In previous work, a three-dimensional left ventricular strain throughout the cardiac cycle was reconstructed using a prolate spheroidal B-spline (PSB) method with displacement measurements obtained from unwrapped tagged MRI (tMRI) harmonic phase images. Manually placed branch cuts were required for each harmonic phase image to resolve phase inconsistencies and to guide the phase unwrapping (mSUP), which is both labor intensive and time consuming and therefore not proper for clinic application. In this paper, we present an automated graph cuts based phase unwrapping method for myocardium displacement measurement (caSUP) which can be used to compute 3D+time cardiac strain. A set of 8 human studies were used to optimize parameters of the energy function and another set of 32 human studies were used to validate the proposed method by comparing resulted strains with those from mSUP and a feature-based (FB) method using the same PSB strain reconstruction. The automated caSUP strains were close to the manual strains and only required 6 minutes after myocardium segmentation versus ∼2 hours for the manual method. © 2014 Springer International Publishing.