Advertisement

Impact of Landmark Parametrization on Monocular EKF-SLAM with Points and Lines

Abstract

This paper explores the impact that landmark parametrization has in the performance of monocular, EKF-based, 6-DOF simultaneous localization and mapping (SLAM) in the context of undelayed landmark initialization.

Undelayed initialization in monocular SLAM challenges EKF because of the combination of non-linearity with the large uncertainty associated with the unmeasured degrees of freedom. In the EKF context, the goal of a good landmark parametrization is to improve the model’s linearity as much as possible, improving the filter consistency, achieving robuster and more accurate localization and mapping.

This work compares the performances of eight different landmark parametrizations: three for points and five for straight lines. It highlights and justifies the keys for satisfactory operation: the use of parameters behaving proportionally to inverse-distance, and landmark anchoring. A unified EKF-SLAM framework is formulated as a benchmark for points and lines that is independent of the parametrization used. The paper also defines a generalized linearity index suited for the EKF, and uses it to compute and compare the degrees of linearity of each parametrization. Finally, all eight parametrizations are benchmarked employing analytical tools (the linearity index) and statistical tools (based on Monte Carlo error and consistency analyses), with simulations and real imagery data, using the standard and the robocentric EKF-SLAM formulations.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.

References

  1. Aidala, V., & Hammel, S. (1983). Utilization of modified polar coordinates for bearings-only tracking. IEEE Transactions on Automatic Control, 28(3), 283–294.

  2. Bailey, T. (2003). Constrained initialisation for bearing-only SLAM. In Int. conf. on robotics and automation (pp. 1966–1971).

  3. Bailey, T., Nieto, J., Guivant, J., Stevens, M., & Nebot, E. (2006). Consistency of the EKF-SLAM algorithm. In IEEE/RSJ int. conf. on intelligent robots and systems, Beijing, China (pp. 3562–3568).

  4. Bar-Shalom, Y., Li, X. R., & Kirubarajan, T. (2001). Estimation with applications to tracking and navigation. New York: Wiley.

  5. Bartoli, A., & Sturm, P. (2001). The 3D line motion matrix and alignment of line reconstructions. In IEEE computer society conference on computer vision and pattern recognition (Vol. 1, pp. 287–292).

  6. Berger, C., & Lacroix, S. (2010). DSeg: Détection directe de segments dans une image. In Reconnaissance des formes et intelligence artificielle.

  7. Bonarini, A., Burgard, W., Fontana, G., Matteucci, M., Sorrenti, D. G., & Tardos, J. D. (2006). RAWSEEDS: robotics advancement through web-publishing of sensorial and elaborated extensive data sets. In Proceedings of IROS’06 workshop on benchmarks in robotics research.

  8. Castellanos, J. A., Neira, J., & Tardós, J. D. (2004). Limits to the consistency of the EKF-based SLAM. In 5th IFAC symp. on intelligent autonomous vehicles, Lisboa, PT.

  9. Castellanos, J. A., Martinez-Cantin, R., Tardós, J. D., & Neira, J. (2007). Robocentric map joining: improving the consistency of EKF-SLAM. In Robotics and autonomous systems (Vol. 55, pp. 21–29).

  10. Ceriani, S., Fontana, G., Giusti, A., Marzorati, D., Matteucci, M., Migliore, D., Rizzi, D., Sorrenti, D. G., & Taddei, P. (2009). Rawseeds ground truth collection systems for indoor self-localization and mapping. Autonomous Robots, 27(4), 353–371.

  11. Chiuso, A., Favaro, P., Jin, H., & Soatto, S. (2002). Structure from motion causally integrated over time. In IEEE trans. on pattern analysis and machine intelligence (Vol. 24, pp. 523–535).

  12. Civera, J. (2009) Real-time EKF-based structure from motion. Ph.D. thesis, Universidad de Zaragoza.

  13. Civera, J., Davison, A. J., & Montiel, J. M. M. (2008). Inverse depth parametrization for monocular SLAM. IEEE Transactions on Robotics, 24(5), 932–945.

  14. Civera, J., Grasa, O. G., Davison, A. J., & Montiel, J. M. M. (2009). 1-point RANSAC for EKF-based structure from motion. In IEEE/RSJ int. conf. on intelligent robots and systems.

