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G3Reg: Pyramid Graph-based Global Registration using Gaussian Ellipsoid Model

Zhijian Qiao, Zehuan Yu, Binqian Jiang, Huan Yin, Shaojie Shen

TL;DR

G3Reg targets robust global LiDAR registration under high outlier rates and large viewpoint changes by replacing heavy keypoints/descriptors with Gaussian Ellipsoid Models (GEMs) that encode plane, line, and cluster primitives and their uncertainty. A distrust-and-verify pipeline, PAGOR, builds a pyramid compatibility graph to generate multiple transformation hypotheses via graduated maximum cliques, followed by a distribution-to-distribution TLS-like estimation and a geometry-based verification over compressed voxel maps. The combination yields fast, robust registration with real-time performance, outperforming state-of-the-art descriptor- and graph-based methods on KITTI, KITTI-LC, KITTI360-LC, Apollo-LC, and Campus-MS, while offering open-source code for integration and extension. The framework highlights the value of low-level geometric priors and multi-hypothesis verification for robust loop-closure and multi-session mapping in robotics applications, and points to future work on integrating higher-level semantics and localizability cues.

Abstract

This study introduces a novel framework, G3Reg, for fast and robust global registration of LiDAR point clouds. In contrast to conventional complex keypoints and descriptors, we extract fundamental geometric primitives, including planes, clusters, and lines (PCL) from the raw point cloud to obtain low-level semantic segments. Each segment is represented as a unified Gaussian Ellipsoid Model (GEM), using a probability ellipsoid to ensure the ground truth centers are encompassed with a certain degree of probability. Utilizing these GEMs, we present a distrust-and-verify scheme based on a Pyramid Compatibility Graph for Global Registration (PAGOR). Specifically, we establish an upper bound, which can be traversed based on the confidence level for compatibility testing to construct the pyramid graph. Then, we solve multiple maximum cliques (MAC) for each level of the pyramid graph, thus generating the corresponding transformation candidates. In the verification phase, we adopt a precise and efficient metric for point cloud alignment quality, founded on geometric primitives, to identify the optimal candidate. The algorithm's performance is validated on three publicly available datasets and a self-collected multi-session dataset. Parameter settings remained unchanged during the experiment evaluations. The results exhibit superior robustness and real-time performance of the G3Reg framework compared to state-of-the-art methods. Furthermore, we demonstrate the potential for integrating individual GEM and PAGOR components into other registration frameworks to enhance their efficacy. Code: https://github.com/HKUST-Aerial-Robotics/G3Reg

G3Reg: Pyramid Graph-based Global Registration using Gaussian Ellipsoid Model

TL;DR

G3Reg targets robust global LiDAR registration under high outlier rates and large viewpoint changes by replacing heavy keypoints/descriptors with Gaussian Ellipsoid Models (GEMs) that encode plane, line, and cluster primitives and their uncertainty. A distrust-and-verify pipeline, PAGOR, builds a pyramid compatibility graph to generate multiple transformation hypotheses via graduated maximum cliques, followed by a distribution-to-distribution TLS-like estimation and a geometry-based verification over compressed voxel maps. The combination yields fast, robust registration with real-time performance, outperforming state-of-the-art descriptor- and graph-based methods on KITTI, KITTI-LC, KITTI360-LC, Apollo-LC, and Campus-MS, while offering open-source code for integration and extension. The framework highlights the value of low-level geometric priors and multi-hypothesis verification for robust loop-closure and multi-session mapping in robotics applications, and points to future work on integrating higher-level semantics and localizability cues.

