  There are many possibilities for how to represent the map in simultaneous
localisation and mapping (SLAM). While sparse, keypoint-based SLAM systems have
achieved impressive levels of accuracy and robustness, their maps may not be
suitable for many robotic tasks. Dense SLAM systems are capable of producing
dense reconstructions, but can be computationally expensive and, like sparse
systems, lack higher-level information about the structure of a scene.
Human-made environments contain a lot of structure, and we seek to take
advantage of this by enabling the use of quadric surfaces as features in SLAM
systems. We introduce a minimal representation for quadric surfaces and show
how this can be included in a least-squares formulation. We also show how our
representation can be easily extended to include additional constraints on
quadrics such as those found in quadrics of revolution. Finally, we introduce a
proof-of-concept SLAM system using our representation, and provide some
experimental results using an RGB-D dataset.
