This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Two Efficient Solutions for Visual Odometry Using Directional Correspondence
April 2012 (vol. 34 no. 4)
pp. 818-824
J. Gallier, Dept. of Comput. & Inf. Sci., Univ. of Pennsylvania, Philadelphia, PA, USA
X. S. Zhou, Dept. of Comput. Sci. & Eng., Univ. of Minnesota, Minneapolis, MN, USA
O. Naroditsky, Dept. of Comput. & Inf. Sci., Univ. of Pennsylvania, Philadelphia, PA, USA
S. I. Roumeliotis, Dept. of Comput. Sci. & Eng., Univ. of Minnesota, Minneapolis, MN, USA
K. Daniilidis, Dept. of Comput. & Inf. Sci., Univ. of Pennsylvania, Philadelphia, PA, USA
This paper presents two new, efficient solutions to the two-view, relative pose problem from three image point correspondences and one common reference direction. This three-plus-one problem can be used either as a substitute for the classic five-point algorithm, using a vanishing point for the reference direction, or to make use of an inertial measurement unit commonly available on robots and mobile devices where the gravity vector becomes the reference direction. We provide a simple, closed-form solution and a solution based on algebraic geometry which offers numerical advantages. In addition, we introduce a new method for computing visual odometry with RANSAC and four point correspondences per hypothesis. In a set of real experiments, we demonstrate the power of our approach by comparing it to the five-point method in a hypothesize-and-test visual odometry setting.

[1] D. Nister, O. Naroditsky, and J. Bergen, "Visual Odometry," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 1, pp. I-652-I-659, Jan. 2004.
[2] M. Byrod, K. Josephson, and K. Åström, "Fast and Stable Polynomial Equation Solving and Its Application to Computer Vision," Int'l J. Computer Vision, vol. 84, pp. 237-256, Jan. 2009.
[3] D. Nister, "An Efficient Solution to the Five-Point Relative Pose Problem," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 6, pp. 756-770, June 2004.
[4] Z. Kukelova and T. Pajdla, "A Minimal Solution to the Autocalibration of Radial Distortion," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2007.
[5] M. Byrod, Z. Kukelova, K. Josephson, and T. Pajdla, "Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion," Proc. IEEE Conf. Computer Vision and Pattern Recognition, Jan. 2008.
[6] M. Bujnak, Z. Kukelova, and T. Pajdla, "A General Solution to the p4p Problem For Camera with Unknown Focal Length," Proc. IEEE Conf. Computer Vision and Pattern Recognition, Jan. 2008.
[7] H. Stewenius, C. Engels, and D. Nister, "An Efficient Minimal Solution for Infinitesimal Camera Motion," Proc. IEEE Conf. Computer Vision and Pattern Recognition, Jan. 2007.
[8] H. Stewenius, "Gröbner Basis Methods for Minimal Problems in Computer Vision," maths.lth.se, Jan. 2005.
[9] M. Byrod, K. Josephson, and K. Astrom, "Improving Numerical Accuracy of Grobner Basis Polynomial Equation Solver," Proc. 11th IEEE Int'l Conf. Computer Vision, 2007.
[10] H. Stewenius, F. Schaffalitzky, and D. Nister, "How Hard Is 3-View Triangulation Really?," Proc. 10th IEEE Int'l Conf. Computer Vision, Jan. 2005.
[11] M. Byrod, K. Josephson, and K. Astrom, "Fast Optimal Three View Triangulation," Proc. Asian Conf. Computer Vision, Jan. 2007.
[12] T. Vieville, E. Clergue, and P. Facao, "Computation of Ego-Motion and Structure from Visual and Inertialsensors Using the Vertical Cue," Proc. Fourth IEEE Int'l Conf. Computer Vision, pp. 591-598, 1993.
[13] M. Kalantari, A. Hashemi, F. Jung, and J. Guedon, "A New Solution to the Relative Orientation Problem Using Only 3 Points and the Vertical Direction," arXiv, vol. cs.CV, May 2009.
[14] M. Kalantari, A. Hashemi, F. Jung, and J. Guedon, "A New Solution to the Relative Orientation Problem Using Only 3 Points and the Vertical Direction," J. Math. Imaging Vision, vol. 39, no. 3, pp. 259-268, 2011.
[15] F. Fraundorfer, P. Tanskanen, and M. Pollefeys, "A Minimal Case Solution to the Calibrated Relative Pose Problem for the Case of Two Known Orientation Angles," Proc. 11th European Conf. Computer Vision, pp. 269-282, 2010.
[16] J. Lobo and J. Dias, "Vision and Inertial Sensor Cooperation Using Gravity as a Vertical Reference," IEEE Trans. Pattern and Machine Intelligence, vol. 25, no. 12, pp. 1597-1608, Dec. 2003.
[17] D. Cox, J. Little, and D. O'Shea, Ideals, Varieties, and Algorithms. Springer, Jan. 1997.
[18] Z. Kukelova, M. Bujnak, and T. Pajdla, "Automatic Generator of Minimal Problem Solvers," Proc. 10th European Conf. Computer Vision, Jan. 2008.
[19] D. Cox, J. Little, and D. O'Shea, Using Algebraic Geometry. Springer, Jan. 2005.
[20] O. Naroditsky and K. Daniilidis, "Optimizing Polynomial Solvers for Minimal Geometry Problems," Proc. IEEE Int'l Conf. Computer Vision, 2011.
[21] M. Armstrong, A. Zisserman, and R. Hartley, "Self-Calibration from Image Triplets," Proc. Fourth European Conf. Computer Vision, pp. 1-16, 1996.
[22] R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision. Cambridge Univ. Press, 2004.
[23] M. Fischler and R. Bolles, "Random Sample Consensus," Comm. ACM, vol. 24, pp. 381-395, Jan. 1981.
[24] O. Naroditsky, X. Zhou, J. Gallier, S. Roumeliotis, and K. Daniilidis, "Structure from Motion with Directional Correspondence for Visual Odometry," MS-CIS-11-15, Univ. of Pennsylvania, Philadelphia, 2011.

Index Terms:
vectors,computer vision,distance measurement,geometry,pose estimation,five-point method,visual odometry,directional correspondence,relative pose problem,image point correspondences,reference direction,three-plus-one problem,five-point algorithm,vanishing point,inertial measurement unit,robots,mobile devices,gravity vector,algebraic geometry,RANSAC,four point correspondences,Polynomials,Cameras,Noise,Vectors,Visualization,Sparse matrices,Groebner basis.,Computer vision,structure from motion,visual odometry,minimal problems
Citation:
J. Gallier, X. S. Zhou, O. Naroditsky, S. I. Roumeliotis, K. Daniilidis, "Two Efficient Solutions for Visual Odometry Using Directional Correspondence," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 4, pp. 818-824, April 2012, doi:10.1109/TPAMI.2011.226
Usage of this product signifies your acceptance of the Terms of Use.