Forward-backward splitting in deformable image registration: A demons approach

TY - CHAP

T1 - Forward-backward splitting in deformable image registration

T2 - 15th IEEE International Symposium on Biomedical Imaging, ISBI 2018

AU - Ebner, Michael

AU - Modat, Marc

AU - Ferraris, Sebastiano

AU - Ourselin, Sebastien

AU - Vercauteren, Tom

PY - 2018/5/24

Y1 - 2018/5/24

N2 - Efficient non-linear image registration implementations are key for many biomedical imaging applications. By using the classical demons approach, the associated optimization problem is solved by an alternate optimization scheme consisting of a gradient descent step followed by Gaussian smoothing. Despite being simple and powerful, the solution of the underlying relaxed formulation is not guaranteed to minimize the original global energy. Implicitly, however, this second step can be recast as the proximal map of the regularizer. This interpretation introduces a parallel to the more general Forward-Backward Splitting (FBS) scheme consisting of a forward gradient descent and proximal step. By shifting entirely to FBS, we can take advantage of the recent advances in FBS methods and solve the original, non-relaxed deformable registration problem for any type of differentiable similarity measure and convex regularization associated with a tractable proximal operator. Additionally, global convergence to a critical point is guaranteed under weak restrictions. For the first time in the context of image registration, we show that Tikhonov regularization breaks down to the simple use of B-Spline filtering in the proximal step. We demonstrate the versatility of FBS by encoding spatial transformation as displacement fields or free-form B-Spline deformations. We use state-of-the-art FBS solvers and compare their performance against the classical demons, the recently proposed inertial demons and the conjugate gradient optimizer. Numerical experiments performed on both synthetic and clinical data show the advantage of FBS in image registration in terms of both convergence and accuracy.

AB - Efficient non-linear image registration implementations are key for many biomedical imaging applications. By using the classical demons approach, the associated optimization problem is solved by an alternate optimization scheme consisting of a gradient descent step followed by Gaussian smoothing. Despite being simple and powerful, the solution of the underlying relaxed formulation is not guaranteed to minimize the original global energy. Implicitly, however, this second step can be recast as the proximal map of the regularizer. This interpretation introduces a parallel to the more general Forward-Backward Splitting (FBS) scheme consisting of a forward gradient descent and proximal step. By shifting entirely to FBS, we can take advantage of the recent advances in FBS methods and solve the original, non-relaxed deformable registration problem for any type of differentiable similarity measure and convex regularization associated with a tractable proximal operator. Additionally, global convergence to a critical point is guaranteed under weak restrictions. For the first time in the context of image registration, we show that Tikhonov regularization breaks down to the simple use of B-Spline filtering in the proximal step. We demonstrate the versatility of FBS by encoding spatial transformation as displacement fields or free-form B-Spline deformations. We use state-of-the-art FBS solvers and compare their performance against the classical demons, the recently proposed inertial demons and the conjugate gradient optimizer. Numerical experiments performed on both synthetic and clinical data show the advantage of FBS in image registration in terms of both convergence and accuracy.

UR - http://www.scopus.com/inward/record.url?scp=85048082420&partnerID=8YFLogxK

U2 - 10.1109/ISBI.2018.8363755

DO - 10.1109/ISBI.2018.8363755

M3 - Conference paper

AN - SCOPUS:85048082420

VL - 2018-April

SP - 1065

EP - 1069

BT - 2018 IEEE 15th International Symposium on Biomedical Imaging, ISBI 2018

PB - IEEE Computer Society

Y2 - 4 April 2018 through 7 April 2018

ER -