Impairment of left ventricular contractility due to cardiovascular diseases is reflected in left ventricle (LV) motion patterns. An abnormal change of torsion or long axis shortening LV values can help with the diagnosis and follow-up of LV dysfunction. Tagged Magnetic Resonance (TMR) is a widely spread medical imaging modality that allows estimation of the myocardial tissue local deformation. In this work, we introduce a novel variational framework for extracting the left ventricle dynamics from TMR sequences. A bi-dimensional representation space of TMR images given by Gabor filter banks is defined. Tracking of the phases of the Gabor response is combined using a variational framework which regularizes the deformation field just at areas where the Gabor amplitude drops, while restoring the underlying motion otherwise. The clinical applicability of the proposed method is illustrated by extracting normality models of the ventricular torsion from 19 healthy subjects.