This paper presents a novel algorithm for the analysis of heart motion from tagged magnetic resonance images. The displacement is estimated from the monogenic phase and is therefore robust to possible variations of the local image energy. A local affine model accounts for the typical contraction, torsion and shear of myocardial tissue. An effective B-spline multiresolution strategy automatically selects the scale returning the most consistent velocity estimate. The multiresolution strategy together with a least-squares estimate of the monogenic orientation make the algorithm robust under image noise. Results on realistic simulated images show the proposed algorithm to return more accurate velocity estimates than the SinMod algorithm, itself shown more accurate and robust than the state-of-the-art Harp method.