Abstract
The LiDAR Odometry and Mapping (LOAM) algorithm ranks in second place in the Karlsruhe Institute of Technology and Toyota Technological Institute (KITTI), Visual Odometry/SLAM Evaluations. It utilizes a feature extraction algorithm based on the evaluation of the curvature of points under test, to produce estimated smooth and non-smooth regions within typically laser based Point Cloud Data (PCD). This feature extractor (FE) however, does not take into account PCD spatial or detection uncertainty, which can result in the divergence of the LOAM algorithm. Therefore, this article proposes the use of the Curvature Scale Space (CSS) algorithm as a replacement for LOAM’s current feature extractor. It justifies the substitution, based on the CSS algorithm’s similar computational complexity but improved feature detection repeatability. LOAM’s current feature extractor and the proposed CSS feature extractor are tested and compared with simulated and real data, including the KITTI odometry-laser data set. Additionally, a recent deep learning based LiDAR Odometry (LO) algorithm, the Convolutional Auto-Encoder (CAE)-LO algorithm, will also be compared, using this data set, in terms of its computational speed and performance. Performance comparisons are made based on the Absolute Trajectory Error (ATE) and Cardinalized Optimal Linear Assignment (COLA) metrics. Based on these metrics, the comparisons show significant improvements of the LOAM algorithm with the CSS feature extractor compared with the benchmark versions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- W :
-
World reference frame.
- L :
-
LiDAR reference frame.
- k :
-
Time index at which a particular LiDAR scan is made.
- \({^{X}}{\mathcal {P}_k}\) :
-
Point cloud array recorded at time k w.r.t reference frame X, \(X \in \{L,W\}\), comprising point vectors with coordinates x, y, z.
- \(\mathcal {C}^{(i)}_k\) :
-
Point cloud array of the i-th channel of \({^{X}}{}{\mathcal {P}_k}\) recorded at time k, comprising point vectors with coordinates x, y, z.
- \(\mathcal {S}^{(j)}_k\) :
-
Point cloud array of the j-th segment of \(\mathcal {C}^{(i)}_k\) recorded at time k, comprising point vectors with coordinates x, y, z.
- \(\mathcal {E}_k\), \(\mathcal {H}_k\) :
-
Edge, Planar feature point arrays recorded at time k, comprising point vectors with coordinates x, y, z.
- \(\kappa _{\text {LOAM/CSS}}(\mathcal {S}_k^{(j)}\)[l]):
-
Curvature parameter corresponding to 3D point l in \(\mathcal {S}_k^{(j)}[l]\).
- C :
-
Array of curvature values \(\kappa _{\text {LOAM}}(\mathcal {S}_k^{(j)}[l])\).
- \(\sigma _{\text {term}}\) :
-
Standard deviation regarding \(\text {term}\). \(\text {term} \in \{\text {CSS}, \text {range}\}\).
- \(K^{(\sigma _{\textrm{CSS}})}\) :
-
Array containing 3-tuples at scale \(\sigma _{\textrm{CSS}}\).
- F :
-
Array containing 3-tuples.
- Y[l]:
-
l-th element of array Y. \(Y \in \{\mathcal {C}^{(i)}_k, \mathcal {S}^{(j)}_k, \mathcal {E}_k, \mathcal {H}_k, C, K^{(\sigma _{\textrm{CSS}})}, F \}\).
- \({^{X}}{}{\textbf{T}_k}\) :
-
Rigid body transform function recorded at time index k w.r.t. reference frame X, \(X \in \{L,W\}\).
- \(\mid \cdot \mid \) :
-
Cardinality of point cloud arrays.
- \(\mid \mid \cdot \mid \mid \) :
-
\(l_2\)-norm.
- \(n_{\alpha }\) :
-
Number of items corresponding to \(\alpha \).
- \(d_{\beta }\) :
-
Threshold corresponding to feature type \(\beta \).
