Left ventricular non-compaction (LVNC) is a rare cardiomyopathy characterized by abnormal trabeculations in the left ventricle cavity. Although traditional computer vision approaches exist for LVNC diagnosis, deep learning-based tools could not be found in the literature. In this paper, a first approach using convolutional neural networks (CNNs) is presented. Four CNNs are trained to automatically segment the compacted and trabecular areas of the left ventricle for a population of patients diagnosed with Hypertrophic cardiomyopathy. Inference results confirm that deep learning-based approaches can achieve excellent results in the diagnosis and measurement of LVNC. The two best CNNs (U-Net and Efficient U-Net B1) perform image segmentation in less than 0.2 s on a CPU and in less than 0.01 s on a GPU. Additionally, a subjective evaluation of the output images with the identified zones is performed by expert cardiologists, with a perfect visual agreement for all the slices, outperforming already existing automatic tools.