In this paper, we propose a resource-efficient approach to provide an autonomous UAV with an on-board perception method to detect safe, hazard-free landing sites during flights over complex 3D terrain. We aggregate 3D measurements acquired from a sequence of monocular images by a Structure-from-Motion approach into a local, robot-centric, multi-resolution elevation map of the overflown terrain, which fuses depth measurements according to their lateral surface resolution (pixel-footprint) in a probabilistic framework based on the concept of dynamic Level of Detail. Map aggregation only requires depth maps and the associated poses, which are obtained from an onboard Visual Odometry algorithm. An efficient landing site detection method then exploits the features of the underlying multi-resolution map to detect safe landing sites based on slope, roughness, and quality of the reconstructed terrain surface. The evaluation of the performance of the mapping and landing site detection modules are analyzed independently and jointly in simulated and real-world experiments in order to establish the efficacy of the proposed approach.