  15. Davison, A. J. (2003). Real-time simultaneous localisation and mapping with a single camera. In Int. conf. on computer vision, Nice (Vol. 2, pp. 1403–1410).

  16. Davison, A. J., Reid, I. D., Molton, N. D., & Stasse, O. (2007). MonoSLAM: real-time single camera SLAM. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(6), 1052–1067.

  17. Eade, E., & Drummond, T. (2006a). Edge landmarks in monocular SLAM. In British machine vision conf., Edinburgh, Scotland.

  18. Eade, E., & Drummond, T. (2006b). Scalable monocular SLAM. IEEE International Conference on Computer Vision and Pattern Recognition, 1, 469–476. http://doi.ieeecomputersociety.org/10.1109/CVPR.2006.263.

  19. Eade, E., & Drummond, T. (2007). Monocular SLAM as a graph of coalesced observations. In IEEE int. conf. on computer vision.

  20. Engels, C., Stewénius, H., & Nistér, D. (2006). Bundle adjustment rules. In Photogrammetric computer vision.

  21. Gee, A. P., & Mayol, W. (2006). Real-time model-based SLAM using line segments. In LNCS proceedings of the 2nd international symposium on visual computing.

  22. Gee, A. P., Chekhlov, D., Calway, A., & Mayol-Cuevas, W. (2008). Discovering higher level structure in visual SLAM. In IEEE trans. on robotics special issue on visual SLAM (Vol. 24, pp. 980–990).

  23. Geeter, J. D., Brussel, H. V., Schutter, J. D., & Decréton, M. (1997). A smoothly constrained Kalman filter. In IEEE trans. on pattern analysis and machine intelligence (Vol. 24, pp. 1171–1177).

  24. Haner, S., & Heyden, A. (2010). On-line structure and motion estimation based on an novel parameterized extended Kalman filter. In Int. conf. on pattern recognition, Istambul, Turkey.

  25. Holmes, S. A., Klein, G., & Murray, D. W. (2008). A square root UKF for visual monoSLAM. In IEEE int. conf. on robotics and automation, Pasadena.

  26. Huang, S., & Dissanayake, G. (2007). Convergence and consistency analysis for extended Kalman filter based SLAM. In IEEE transactions on robotics (Vol. 23, pp. 1036–1049).

  27. Huang, G., Mourikis, A., & Roumeliotis, S. (2008). Analysis and improvement of the consistency of extended Kalman filter based SLAM. In IEEE int. conf. on robotics and automation (pp. 473–479).

  28. Klein, G., & Murray, D. (2007). Parallel tracking and mapping for small AR workspaces. In Proceedings of the 2007 6th IEEE and ACM international symposium on mixed and augmented reality (pp. 1–10). Los Alamitos: IEEE Comput. Soc.

  29. Klein, G., & Murray, D. (2008). Improving the agility of keyframe-based SLAM. In 10th European conference on computer vision (pp. 802–815). Marseille.

  30. Konolige, K., & Agrawal, M. (2008). FrameSLAM: From bundle adjustment to real-time visual mapping. IEEE Transactions on Robotics, 24(5), 1066–1077.

  31. Kwok, N. M., & Dissanayake, G. (2003). Bearing-only SLAM in indoor environments using a modified particle filter. In Australasian conf. on robotics and automation (ACRA), Brisbane, Australia.

  32. Kwok, N. M., & Dissanayake, G. (2004). An efficient multiple hypothesis filter for bearing-only SLAM. In IEEE/RSJ int. conf. on intelligent robots and systems, Sendai, Japan.

  33. Lemaire, T., & Lacroix, S. (2007). Monocular-vision based SLAM using line segments. In IEEE int. conf. on robotics and automation (pp. 2791–2796). Rome, Italy.

  34. Lemaire, T., Lacroix, S., & Solà, J. (2005). A practical 3D bearing only SLAM algorithm. In IEEE/RSJ int. conf. on intelligent robots and systems, Edmonton, Canada.

  35. Lourakis, M., & Argyros, A. (2004). The design and implementation of a generic sparse bundle adjustment software package based on the levenberg-marquardt algorithm (Tech. Rep. 340). Institute of Computer Science—FORTH, Heraklion, Crete, Greece, available from http://www.ics.forth.gr/~lourakis/sba.

