The dependency of unmanned aerial vehicles (UAVs) on precise knowledge of their environment to fulfill missions without collision has restricted their application until today. Although aerial mapping has already become an astounding economic sector for example in the field of construction checking, surveying, and insurance inspection, there is still more potential for missions needing a higher degree of autonomy. It is comprehensible that developing accurate maps will expand the field of UAV application. Often the mission time and limited payload to bounded electrical energy or fuel is a further restriction. This makes less power consuming and lightweight exteroceptive sensors like the monocular camera especially interesting. This paper introduces a mapping system based on a monocular camera for UAVs. The core of this work is the development of a high accurate, memory efficient, extreme fast and C-language based occupancy map in 3D, operating under real-time constraints using only a single camera. First, a mapping system is constructed, which is based on the structure from motion extended Kalman filter and an occupancy grid filter. Research findings demonstrate that the mapping algorithm is more precise compared to the current state of science. Furthermore, an octree data structure is developed, to store the map efficiently and enable fast algorithms based on this map. The structure stands out of the mass by his compactness and clarity combined with a high efficiency in both memory and processing time.