References
Bailey, T., Durrant-Whyte, H.: Simultaneous localization and mapping (slam): Part i. IEEE Robot. Autom. Mag. 13, 108–117 (2006). https://doi.org/10.1109/MRA.2006.1678144
Bailey, T., Durrant-whyte, H.: Simultaneous localization and mapping ( slam ): Part ii. IEEE Robot. Autom. Mag. 13, 108–117 (2006). https://doi.org/10.1109/MRA.2006.1678144
Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. Intelligent Robotics and Autonomous Agents series. MIT Press, Cambridge (2005)
Zhang, J., Singh, S.: Low-drift and real-time lidar odometry and mapping. Auton. Robot. 41, 401–416 (2017). https://doi.org/10.1007/s10514-016-9548-2
Geiger, A., Lenz, P., Urtasun, R.: Are we ready for autonomous driving? the kitti vision benchmark suite. In: 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp. 3354��3361. Providence (2012). https://doi.org/10.1109/CVPR.2012.6248074
Tong, Q., Shaozu, C.: A-LOAM: advanced implementation of LOAM (2019). https://github.com/HKUST-Aerial-Robotics/A-LOAM
Wang, H., Wang, C., Chen, C.-L, Xie, L.: F-loam : Fast lidar odometry and mapping. In: 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , pp. 4390–4396. Prague (2021). https://doi.org/10.1109/IROS51168.2021.9636655
Shan, T., Englot, B.: Lego-loam: Lightweight and ground-optimized lidar odometry and mapping on variable terrain. In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4758–4765. Madrid (2018). https://doi.org/10.1109/IROS.2018.8594299
Chen, S.W., Nardari, G.V., Lee, E.S., Qu, C., Liu, X., Romero, R.A.F., Kumar, V.: Sloam: Semantic lidar odometry and mapping for forest inventory. IEEE Robot. Autom. Lett. 5(2), 612–619 (2020). https://doi.org/10.1109/LRA.2019.2963823
Park, Y.S., Jang, H., Kim, A.: I-loam: Intensity enhanced lidar odometry and mapping. In: 2020 17th International Conference on Ubiquitous Robots (UR), pp. 455–458. Kyoto (2020). https://doi.org/10.1109/UR49135.2020.9144987
Masci, J., Meier, U., Cireşan, D., Schmidhuber, J.: Stacked convolutional auto-encoders for hierarchical feature extraction. In: Artificial Neural Networks and Machine Learning-ICANN 2011: 21st International Conference on Artificial Neural Networks, Espoo, Finland, June 14-17, 2011, Proceedings, Part I 21, pp. 52–59. Springer (2011)
Yin, D., Zhang, Q., Liu, J., Liang, X., Wang, Y., Maanpää, J., Ma, H., Hyyppä, J., Chen, R.: CAE-LO: Lidar odometry leveraging fully unsupervised convolutional auto-encoder for interest point detection and feature description. arXiv preprint arXiv:2001.01354
Yin, D.: CAE-LO (2020). https://github.com/SRainGit/CAE-LO
Mokhtarian, F., Mackworth, A.: Scale-based description and recognition of planar curves and two-dimensional shapes. IEEE Trans. Pattern Anal. Mach. Intell. PAMI–8(1), 34–43 (1986). https://doi.org/10.1109/TPAMI.1986.4767750
Gonzalez, C., Adams, M.: An improved feature extractor for the lidar odometry and mapping (LOAM) algorithm. In: 2019 International Conference on Control, Automation and Information Sciences (ICCAIS), pp. 1–7. Chengdu (2019). https://doi.org/10.1109/ICCAIS465282019.9074665
Barrios, P., Adams, M., Leung, K., Inostroza, F., Naqvi, G., Orchard, M.E.: Metrics for evaluating feature-based mapping performance. IEEE Trans. Rob. 33, 198–213 (2017). https://doi.org/10.1109/TRO.2016.2627027
Knuth, D.: Section 5.2.4: Sorting by Merging. Sorting and Searching. The Art of Computer Programming, 2nd edn., pp. 158–168. Addison-Wesley (1998)
Zhang, J.: LOAM Velodyne. ROS (2014). http://docs.ros.org/en/indigo/api/loam velodyne/html/files.html
Harris, C., Stephens, M.: A combined corner and edge detector. In: Proceedings of the Alvey Vision Conference, pp. 23–1236. Manchester (1988). https://doi.org/10.5244/C.2.23
