$ and on the object geometry as given by the metric $g$. I will also review a bit of the history of image registration and the large deformation diffeomorphic metric mapping method as it relates to the gradient flow problem I will present.

 

This is joint work with Klas Modin & Carl-Joar Karlsson at Chalmers University of Technology and the University of Gothenburg.