Segmentation of the left ventricle is a key approach in Cardiac Magnetic Resonance Imaging for calculating biomarkers in diagnosis. Since there is substantial effort required from the expert, many automatic segmentation methods have been proposed, in which deep learning networks have obtained remarkable performance. However, one of the main limitations of these approaches is the production of segmentations that contain anatomical errors. To avoid this limitation, we propose a new fully-automatic left ventricle segmentation method combining deep learning and deformable models. We propose a new level set energy formulation that includes exam-specific information estimated from the deep learning segmentation and shape constraints. The method is part of a pipeline containing pre-processing steps and a failure correction post-processing step. Experiments were conducted with the Sunnybrook and ACDC public datasets, and a private dataset. Results suggest that the method is competitive, that it can produce anatomically consistent segmentations, has good generalization ability, and is often able to estimate biomarkers close to the expert.