A LAGRANGIAN GAUSS-NEWTON-KRYLOV SOLVER FOR MASS- AND INTENSITY-PRESERVING DIFFEOMORPHIC IMAGE REGISTRATION

SIAM Journal on Scientific Computing : a Publication of the Society for Industrial and Applied Mathematics
Andreas Mang, Lars Ruthotto

Abstract

We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity fiel...Continue Reading

References

Sep 1, 2007·NeuroImage·John Ashburner
Jan 1, 1992·IEEE Transactions on Medical Imaging·H Chang, J M Fitzpatrick
Jan 1, 1996·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·G E ChristensenM I Miller
Dec 2, 2008·NeuroImage·Tom VercauterenNicholas Ayache
Dec 9, 2008·NeuroImage·Laurent YounesMichael I Miller
Jan 13, 2009·Medical Image Analysis·Tauseef Ur RehmanAllen Tannenbaum
Jan 11, 2011·NeuroImage·John Ashburner, Karl J Friston
Nov 16, 2011·IEEE Transactions on Medical Imaging·Fabian GigengackKlaus P Schäfers
Sep 4, 2012·Physics in Medicine and Biology·L RuthottoC H Wolters
Jun 7, 2013·IEEE Transactions on Medical Imaging·Aristeidis SotirasNikos Paragios
Feb 4, 2016·IEEE Transactions on Medical Imaging·Akshay PaiMads Nielsen
Jan 1, 2015·SIAM Journal on Imaging Sciences·Andreas Mang, George Biros
Jan 1, 2016·SIAM Journal on Imaging Sciences·Andreas Mang, George Biros

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Citations

Apr 11, 2020·Proceedings of the National Academy of Sciences of the United States of America·Lars RuthottoSamy Wu Fung
Dec 21, 2019·Computer Methods in Applied Mechanics and Engineering·Klaudius ScheufeleMiriam Mehl
Mar 23, 2021·Inverse Problems·Carlos Borges, George Biros

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