  Micro-Aerial Vehicles (MAVs) have the advantage of moving freely in 3D space.
However, creating compact and sparse map representations that can be
efficiently used for planning for such robots is still an open problem. In this
paper, we take maps built from noisy sensor data and construct a sparse graph
containing topological information that can be used for 3D planning. We use a
Euclidean Signed Distance Field, extract a 3D Generalized Voronoi Diagram
(GVD), and obtain a thin skeleton diagram representing the topological
structure of the environment. We then convert this skeleton diagram into a
sparse graph, which we show is resistant to noise and changes in resolution. We
demonstrate global planning over this graph, and the orders of magnitude
speed-up it offers over other common planning methods. We validate our planning
algorithm in real maps built onboard an MAV, using RGB-D sensing.
