# Visual Odometry from Two Point Correspondences and Initial Automatic Camera Tilt Calibration

### Mårten Wadenbäck, Martin Karlsson, Anders Heyden, Anders Robertsson, Rolf Johansson

#### Abstract

Ego-motion estimation is an important step towards fully autonomous mobile robots. In this paper we propose the use of an initial but automatic camera tilt calibration, which transforms the subsequent motion estimation to a 2D rigid body motion problem. This transformed problem is solved $\ell_2$-optimally using RANSAC and a two-point method for rigid body motion. The method is experimentally evaluated using a camera mounted onto a mobile platform. The results are compared to measurements from a highly accurate external camera positioning system which are used as gold standard. The experiments show promising results on real data.

#### References

1. Arun, K. S., T. S. Huang and S. D. Blostein (1987). “Least Squares Fitting of Two 3-D Point Sets”. In: IEEE Transactions on Pattern Analysis and Machine Intelligence 9(5), pp. 698-700.
2. Axis Communications AB (2012). AXIS P3364-VE Network Camera. URL: http://www.axis.com/global/en/ products/axis-p3364-ve (visited on 27/02/2016).
3. Bay, H., T. Tuytelaars and L. Van Gool (2006). “SURF: Speeded Up Robust Features”. In: Proceedings of the 9th European Conference on Computer Vision (ECCV). Vol. 3951. in series Lecture Notes in Computer Science. Graz, Austria: Springer-Verlag, pp. 404-417.
4. Davison, A. J., I. D. Reid, N. D. Molton and O. Stasse (2007). “MonoSLAM: Real-Time Single Camera SLAM”. In: IEEE Transactions on Pattern Analysis and Machine Intelligence 29(6), pp. 1052-1067.
5. Durrant-Whyte, H. F. (1987). “Consistent Integration and Propagation of Disparate Sensor Observations”. In: The International Journal of Robotics Research 6(3), pp. 3-24.
6. Fischler, M. A. and R. C. Bolles (1981). “Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography”. In: Communications of the ACM 24(6), pp. 381-395.
7. Fraunhofer IPA (2012). Compact Drive Modules for Omnidirectional Robot Platforms. URL: http:// www.care-o-bot.de/en/rob-work.html (visited on 26/02/2016).
8. Gustafsson, F. (2012). Statistical Sensor Fusion. Second ed. Lund, Sweden: Studentlitteratur AB.
9. Hajjdiab, H. and R. Laganière (2004). “Vision-based MultiRobot Simultaneous Localization and Mapping”. In: Proceedings of the 1st Canadian Conference on Computer and Robot Vision (CRV). London, ON, Canada: IEEE Computer Society, pp. 155-162.
10. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (2005). Barcelona, Spain: IEEE Robotics and Automation Society.
11. Harris, C. G. and J. M. Pike (1988). “3D Positional Integration from Image Sequences”. In: Image and Vision Computing 6(2), pp. 87-90.
12. Hartley, R. I. and A. Zisserman (2004). Multiple View Geometry in Computer Vision. Second ed. Cambridge, England, UK: Cambridge University Press.
13. Jones, E. S. and S. Soatto (2011). “Visual-inertial navigation, mapping and localization: A scalable real-time causal approach”. In: The International Journal of Robotics Research 30(4), pp. 407-430.
14. Karlsson, N. et al. (2005). “The vSLAM Algorithm for Robust Localization and Mapping”. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA). Barcelona, Spain: IEEE Robotics and Automation Society, pp. 24-29.
15. Liang, B. and N. Pears (2002). “Visual Navigation using Planar Homographies”. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA). Vol. 1.Washington, DC, USA: IEEE Robotics and Automation Society, pp. 205-210.
16. Muja, M. and D. G. Lowe (2009). “Fast Approximate Nearest Neighbors with Automatic Algorithm Configuration”. In: Proceedings of the Fourth International Conference on Computer Vision Theory and Applications (VISAPP). Vol. 1. Lisbon, Portugal: INSTICC Press, pp. 331-340.
17. Muja, M. and D. G. Lowe (2014). “Scalable Nearest Neighbor Algorithms for High Dimensional Data”. In: IEEE Transactions on Pattern Analysis and Machine Intelligence 36(11), pp. 2227-2240.
18. Newman, P. and K. Ho (2005). “SLAM- Loop Closing with Visually Salient Features”. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA). Barcelona, Spain: IEEE Robotics and Automation Society, pp. 635-642.
19. Nikon Corporation (2011). K-Series Optical CMM solutions - supporting a variety of metrology applocations. URL: http://www.nikonmetrology.com (visited on 26/02/2016).
20. Ortín, D. and J. M. M. Montiel (2001). “Indoor robot motion based on monocular images”. In: Robotica 19(3), pp. 331-342.
21. Scaramuzza, D. (2011a). “1-Point-RANSAC Structure from Motion for Vehicle-Mounted Cameras by Exploiting Non-holonomic Constraints”. In: International Journal of Computer Vision 95(1), pp. 74-85.
22. Scaramuzza, D. (2011b). “Performance Evaluation of 1- Point-RANSAC Visual Odometry”. In: Journal of Field Robotics 28(5), pp. 792-811.
23. Wadenbäck, M. and A. Heyden (2014). “Ego-Motion Recovery and Robust Tilt Estimation for Planar Motion Using Several Homographies”. In: Proceedings of the 9th International Conference on Computer Vision Theory and Applications (VISAPP). Vol. 3. Lisbon, Portugal: SCITEPRESS, pp. 635-639.
24. Zienkiewicz, J. and A. J. Davison (2015). “Extrinsics Autocalibration for Dense Planar Visual Odometry”. In: Journal of Field Robotics 32(5), pp. 803-825.

#### in Harvard Style

Wadenbäck M., Karlsson M., Heyden A., Robertsson A. and Johansson R. (2017). Visual Odometry from Two Point Correspondences and Initial Automatic Camera Tilt Calibration . In Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 6: VISAPP, (VISIGRAPP 2017) ISBN 978-989-758-227-1, pages 340-346. DOI: 10.5220/0006079903400346

#### in Bibtex Style

@conference{visapp17,
author={Mårten Wadenbäck and Martin Karlsson and Anders Heyden and Anders Robertsson and Rolf Johansson},
title={Visual Odometry from Two Point Correspondences and Initial Automatic Camera Tilt Calibration},
booktitle={Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 6: VISAPP, (VISIGRAPP 2017)},
year={2017},
pages={340-346},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006079903400346},
isbn={978-989-758-227-1},
}

#### in EndNote Style

TY - CONF
JO - Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 6: VISAPP, (VISIGRAPP 2017)
TI - Visual Odometry from Two Point Correspondences and Initial Automatic Camera Tilt Calibration
SN - 978-989-758-227-1