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.

该文提出了一种使用二次曲面描述三维场景的方法，以提高 LiDAR 测距、定位和映射的空间和时间效率。通过分解成稀疏的二次曲面贴片来代替原始点云数据，该方法避免了点对点的最近邻搜索过程，具有更高的存储效率和准确性，适用于 KITTI 和 UrbanLoco 数据集中大容量点云的实验。

利用二次曲面表示法进行 LiDar 里程计、地图绘制和定位

Quadric Representations for LiDAR Odometry, Mapping and Localization

We present a novel and effective method for detecting 3D primitives in
cluttered, unorganized point clouds, without axillary segmentation or type
specification. We consider the quadric surfaces for encapsulating the basic
building blocks of our environments - planes, spheres, ellipsoids, cones or
cylinders, in a unified fashion. Moreover, quadrics allow us to model higher
degree of freedom shapes, such as hyperboloids or paraboloids that could be
used in non-rigid settings.
We begin by contributing two novel quadric fits targeting 3D point sets that
are endowed with tangent space information. Based upon the idea of aligning the
quadric gradients with the surface normals, our first formulation is exact and
requires as low as four oriented points. The second fit approximates the first,
and reduces the computational effort. We theoretically analyze these fits with
rigor, and give algebraic and geometric arguments. Next, by re-parameterizing
the solution, we devise a new local Hough voting scheme on the null-space
coefficients that is combined with RANSAC, reducing the complexity from
$O(N^4)$ to $O(N^3)$ (three points). To the best of our knowledge, this is the
first method capable of performing a generic cross-type multi-object primitive
detection in difficult scenes without segmentation. Our extensive qualitative
and quantitative results show that our method is efficient and flexible, as
well as being accurate.

我们提出了一种新颖有效的方法来检测杂乱无序的点云中的 3D 原始体，无需辅助分割或类型说明，并考虑到了用于封装环境基本构建块 - 平面、球体、椭球体、圆锥或圆柱体的二次曲面的统一方式。本文的方法具有较高的准确性，并且是一种能够在困难场景下进行通用交叉类型多对象原始体检测的方法。