Abstract
Plane adjustment (PA) is crucial for many 3D applications, involving simultaneous pose estimation and plane recovery. Despite recent advancements, it remains a challenging problem in the realm of multi-view point cloud registration. Current state-of-the-art methods can achieve globally optimal convergence only with good initialization. Furthermore, their high time complexity renders them impractical for large-scale problems. To address these challenges, we first exploit a novel optimization strategy termed Bi-Convex Relaxation, which decouples the original problem into two simpler sub-problems, reformulates each sub-problem using a convex relaxation technique, and alternately solves each one until the original problem converges. Building on this strategy, we propose two algorithmic variants for solving the plane adjustment problem, namely GlobalPointer and GlobalPointer++, based on point-to-plane and plane-to-plane errors, respectively. Extensive experiments on both synthetic and real datasets demonstrate that our method can perform large-scale plane adjustment with linear time complexity, larger convergence region, and robustness to poor initialization, while achieving similar accuracy as prior methods. The code is available at github.com/wu-cvgl/GlobalPointer.
B. Lioa and Z. Zhao—Equal contribution.
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References
Anstreicher, K.M.: On convex relaxations for quadratically constrained quadratic programming. Math. Program. 136(2), 233–251 (2012). https://doi.org/10.1007/s10107-012-0602-3
ApS, M.: Mosek optimization toolbox for matlab. User’s Guide Ref. Manual, Version 4(1) (2019)
Briales, J., Gonzalez-Jimenez, J.: Convex global 3d registration with lagrangian duality. In: CVPR, pp. 4960–4969 (2017). https://doi.org/10.1109/CVPR.2017.595
Chen, Y., Zhao, J., Kneip, L.: Hybrid rotation averaging: a fast and robust rotation averaging approach. In: CVPR, pp. 10353–10362 (2021). https://doi.org/10.1109/CVPR46437.2021.01022
Dellaert, F., Rosen, D.M., Wu, J., Mahony, R., Carlone, L.: Shonan rotation averaging: global optimality by surfing \(so(p)^n\). In: ECCV, pp. 292–308 (2020). https://doi.org/10.1007/978-3-030-58539-6_18
Eriksson, A., Olsson, C., Kahl, F., Chin, T.J.: Rotation averaging and strong duality. In: CVPR, pp. 127–135 (2018). https://doi.org/10.1109/CVPR.2018.00021
Ferrer, G.: Eigen-factors: plane estimation for multi-frame and time-continuous point cloud alignment. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1278–1284 (2019). https://doi.org/10.1109/IROS40897.2019.8967573
Ferrer, G., Iarosh, D., Kornilova, A.: Eigen-factors an alternating optimization for back-end plane slam of 3d point clouds. arXiv preprint arXiv:2304.01055 (2023). https://doi.org/10.21203/rs.3.rs-4601229/v1
Härenstam-Nielsen, L., Zeller, N., Cremers, D.: Semidefinite relaxations for robust multiview triangulation. In: CVPR, pp. 749–757 (2023). https://doi.org/10.1109/CVPR52729.2023.00079
Helmberger, M., Morin, K., Berner, B., Kumar, N., Cioffi, G., Scaramuzza, D.: The hilti slam challenge dataset. IEEE Rob. Autom. Lett. 7(3), 7518–7525 (2022). https://doi.org/10.1109/LRA.2022.3183759
Hsiao, M., Westman, E., Zhang, G., Kaess, M.: Keyframe-based dense planar slam. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 5110–5117 (2017). https://doi.org/10.1109/ICRA.2017.7989597
Kaess, M.: Simultaneous localization and mapping with infinite planes. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 4605–4611 (2015). https://doi.org/10.1109/ICRA.2015.7139837
Liu, Z., Liu, X., Zhang, F.: Efficient and consistent bundle adjustment on lidar point clouds. IEEE Trans. Rob. 39(6), 4366–4386 (2023). https://doi.org/10.1109/TRO.2023.3311671
