We propose a new method for the localization of a Micro Aerial Vehicle (MAV) with respect to a ground robot. We solve the problem of registering the 3D maps computed by the robots using different sensors: a dense 3D reconstruction from the MAV monocular camera is aligned with the map computed from the depth sensor on the ground robot. Once aligned, the dense reconstruction from the MAV is used to augment the map computed by the ground robot, by extending it with the information conveyed by the aerial views. The overall approach is novel, as it builds on recent developments in live dense reconstruction from moving cameras to address the problem of air-ground localization. The core of our contribution is constituted by a novel algorithm integrating dense reconstructions from monocular views, Monte Carlo localization, and an iterative pose refinement. In spite of the radically different vantage points from which the maps are acquired, the proposed method achieves high accuracy whereas appearance-based, state-of-the-art approaches fail. Experimental validation in indoor and outdoor scenarios reported an accuracy in position estimation of 0.08 meters and real time performance. This demonstrates that our new approach effectively overcomes the limitations imposed by the difference in sensors and vantage points that negatively affect previous techniques relying on matching visual features.