Abstract

This study introduces a novel framework, G3Reg, for fast and robust global registration of LiDAR point clouds. In contrast to conventional complex keypoints and descriptors, we extract fundamental geometric primitives, including planes, clusters, and lines (PCL) from the raw point cloud to obtain low-level semantic segments. Each segment is represented as a unified Gaussian Ellipsoid Model (GEM), using a probability ellipsoid to ensure the ground truth centers are encompassed with a certain degree of probability. Utilizing these GEMs, we present a distrust-and-verify scheme based on a Pyramid Compatibility Graph for Global Registration (PAGOR). Specifically, we establish an upper bound, which can be traversed based on the confidence level for compatibility testing to construct the pyramid graph. Then, we solve multiple maximum cliques (MAC) for each level of the pyramid graph, thus generating the corresponding transformation candidates. In the verification phase, we adopt a precise and efficient metric for point cloud alignment quality, founded on geometric primitives, to identify the optimal candidate. The algorithm's performance is validated on three publicly available datasets and a self-collected multi-session dataset. Parameter settings remained unchanged during the experiment evaluations. The results exhibit superior robustness and real-time performance of the G3Reg framework compared to state-of-the-art methods. Furthermore, we demonstrate the potential for integrating individual GEM and PAGOR components into other registration frameworks to enhance their efficacy. Code: https://github.com/HKUST-Aerial-Robotics/G3Reg
Paper Structure (34 sections, 1 theorem, 27 equations, 10 figures, 9 tables, 2 algorithms)

This paper contains 34 sections, 1 theorem, 27 equations, 10 figures, 9 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. 3D Point Matching
  4. 3D Keypoint Detection
  5. 3D Descriptor-based Matching
  6. Outlier Pruning
  7. Robust Transformation Estimation
  8. Problem Formulation
  9. GEM-based Data Association
  10. Plane-aided Segmentation
  11. Parameter Estimation
  12. Soft Association
  13. Graph-theoretic Outlier Pruning
  14. Compatibility Graph Construction
  15. Multi-Threshold Compatibility Test
  16. ...and 19 more sections

Key Result

Proposition 1

Given $\chi_{(p_{m+1})}^{2} > \chi_{(p_{m})}^{2}$, it follows that $|{{\mathcal{G}}^{MC}_{m+1}}| \geq |{{\mathcal{G}}^{MC}_m}|$.

Figures (10)

  • Figure 1: Global registration procedure using our proposed G3Reg. (a) Front-end GEM matching for Gaussian ellipsoid modeling and correspondence building. (b) Back-end PAGOR for outlier pruning and pose estimation under a distrust-and-verify scheme. (c) A challenging global registration result at a road intersection, in which the two LiDAR point clouds are with low overlap and a large view difference.
  • Figure 2: The proposed global registration method G3Reg adopts a distrust-and-verify framework, consisting of three components. First, putative correspondences between input point clouds are established via GEM-based data association (block in yellow). Then a pyramid compatibility graph is constructed to generate maximal cliques to obtain transformation candidates (block in green). Finally, the original point cloud information is re-utilized to select the optimal candidate (block in brownish-orange).
  • Figure 3: Visualization of GEM-based data association. Green, yellow, and orange represent planes, clusters, and lines respectively. (a) and (b) show the difference in segmentation results without or with plane assistance. As the arrow indicates, the former leads to under-segmentation. (c) is a different frame from (b). We use different colors and indices to illustrate the matching between GEMs of these two frames.
  • Figure 4: (a) The blue and orange point clouds are from a pair of loop closure frames. The figure shows two clusters and their centers (the red and green spheres represent the centers of the blue and yellow clusters, respectively) with 3D OBBs. (b) The red and green spheres are defined the same as in (a), and the blue pentagrams are the ground truth centers of the two clusters. The deviations of the observed centers from the ground truth are constrained within OBEs tangent to the OBBs. In addition, the translation and rotation invariant measurements (TRIMs) $\|\mu^{ij}_x{\|_{2}}$ and $\|\mu^{ij}_y{\|_{2}}$ and their ground truths $\|\hat{\mu}_{x}^{ij}{\|_{2}}$ are denoted by the red, green and blue lines, respectively.
  • Figure 5: The distributions of ground truth rotations and translations in different datasets. This figure shows broader distributions that can effectively validate global registration performances.
  • ...and 5 more figures

Theorems & Definitions (2)

  • Proposition 1: Lower Bound of Clique Cardinality
  • proof