Talk by Henry O. Jacobs – Københavns Universitet

Talk by Henry O. Jacobs

Title: Higher order accuracy in diffeomorphic image registration: An introduction to jet-groupoids

In Henry's own words: "rather than doing a fancy slide talk with pretty pictures it might be better for me to give a slow chalk talk that just introduces people to the idea of the jet-groupoid." 

Abstract: Diffeomorphic image registration seeks to find a diffeomorphism which brings image data into a common coordinate system for the purpose of comparison.  This is particularly important in computational anatomy where one seeks to compare functionally identical regions of medical image data across patients and/or time. Unfortunately, the space of diffeomorphisms is infinite-dimensional. Finite dimensional approximations must be found in order to produce tractable algorithms.  In this talk we will present one such approximation, known as the "jet-groupoid".  This is a well known object to differential geometers and other "pure" mathematicians, but it has little presence in applied mathematics.  We will see that the jet-groupoid inherits much the algebraic and geometric properties of the diffeomorphism group, and therefore serves as a good model of the diffeomorphism group. We will also pose a standard image registration problem, and we will see how the jet-groupoid is naturally invoked in the solution.

About the speaker: Henry O. Jacobs is currently a post-doctoral research associate in the Mathematics Department at Imperial College London. His research interests include lagrangian methods for fluids, fluid-structure interaction, bio-locomotion and medical imaging.