QuadricsReg: Large-Scale Point Cloud Registration using Quadric Primitives

TL;DR

QuadricsReg tackles large-scale LiDAR point cloud registration by representing scenes with a compact set of quadric primitives, enabling robust correspondences under significant viewpoint changes and occlusions. It constructs multi-level compatibility graphs to establish quadric correspondences and employs a degeneracy-aware distance in a factor-graph optimization to estimate the 6-DoF transformation, achieving high accuracy and robustness. Extensive experiments across diverse public datasets and a real heterogeneous-sensor dataset demonstrate strong registration success rates, lower errors, and good generalization, with notable gains in loop closure and multi-session mapping scenarios. The approach offers a scalable, symbolically expressive alternative to dense geometric representations for global registration and SLAM backends, with potential for further gains by fusing image information and handling dynamic scenes.

Abstract

In the realm of large-scale point cloud registration, designing a compact symbolic representation is crucial for efficiently processing vast amounts of data, ensuring registration robustness against significant viewpoint variations and occlusions. This paper introduces a novel point cloud registration method, i.e., QuadricsReg, which leverages concise quadrics primitives to represent scenes and utilizes their geometric characteristics to establish correspondences for 6-DoF transformation estimation. As a symbolic feature, the quadric representation fully captures the primary geometric characteristics of scenes, which can efficiently handle the complexity of large-scale point clouds. The intrinsic characteristics of quadrics, such as types and scales, are employed to initialize correspondences. Then we build a multi-level compatibility graph set to find the correspondences using the maximum clique on the geometric consistency between quadrics. Finally, we estimate the 6-DoF transformation using the quadric correspondences, which is further optimized based on the quadric degeneracy-aware distance in a factor graph, ensuring high registration accuracy and robustness against degenerate structures. We test on 5 public datasets and the self-collected heterogeneous dataset across different LiDAR sensors and robot platforms. The exceptional registration success rates and minimal registration errors demonstrate the effectiveness of QuadricsReg in large-scale point cloud registration scenarios. Furthermore, the real-world registration testing on our self-collected heterogeneous dataset shows the robustness and generalization ability of QuadricsReg on different LiDAR sensors and robot platforms. The codes and demos will be released at \url{https://levenberg.github.io/QuadricsReg}.

Figures (17)

• Figure 1: Global point cloud registration using QuadricsReg. The raw point clouds are collected by an Unmanned Ground Vehicle (UGV), Unmanned Aerial Vehicle (UAV), and handheld platform equipped with different LiDAR sensors in a roof garden. Accurate map integration results demonstrate the effectiveness of QuadricsReg.
• Figure 2: The pipeline of QuadricsReg mainly consists of three parts: Quadric-based scene representation, quadric matching, and quadric-based 6-DoF transformation estimation.
• Figure 3: Illustration of quadric derivation and degeneracy. Ellipsoid $\mathbf{Q}_{1}$, cylinder $\mathbf{Q}_{2}$, line $\mathbf{Q}_{3}$, and plane $\mathbf{Q}_{4}$ are transformed from canonical quadrics $\mathbf{C}_{1}$, $\mathbf{C}_{2}$, $\mathbf{C}_{3}$, and $\mathbf{C}_{4}$. For $\mathbf{Q}_{1}$, rotation around axis $a$ is degenerate due to symmetry along axes $b$ and $c$. For $\mathbf{Q}_{2}$, scale and translation along axis $c$, and rotation around it, are degenerate due to openness along $c$ and symmetry on axes $a$, $b$. The other quadrics can be similarly analyzed.
• Figure 4: Quadric-based representation for LiDAR scans from KITTI dataset. The point scans are represented compactly using quadrics. Road structures like the ground, buildings, and poles can be modeled as planes and lines, while objects such as vehicles and trunks are treated as ellipsoids and elliptic cylinders. Additionally, we find that modeling vegetation as ellipsoids can effectively enrich scene representation. The top scene has an adequate number of key elements, whereas the bottom scene features extended and repetitive elements in a sparse arrangement.
• Figure 5: The quadric fitting strategy of point clouds. From a partially observed quadric point cloud, we first fit the canonical $\mathbf{C}$ and the pose $\mathbf{P}_q$, define the type and scale. Then we combine these attributes to form the quadric parameter $\mathbf{Q}$.