  Current LiDAR odometry, mapping and localization methods leverage point-wise
representations of 3D scenes and achieve high accuracy in autonomous driving
tasks. However, the space-inefficiency of methods that use point-wise
representations limits their development and usage in practical applications.
In particular, scan-submap matching and global map representation methods are
restricted by the inefficiency of nearest neighbor searching (NNS) for
large-volume point clouds. To improve space-time efficiency, we propose a novel
method of describing scenes using quadric surfaces, which are far more compact
representations of 3D objects than conventional point clouds. In contrast to
point cloud-based methods, our quadric representation-based method decomposes a
3D scene into a collection of sparse quadric patches, which improves storage
efficiency and avoids the slow point-wise NNS process. Our method first
segments a given point cloud into patches and fits each of them to a quadric
implicit function. Each function is then coupled with other geometric
descriptors of the patch, such as its center position and covariance matrix.
Collectively, these patch representations fully describe a 3D scene, which can
be used in place of the original point cloud and employed in LiDAR odometry,
mapping and localization algorithms. We further design a novel incremental
growing method for quadric representations, which eliminates the need to
repeatedly re-fit quadric surfaces from the original point cloud. Extensive
odometry, mapping and localization experiments on large-volume point clouds in
the KITTI and UrbanLoco datasets demonstrate that our method maintains low
latency and memory utility while achieving competitive, and even superior,
accuracy.