Lowe, D.G.: Distinctive image features from scale invariant keypoints. Int. J. Comput. Vision 60, 91–110 (2004). https://doi.org/10.1023/B:VISI.0000029664.99615.94
Yu, Z.: Intrinsic shape signatures: A shape descriptor for 3d object recognition. In: 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops, pp. 689–696. Kyoto (2009). https://doi.org/10.1109/ICCVW.2009.5457637
Rusu, R.B., Cousins, S.: 3d is here: Point cloud library (pcl). In: 2011 IEEE International Conference on Robotics and Automation, pp. 1–4. Shanghai (2011). https://doi.org/10.1109/ICRA.2011.5980567
Besl, P.J., McKay, N.D.: A method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 239–256 (1992). https://doi.org/10.1109/34.12179
Yin, D., Zhang, Q., Liu, J., Liang, X., Wang, Y., Chen, S., Maanpää, J., Hyyppä, J., Chen, R.: Interest point detection from multi-beam light detection and ranging point cloud using unsupervised convolutional neural network. IET Image Proc. 15, 369–377 (2021). https://doi.org/10.1049/ipr2.12027
Nguyen, V., Martinelli, A., Tomatis, N., Siegwart, R.: A comparison of line extraction algorithms using 2d laser rangefinder for indoor mobile robotics. In: 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1929–1934. Edmonton (2005). https://doi.org/10.1109/IROS.2005.1545234
Nez, P., Vzquez-Martn, R., del Toro, J.C., Bandera, A., Sandoval, F.: Natural landmark extraction for mobile robot navigation based on an adaptive curvature estimation. Robot. Auton. Syst. 56, 247–264 (2008). https://doi.org/10.1016/j.robot.2007.07.005
Gonzalez, C.: An improved feature extractor for the lidar odometry and mapping algorithm. Master’s thesis, University of Chile - Electrical Engineering Department, Santiago, Chile (July 2019). https://repositorio.uchile.cl/handle/2250/171499
Borges, G.A., Aldon, M.-J.: Line extraction in 2d range images for mobile robotics. J. Intell. Rob. Syst. 40, 267–297 (2004). https://doi.org/10.1023/B:JINT.0000038945.55712.65
Li, Y., Olson, E.B.: Extracting general-purpose features from lidar data. In: 2010 IEEE International Conference on Robotics and Automation, pp. 1388–1393. Anchorage (2010). https://doi.org/10.1109/ROBOT.2010.5509690
Im, J.H., Im, S.H., Jee, G.I.: Vertical corner feature based precise vehicle localization using 3d lidar in urban area. Sensors 16(18) (2016). https://doi.org/10.3390/s16081268
Madhavan, R., Durrant-Whyte, H.F.: Natural landmark-based autonomous vehicle navigation. Robotics and Autonomous Systems (2004). https://doi.org/10.1016/j.robot.2003.11.003
Asada, H., Brady, M.: The curvature primal sketch. IEEE Trans. Pattern Anal. Mach. Intell. 8, 2–14 (1986) https://doi.org/10.1109/TPAMI.1986.4767747
Acknowledgements
This work was supported by Agencia Nacional de Investigación y Desarrollo (ANID - National Research Agency, Chile)/Programa de Investigación Asociativa (PIA) Project AFB180004 and ANID Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) project 1231658.
Funding
This work was supported by Agencia Nacional de Investigación y Desarrollo (ANID - National Research Agency, Chile)/Programa de Investigación Associativa (PIA) Project AFB180004 and ANID Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) project 1231658.
Author information
Authors and Affiliations
Contributions
The authors contributed equally to this work. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Ethics approval
Not applicable.
Consent to participate
Not applicable.
Consent to publish
Not applicable.
Competing interests
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Gonzalez, C., Adams, M. Curvature Scale Space LiDAR Odometry And Mapping (LOAM). J Intell Robot Syst 110, 67 (2024). https://doi.org/10.1007/s10846-024-02096-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10846-024-02096-1