A novel automatic 3D+time left ventricle (LV) segmentation framework is proposed for cardiac magnetic resonance (CMR) datasets. The proposed framework consists of three conceptual blocks to delineate both endo and epicardial contours throughout the cardiac cycle: (1) an automatic 2D mid-ventricular initialization and segmentation; (2) an automatic stack initialization followed by a 3D segmentation at the end-diastolic phase; and (3) a tracking procedure. Hereto, we propose to adapt the recent B-spline Explicit Active Surfaces (BEAS) framework to the properties of CMR images by integrating dedicated energy terms. Moreover, we extend the coupled BEAS formalism towards its application in 3D MR data by adapting it to a cylindrical space suited to deal with the topology of the image data. Furthermore, a fast stack initialization method is presented for efficient initialization and to enforce consistent cylindrical topology. Finally, we make use of an anatomically constrained optical flow method for temporal tracking of the LV surface. The proposed framework has been validated on 45 CMR datasets taken from the 2009 MICCAI LV segmentation challenge. Results show the robustness, efficiency and competitiveness of the proposed method both in terms of accuracy and computational load.