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Robust L∞ convex optimisation for monocular visual odometry trajectory estimation

Published online by Cambridge University Press:  09 July 2014

Mohammed Boulekchour ,
Nabil Aouf  and
Mark Richardson
Mohammed Boulekchour*
Affiliation:
Department of Informatics and Systems Engineering, Cranfield University, Shrivenham SN6 8LA, United Kingdom E-mails: n.aouf@cranfield.ac.uk, m.a.richardson@cranfield.ac.uk
Nabil Aouf
Affiliation:
Department of Informatics and Systems Engineering, Cranfield University, Shrivenham SN6 8LA, United Kingdom E-mails: n.aouf@cranfield.ac.uk, m.a.richardson@cranfield.ac.uk
Mark Richardson
Affiliation:
Department of Informatics and Systems Engineering, Cranfield University, Shrivenham SN6 8LA, United Kingdom E-mails: n.aouf@cranfield.ac.uk, m.a.richardson@cranfield.ac.uk
*
*Corresponding author. E-mail: m.boulekchour@cranfield.ac.uk
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Summary

The most important applications of many computer vision systems are based on robust features extraction, matching and tracking. Due to their extraction techniques, image features locations accuracy is heavily dependent on the variation in intensity within their neighbourhoods, from which their uncertainties are estimated. In the present work, a robust L∞ optimisation solution for monocular motion estimation systems has been presented. The uncertainty estimation techniques based on SIFT derivative approach and its propagation through the eight-point algorithm, singular value decomposition SVD and the triangulation algorithm have proved an improvement to the global motion estimation. Using monocular systems makes the motion estimation challenging due to the absolute scale ambiguity caused by projective effects. For this, we propose robust tools to estimate both the trajectory of a moving object and the unknown absolute scale ratio between consecutive image pairs. Experimental evaluations showed that robust convex optimisation with the L∞ norm under uncertain data and the Robust Least Squares clearly outperform classical methods based on Least Squares and Levenberg-Marquardt algorithms.

Keywords

Robust optimisationUncertainty propagationL∞ NormConvex optimisationMonocular visual odometrySOCP
Type
Articles
Information
Robotica , Volume 34 , Issue 3 , March 2016 , pp. 703 - 722
Copyright
Copyright © Cambridge University Press 2014 

