Localization of a robotic system within a previously mapped environment is important for reducing estimation drift and for reusing previously built maps. Existing techniques for geometry-based localization have focused on the description of local surface geometry, usually using pointclouds as the underlying representation. We propose a system for geometry-based localization that extracts features directly from an implicit surface representation: the Signed Distance Function (SDF). The SDF varies continuously through space, which allows the proposed system to extract and utilize features describing both surfaces and free-space. Through evaluations on public datasets, we demonstrate the flexibility of this approach, and show an increase in localization performance over state-of-the-art handcrafted surfaces-only descriptors. We achieve an average improvement of ~12% on an RGB-D dataset and ~18% on a LiDAR-based dataset. Finally, we demonstrate our system for localizing a LiDAR-equipped MAV within a previously built map of a search and rescue training ground.
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