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This paper presents an automated method for measuring 3D left ventricular (LV) strain in each imaged time frame from phase unwrapped harmonic phase (HARP) images derived from tagged cardiac magnetic resonance imaging. In previous work, manually-placed branch cuts were used to resolve phase inconsistencies in HARP images before they were unwrapped. This paper presents an automated method for placing branch cuts in short-axis images based on simulated annealing with a new cost function based on temporal phase consistency. This method significantly reduces the amount of user interaction needed to compute 3D strain maps in the entire LV in each imaged time frame. The unwrapped-phase-derived strains were validated on a set of 40 human studies by comparing them to strains estimated by a previously published feature based technique and a previously published unwrapped-phase technique with manual branch cut placement.