Monocular depth map prediction has become in recent years a major research topic in computer vision. Especially with the emergence of self-supervised methods that have demonstrated that based on geometric properties, it is possible to obtain good results without human generated labels. But these methods are, for the moment, mainly oriented towards high resolution dense reconstruction and therefore neglect applications for robotic navigation. In this paper, we propose addressing this problem by developing a solution for navigation and obstacle avoidance. The method takes advantage of dense depth prediction to segment the view into a limited number of classes of interest for navigation. Four classes have been thus retained: one to segment the road and three to cluster obstacles by their distance (close, middle and far). As a result, the system is able to directly identify threats and areas where it can navigate. Furthermore, efficient information compression can be considered using a quadtree data structure derived from Quadtree Generating Network. Experiments conducted on the Kitti dataset have shown our proposed method can efficiently predict a quadtree segmentation directly from monocular input images. In addition, the approach tends to significantly reduce the amount of information to be predicted without any loss of accuracy.