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References

1.Boni, O., Ben-Tal, A. and Nemirovski, A., “Robust solutions to conic quadratic problems and their applications,” Optim. Eng. 9, 1–18 (2007).CrossRefGoogle Scholar
2.Gabrel, V., Murat, C. and Thiele, A., “Recent advances in robust optimization: An overview,” Eur. J. Oper. Res. 235 (3), 471–483 (2014)CrossRefGoogle Scholar
3.Hartley, R. and Zisserman, A., Multiple View Geometry in Computer Vision, 2nd Edn. (Cambridge University Press, Cambridge, UK, 2004).CrossRefGoogle Scholar
4.Nistr, D., Naroditsky, O. and Bergen, J., “Visual odometry for ground vehicle applications,” Journal of Field Robotics 23, 3–20 (2006).CrossRefGoogle Scholar
5.Scaramuzza, D. and Fraundorfer, F., “Visual odometry [tutorial],” IEEE Robot. Autom. Mag. 18, 80–92 (2011).CrossRefGoogle Scholar
6.Esteban, I., Dorst, L. and Dijk, J., “Closed form solution for the scale ambiguity problem in monocular visual odometry,” Intell. Robot. Appl. 665–679 (2010).CrossRefGoogle Scholar
7.Boyd, S. and Vandenberghe, L., Convex Optimization (Cambridge University Press, Cambridge, UK, 2004).CrossRefGoogle Scholar
8.Kahl, F., “Multiple View Geometry and the Li-norm,” Proceedings of the Tenth IEEE International Conference on Computer Vision, 2005. ICCV 2005, 2 (2005) pp. 1002–1009.Google Scholar
9.Mitra, K. and Chellappa, R., “A Scalable Projective Bundle Adjustment Algorithm using the L infinity Norm,” Proceedings of the Sixth Indian Conference Computer Vision, Graphics & Image Processing, 2008. ICVGIP'08 (2008) pp. 79–86.Google Scholar
10.Chesi, G., “Estimation of the Camera Pose from Image Point Correspondences through the Essential Matrix and Convex Optimization,” Proceedings of the IEEE International Conference on Robotics and Automation, 2009. ICRA'09 (2009) pp. 35–40.Google Scholar
11.Brooks, M. J., Chojnacki, W., Gawley, D. and Van Den Hengel, A., “What Value Covariance Information in Estimating Vision Parameters?.” Proceedings of the Eighth IEEE International Conference on Computer Vision, 2001. ICCV 2001, Vol. 1 (2001) pp. 302–308.Google Scholar
12.Kanazawa, Y. and Kanatani, K.-i., “Do we really have to Consider Covariance Matrices for Image Features?,” Proceedings of the Eighth IEEE International Conference on Computer Vision, 2001. ICCV 2001, Vol. 2 (2001) pp. 301–306.Google Scholar
13.Zeisl, B., Georgel, P. F., Schweiger, F., Steinbach, E. G., Navab, N. and Munich, G. E. R., “Estimation of Location Uncertainty for Scale Invariant Features Points.” In: BMVC (2009) pp. 1–12.Google Scholar
14.Haralick, R. M., Propagating Covariance in Computer Vision Performance in Characterization in Computer Vision (Springer, Netherlands, 2000).Google Scholar
15.Di Leo, G., Liguori, C. and Paolillo, A., “Covariance propagation for the uncertainty estimation in stereo vision,” IEEE Trans. Instrum. Meas. 60 (5), 1664–1673 (2011).CrossRefGoogle Scholar
16.El Ghaoui, L. and Lebret, H., “Robust solutions to least-squares problems with uncertain data,” SIAM J. Matrix Anal. Appl. 18 (4), 1035–1064 (1997).CrossRefGoogle Scholar
17.Scaramuzza, D. and Siegwart, R., “Appearance-guided monocular omnidirectional visual odometry for outdoor ground vehicles,” IEEE Trans. Robot. 24 (5), 1015–1026 (2008).CrossRefGoogle Scholar
18.Bertsimas, D., Brown, D. B. and Caramanis, C., “Theory and applications of robust optimization,” SIAM Review 53 (3), 464–501 (2011).CrossRefGoogle Scholar
19.Lfberg, Johan, “Automatic robust convex programming,” Optim. Methods Softw. 27 (1), 115–129 (2012).CrossRefGoogle Scholar
20.Ke, Qifa and Kanade, T., “Quasiconvex optimization for robust geometric reconstruction,” IEEE Trans. Pattern Anal. Mach. Intell. 29 (10), 1834–1847 (2007).CrossRefGoogle ScholarPubMed
21.Schmid, Cordelia, Mohr, R. and Bauckhage, C., “Evaluation of interest point detectors,” Int. J. Comput. Vis. 37 (2), 151–172 (2000).CrossRefGoogle Scholar
22.Di Leo, G., Liguori, C. and Paolillo, A., “Propagation of Uncertainty through Stereo Triangulation,” Proceedings of the Instrumentation and Measurement Technology Conference (I2MTC), 2010 IEEE (2010) pp. 12–17.Google Scholar
23.Lowe, D. G. “Distinctive image features from scale-invariant keypoints,” Int. J. Comput. Vis. 60 (2), 91–110 (2004).CrossRefGoogle Scholar
24.Bay, H., Tuytelaars, T. and Van Gool, L., “Surf: Speeded up Robust Features,” In: Computer VisionECCV 2006 (Springer Berlin Heidelberg, 2006) pp. 404-417.Google Scholar
25.Geiger, A., Roser, M. and Urtasun, R., “Efficient Large-scale Stereo Matching,” In: Computer VisionACCV 2010 (Springer Berlin Heidelberg, 2011) pp. 25–38.CrossRefGoogle Scholar
26.Furgale, P., Carle, P., Enright, J. and Barfoot, T. D., “The Devon Island rover navigation dataset,” Int. J. Robot. Res. 31 (6), 707–713 (2012).CrossRefGoogle Scholar
27.Sur, F., Noury, N. and Berger, M.-O., “Computing the Uncertainty of the 8 point Algorithm for Fundamental Matrix Estimation,” In: Proceedings of the 19th British Machine Vision Conference-BMVC 2008 (2008).CrossRefGoogle Scholar
28.Fischler, M. A. and Bolles, R. C., “Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24 (6), 381–395 (1981).CrossRefGoogle Scholar
29.Papadopoulo, T. and Lourakis, M. I. A., “Estimating the Jacobian of the Singular Value Decomposition: Theory and Applications,” Computer Vision-ECCV 2000 (Springer Berlin Heidelberg, 2000) pp. 554–570.CrossRefGoogle Scholar
30.Chen, J., Ding, Z. and Yuan, F. “Theoretical uncertainty evaluation of stereo reconstruction,” Proceeding of the 2nd International Conference on Bioinformatics and Biomedical Engineering, 2008. ICBBE 2008 (2008) pp. 2378–2381.Google Scholar
31.Lobo, M. S., Vandenberghe, L., Boyd, S. and Lebret, H., “Applications of second-order cone programming,” Linear Algebr. Appl. 284 (1), 193–228 (1998).CrossRefGoogle Scholar
32.Eldn, Lars, “Perturbation theory for the least squares problem with linear equality constraints,” SIAM J. Numer. Anal. 17 (3), 338–350 (1980).CrossRefGoogle Scholar
33.Sturm, Jos F., “Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,” Optim. Methods Softw. 11 (1–4), 625–653 (1999).CrossRefGoogle Scholar