We study how autonomous robots can learn by themselves to improve their depth estimation capability. In particular, we investigate a self-supervised learning setup in which stereo vision depth estimates serve as targets for a convolutional neural network (CNN) that transforms a single still image to a dense depth map. After training, the stereo and mono estimates are fused with a novel fusion method that preserves high confidence stereo estimates, while leveraging the CNN estimates in the low-confidence regions. The main contribution of the article is that it is shown that the fused estimates lead to a higher performance than the stereo vision estimates alone. Experiments are performed on the KITTI dataset, and on board of a Parrot SLAMDunk, showing that even rather limited CNNs can help provide stereo vision equipped robots with more reliable depth maps for autonomous navigation.