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.

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