Depth images generated by direct projection of LiDAR point clouds on the image plane suffer from a great level of sparsity which is difficult to interpret by classical computer vision algorithms. We propose a method for completing sparse depth images in a semantically accurate manner by training a novel morphological neural network. Our method approximates morphological operations by Contraharmonic Mean Filter layers which are easily trained in a contemporary deep learning framework. An early fusion U-Net architecture then combines dilated depth channels and RGB using multi-scale processing. Using a large scale RGBD dataset we are able to learn the optimal morphological and convolutional filter shapes that produce an accurate and fully sampled depth image at the output. Independent experimental evaluation confirms that our method outperforms classical image restoration techniques as well as current state-of-the-art neural networks. The resulting depth images preserve object boundaries and can easily be used to augment various tasks in intelligent vehicles perception systems.