The opposite phase encoded echo planar images (EPI) are registered to each other.
We use one model for the forward and backward transformation, which estimates a shift map/voxel displacement map, so the forward and backward transformations are exactly each others inverse.
In the “simple” approach, the optimal transformations (scaling and translation) in the y-direction are estimated column-wise; for each iteration, the distance between the images is established via sum of square differences (SSD) or normalised cross-correlation (NCC). Via the successive approach, a local search is performed to find the most plausible deformation (measured via NCC or SSD); also, smoothing and intensity correction is applied during the process. The voxel displacement map is then applied using cubic spline interpolation.
The local search is inspired by Heinrich et al [1]. The algorithm in general is based on Andersson et al [2] and Ruthotto et al [3].
Image registration starts with an objective/cost function. This function specifies what needs to be minimised. This is usually the distance between the template image and the transformed reference image, so that the images are as similar as possible. The aim of the image registration process is to find the optimal geometric transformation between the images (see [4]). This geometric transformation can consist of displacements ("translation"), rotations, scaling and shear.
To find the optimal transformation, initial parameters and a distance measure are chosen. Then the optimisation process starts (see figure below).
[1]Heinrich, M.P., Papie, B.W., Schnabel, J.A., and Handels, H. (2014) Non-parametric Discrete Registration with Convex Optimisation. In S. Ourselin and M. Modat (Eds.): WBIR 2014, LNCS 8545, pp. 51-61.
Latest update of this page: 23 February 2015
[2] Andersson, J.L.R. and Skare, S. (2001) A Model-Based Method for Retrospective Correction of Geometric Distortions in Diffusion-Weighted EPI. NeuroImage 16, 177-199.
[3] Ruthotto, L, Mohammadi, S, Heck, C, Modersitzki, J, and Weiskopf, N. (2013) HySCO - Hyperelastic Susceptibility Artifact Correction of DTI in SPM. Presented at the Bildverarbeitung fuer die Medizin 2013.
[4] Modersitzki, J. (2004) Numerical Methods for Image Registration. Oxford, UK: Oxford University Press.