  36. Marzorati, D., Matteucci, M., Migliore, D., & Sorrenti, D. G. (2008). Monocular SLAM with inverse scaling parametrization. In Proc. of the British machine vision conference, Leeds.

  37. Montiel, J. M. M., Civera, J., & Davison, A. J. (2006). Unified inverse depth parametrization for monocular SLAM. In Robotics: science and systems, Philadelphia, USA.

  38. Paz, L. M., Piniés, P., Tardós, J. D., & Neira, J. (2008). Large scale 6DOF SLAM with stereo-in-hand. IEEE Transactions on Robotics, 24(5), 946–957.

  39. Piniés, P., Lupton, T., Sukkarieh, S., & Tardós, J. D. (2007). Inertial aiding of inverse depth SLAM using a monocular camera. In Int. conf. on robotics and automation.

  40. Smith, R., & Cheeseman, P. (1987). On the representation and estimation of spatial uncertainty. The International Journal of Robotics Research, 5(4), 56–68.

  41. Smith, P., Reid, I., & Davison, A. J. (2006). Real-time monocular SLAM with straight lines. In British machine vision conf (Vol. 1, pp. 17–26).

  42. Solà, J. (2007). Towards visual localization, mapping and moving objects tracking by a mobile robot: a geometric and probabilistic approach. Ph.D. thesis, Institut National Polytechnique de Toulouse.

  43. Solà, J. (2010). Consistency of the monocular EKF-SLAM algorithm for 3 different landmark parametrizations. In IEEE int. conf. on robotics and automation, Anckorage, USA.

  44. Solà, J., Monin, A., Devy, M., & Lemaire, T. (2005). Undelayed initialization in bearing only SLAM. In IEEE/RSJ int. conf. on intelligent robots and systems (pp. 2499–2504). Edmonton, Canada.

  45. Solà, J., Monin, A., Devy, M., & Vidal-Calleja, T. (2008). Fusing monocular information in multi-camera SLAM. IEEE Transactions on Robotics, 24(5), 958–968.

  46. Solà, J., Marquez, D., Codol, J. M., & Vidal-Calleja, T. (2009a). An EKF-SLAM toolbox for MATLAB. http://homepages.laas.fr/jsola/JoanSola/eng/toolbox.html.

  47. Solà, J., Vidal-Calleja, T., & Devy, M. (2009b). Undelayed initialization of line segments in monocular SLAM. In IEEE/RSJ int. conf. on intelligent robots and systems (pp. 1553–1558). Saint Louis, USA.

  48. Strasdat, H., Montiel, J. M. M., & Davison, A. J. (2010). Real-time monocular SLAM: Why filter? In Int. conf. on robotics and automation, Anckorage, USA.

  49. Sunderhauf, N., Lange, S., & Protzel, P. (2007). Using the unscented kalman filter in mono-SLAM with inverse depth parametrization for autonomous airship control. In IEEE int. workshop on safety, security and rescue robotics, Rome.

  50. Triggs, B., McLauchlan, P., Hartley, R., & Fitzgibbon, A. (2000). Bundle adjustment—A modern synthesis. In W. Triggs, A. Zisserman, & R. Szeliski (Eds.), LNCS. Vision algorithms: theory and practice (pp. 298–375). Berlin: Springer.

Download references

Author information

Correspondence to Joan Solà.

Electronic Supplementary Material

Below are the links to the electronic supplementary material.

(MOV 4.62 MB)

(MOV 4.87 MB)

(MOV 4.80 MB)

(MOV 4.92 MB)

(MOV 4.62 MB)

(MOV 4.87 MB)

(MOV 4.80 MB)

(MOV 4.92 MB)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Solà, J., Vidal-Calleja, T., Civera, J. et al. Impact of Landmark Parametrization on Monocular EKF-SLAM with Points and Lines. Int J Comput Vis 97, 339–368 (2012) doi:10.1007/s11263-011-0492-5

Download citation

Keywords

  • Monocular vision
  • Simultaneous localization and mapping
  • Structure from motion
  • Landmark parametrization
  • Kalman filtering
  • Benchmarking
  • Linearity
  • Consistency