Obtaining higher-order spatial accuracy in LDDMM with jet-particles – Københavns Universitet

Obtaining higher-order spatial accuracy in LDDMM with jet-particles

Talk by Henry Jacobs; Department of Mathematics, Imperial College London

Abstract

The matching term in large deformation diffeomorphic metric mapping (LDDMM) typically invokes the value of images at all the points in the computational domain. However, in practice one must approximate the matching term with something finite, such as a Riemann sum in the case of an integral. When one uses an approximation, which only depends on the value of an image at a finite set of points, the modified LDDMM problem may be solved up to time-discretization (i.e. no spatial error). Thus we may obtain a nearly exact answer to a deformation of the original problem. We can generalize this to higher order approximations which invoke the value and spatial derivatives of images at a finite set of points. This suggest the use of jet-particles. Jet-particles are particles which carry a Taylor expansion as an internal degree of freedom. The advantage of this approach is that we may be able to get an equal accuracy with fewer and more sparsely placed jet-particles.

In summary, jet-particles could offer us something comparable to what higher-order spatial schemes on Eulerian grids have traditionally provided. That is to say, fewer and more sparsely distributed computational nodes without a loss in accuracy.