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.

翻译：当前激光雷达里程计、建图与定位方法利用3D场景的点级表示，在自动驾驶任务中取得了高精度。然而，使用点级表示的方法空间效率低下，限制了其在实际应用中的发展与使用。特别是，扫描-子图匹配与全局地图表示方法受限于大容量点云中最近邻搜索的低效率。为提升时空效率，我们提出一种利用二次曲面描述场景的新方法，相较于传统点云，二次曲面是3D对象更为紧凑的表示。与基于点云的方法不同，我们的基于二次曲面表示的方法将3D场景分解为一组稀疏的二次曲面片，从而提升存储效率并避免缓慢的点级最近邻搜索过程。我们的方法首先将给定点云分割成多个面片，并将每个面片拟合为二次隐函数。随后，每个函数与该面片的其他几何描述子（如中心位置与协方差矩阵）相结合。这些面片表示共同完整描述了一个3D场景，可用于替代原始点云，并应用于激光雷达里程计、建图与定位算法中。我们进一步设计了一种新颖的二次曲面表示增量生长方法，无需从原始点云反复重新拟合二次曲面。在KITTI与UrbanLoco数据集的大容量点云上进行的广泛里程计、建图与定位实验表明，我们的方法在保持低延迟与内存利用率的同时，达到了具有竞争力甚至更优的精度。