The zero-mean normalized cross-correlation is shown to improve the accuracy of optical flow, but its analytical form is quite complicated for the variational framework. This paper addresses this issue and presents a new direct approach to this matching measure. Our approach uses the correlation transform to define very discriminative descriptors that are pre-computed and that have to be matched in the target frame. It is equivalent to the computation of the optical flow for the correlation transforms of the images. The smoothness energy is non-local and uses a robust penalty in order to preserve motion discontinuities. The model is associated with a fast and parallelizable minimization procedure based on the projected-proximal point algorithm. The experiments confirm the strength of this model and implicitly demonstrate the correctness of our solution. The results demonstrate that the involved data term is very robust with respect to changes in illumination, especially where large illumination exists.