Liu, Z., Zhang, F.: Balm: bundle adjustment for lidar mapping. IEEE Rob. Autom. Lett. 6(2), 3184–3191 (2021). https://doi.org/10.1109/LRA.2021.3062815
Parra, A., Chng, S.F., Chin, T.J., Eriksson, A., Reid, I.: Rotation coordinate descent for fast globally optimal rotation averaging. In: CVPR, pp. 4296–4305 (2021). https://doi.org/10.1109/CVPR46437.2021.00428
Rosen, D.M., Carlone, L., Bandeira, A.S., Leonard, J.J.: Se-sync: a certifiably correct algorithm for synchronization over the special euclidean group. Int. J. Rob. Res. 38(2–3), 95–125 (2019). https://doi.org/10.1177/0278364918784361
Segal, A., Haehnel, D., Thrun, S.: Generalized-icp. In: Robotics: Science and Systems, p. 435 (2009). https://doi.org/10.15607/RSS.2009.V.021
Shan, T., Englot, B.: Lego-loam: lightweight and ground-optimized lidar odometry and mapping on variable terrain. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4758–4765 (2018). https://doi.org/10.1109/IROS.2018.8594299
Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle adjustment—a modern synthesis. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) IWVA 1999. LNCS, vol. 1883, pp. 298–372. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44480-7_21
Wang, Y., Yang, J., Yin, W., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci. 1(3), 248–272 (2008). https://doi.org/10.1137/080724265
Wolkowicz, H., Saigal, R., Vandenberghe, L. (eds.): Handbook of Semidefinite Programming: Theory, Algorithms, and Applications. Springer, Heidelberg (2000). https://doi.org/10.1007/978-1-4615-4381-7
Yang, H., Shi, J., Carlone, L.: Teaser: fast and certifiable point cloud registration. IEEE Trans. Rob. 37(2), 314–333 (2020). https://doi.org/10.1109/TRO.2020.3033695
Zhang, G., Larsson, V., Barath, D.: Revisiting rotation averaging: uncertainties and robust losses. In: CVPR, pp. 17215–17224 (2023). https://doi.org/10.1109/CVPR52729.2023.01651
Zhang, J., Singh, S.: Loam: lidar odometry and mapping in real-time. In: Robotics: Science and Systems, pp. 1–9 (2014). https://doi.org/10.15607/RSS.2014.X.007
Zhao, J.: An efficient solution to non-minimal case essential matrix estimation. IEEE TPAMI 44(4), 1777–1792 (2020). https://doi.org/10.1109/TPAMI.2020.3030161
Zhou, L.: Efficient second-order plane adjustment. In: CVPR, pp. 13113–13121 (2023). https://doi.org/10.1109/CVPR52729.2023.01260
Zhou, L., Koppel, D., Ju, H., Steinbruecker, F., Kaess, M.: An efficient planar bundle adjustment algorithm. In: IEEE International Symposium on Mixed and Augmented Reality (ISMAR), pp. 136–145 (2020). https://doi.org/10.1109/ISMAR50242.2020.00035
Zhou, L., Wang, S., Kaess, M.: \(\pi \)-lsam: lidar smoothing and mapping with planes. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 5751–5757 (2021). https://doi.org/10.1109/ICRA48506.2021.9561933
Zhou, Q.Y., Park, J., Koltun, V.: Open3d: a modern library for 3d data processing. arXiv preprint arXiv:1801.09847 (2018)
Acknowledgments
This work was supported in part by NSFC under Grant 62202389, in part by a grant from the Westlake University-Muyuan Joint Research Institute, and in part by the Westlake Education Foundation.
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Liao, B., Zhao, Z., Chen, L., Li, H., Cremers, D., Liu, P. (2025). GlobalPointer: Large-Scale Plane Adjustment with Bi-Convex Relaxation. In: Leonardis, A., Ricci, E., Roth, S., Russakovsky, O., Sattler, T., Varol, G. (eds) Computer Vision – ECCV 2024. ECCV 2024. Lecture Notes in Computer Science, vol 15117. Springer, Cham. https://doi.org/10.1007/978-3-031-73202-7_21
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