A robust multigrid approach for variational image registration models

Vectorial Total Variation-Based Regularization for Variational Image Registration

“…Note that this work is related to some previous works in [14]- [17]. Although they share similar backgrounds (e.g.…”

“…Some numerical tests in the previous works by [14]- [16] show that both parabolic and elliptic methods provide well matched images in most of the cases, but the MG methods are much faster than the other methods in fulfilling the necessary condition for being a minimizer of the variational problem (2), i.e. in achieving convergence.…”

“…gradient descent and multigrid (MG) methods. Refer to [14]- [19], [25], [29]- [33] and references therein. On the other hand the latter approach aims to discretize the joint functional J α in (2) and then solve the discrete minimization problem by standard optimization techniques, e.g.…”

“…On the other hand, the elliptic method solves the PDEs directly, with the common choice being the fixed-point (FP) iteration, Newton-type methods, and MG methods; see e.g. [14]- [17], [25], [29]- [33] and references therein.…”

“…The authors mentioned that the AOS-type method is quite slow because the time-step is requited to be sufficiently small and then the associated linearized system has to be solved many times with changing the right-hand side of the EL system. This situation by the AOS-type methods would also occur for solving the EL systems like the ones in (14) and (16). Due to this fact, this work focuses only on developing an efficient MG method for a computation of a numerical solution of the associated EL system resulting from the variational problem (2) using the recommended VTV-based regularization (R VTV 1 ) as can be seen later in Section II.…”