Image registration describes the process of manipulating a distorted version of an image such that its pixels overlay the equivalent pixels in a clean, master or reference image. The need for it has assumed particular prominence in the analysis of images of electrophoretic gels used in the analysis of protein expression levels in living cells, but also has fundamental applications in most other areas of image analysis. Much of the positional information of a data feature is carried in the phase of a complex transform, so a complex transform allows explicit specification of the phase, and hence of the position of features in the image. Registration of a test gel to a reference gel is achieved by using a multiresolution movement map derived from the phase of a complex wavelet transform (the Q-shift wavelet transform) to dictate the warping directly via movement of the nodes of a Delaunay-triangulated mesh of points. This warping map is then applied to the original untransformed image such that the absolute magnitude of the spots remains unchanged. The technique is general to any type of image. Results are presented for a simple computer simulated gel, a simple real gel registration between similar "clean" gels with local warping vectors distributed about one main direction, a hard problem between a reference gel and a "dirty" test gel with multi-directional warping vectors and many artifacts, and some typical gels of present interest in post-genomic biology. The method compares favourably with others, since it is computationally rapid, effective and entirely automatic.