In this paper, we propose a resource-efficient system for real-time 3D terrain reconstruction and landing-spot detection for micro aerial vehicles. The system runs on an on-board smartphone processor and requires only the input of a single downlooking camera and an inertial measurement unit. We generate a two-dimensional elevation map that is probabilistic, of fixed size, and robot-centric, thus, always covering the area immediately underneath the robot. The elevation map is continuously updated at a rate of 1 Hz with depth maps that are triangulated from multiple views using recursive Bayesian estimation. To highlight the usefulness of the proposed mapping framework for autonomous navigation of micro aerial vehicles, we successfully demonstrate fully autonomous landing including landing-spot detection in real-world experiments.