An apparatus and method are provided for performing
phase unwrapping for an acquired magnetic
resonance (MR) image. The method includes modelling the MR phase in the MR image using a Markov random field (MRF) in which the true phase φ(t) and the wrapped phase φ(w) are modelled as random variables such that at
voxel i of said MR image φ(t)(i)=φ(w)(i)+2πn(i), where n(i) is an unknown integer that needs to be estimated for each
voxel i. The method further includes constructing a graph consisting of a set of vertices V and edges E and two special terminal vertices representing a source s and sink t, where there is a one-to-one correspondence between cuts on the graph and configurations of the MRF, a
cut representing a partition of the vertices V into disjoint sets S and T such that sεS and tεT. The method further includes finding the minimum energy configuration, E(n(i)|φ(w)) of the MRF on the basis that the total cost of a given
cut represents the energy of the corresponding MRF configuration, where the cost of a
cut is the sum of all edges going from S to T across the cut boundary. The method further includes using the values of n(i) in the minimum energy configuration to perform the
phase unwrapping from φ(w) to φ(t) for the MR image. A confidence may be computed for each
voxel using dynamic graph cuts. The unwrapped phase from two
MR images acquired at different times may be used to estimate a field map from the
phase difference between the two
MR images. The field map may be converted into a deformation field which is then used to initialise a non-rigid
image registration of the acquired MR image against a
reference image. The deformation field of the non-rigid registration is controlled to be smoother where the confidence is high.