Abstract
In this paper, we propose a novel formulation to solve the pose estimation problem of a calibrated multi-camera system. The non-central rays that pass through the 3D world points and multi-camera system are elegantly represented as Plücker lines. This allows us to solve for the depth of the points along the Plücker lines with a minimal set of 3-point correspondences. We show that the minimal solution for the depth of the points along the Plücker lines is an 8 degree polynomial that gives up to 8 real solutions. The coordinates of the 3D world points in the multi-camera frame are computed from the known depths. Consequently, the pose of the multi-camera system, i.e. the rigid transformation between the world and multi-camera frames can be obtained from absolute orientation. We also derive a closed-form minimal solution for the absolute orientation. This removes the need for the computationally expensive Singular Value Decompositions (SVD) during the evaluations of the possible solutions for the depths. We identify the correct solution and do robust estimation with RANSAC. Finally, the solution is further refined by including all the inlier correspondences in a non-linear refinement step. We verify our approach by showing comparisons with other existing approaches and results from large-scale real-world datasets.
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- 1.
http://code.google.com/p/ceres-solver/.
References
Bay, H., Ess, A., Tuytelaars, T., Van Gool, L.: Speeded-up robust features (surf). Comput. Vis. Image Underst. 110, 346–359 (2008)
Chen, C.S., Chang, W.Y.: On pose recovery for generalized visual sensors. Pattern Anal. Mach. Intell. 26, 848–861 (2004)
Cox, D.A., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms—an Introduction to Computational Algebraic Geometry and Commutative Algebra, 2 edn. Springer, Berlin (1997)
Ess, A., Neubeck, A., Van Gool, L.: Generalised linear pose estimation. In: British Machine Vision Conference (2007)
Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24, 381–395 (1981)
Haralick, R.M., Lee, D., Ottenburg, K., Nolle, M.: Analysis and solutions of the three point perspective pose estimation problem. In: Computer Vision and Pattern Recognition, pp. 592–598 (1991)
Hartley, R.I., Gupta, R.: Linear pushbroom cameras. IEEE Trans. Pattern Anal. Mach. Intell. 19, 963–975 (1994)
Horn, B.K.P.: Closed form solutions of absolute orientation using unit quaternions. JOSA-A 4, 629–642 (1987)
Kneip, L., Furgale, P., Siegwart, R.: Using multi-camera systems in robotics: efficient solutions to the npnp problem. In: International Conference on Robotics and Automation (2013)
Lee, G.H., Fraundorfer, F., Pollefeys, M.: Motion estimation for a self-driving car with a generalized camera. In: Computer Vision and Pattern Recognition (2013)
Lee, G.H., Fraundorfer, F., Pollefeys, M.: Structureless pose-graph loop-closures with a multi-camera system on a self-driving car. In: International Conference on Intelligent Robots and Systems (2013)
Li, H.D., Hartley, R., Kim, J.H.: A linear approach to motion estimation using generalized camera models. In: Computer Vision and Pattern Recognition, pp. 1–8 (2008)
Moreno-Noguer, F., Lepetit, V., Fua, P.: Accurate non-iterative o(n) solution to the pnp problem. In: International Conference on Computer Vision, pp. 1–8 (2007)
Nistér, D.: A minimal solution to the generalised 3-point pose problem. Comput. Vis. Pattern Recognit. 1, 560–567 (2004)
Nistér, D., Stewénius, H.: Scalable recognition with a vocabulary tree. Comput. Vis. Pattern Recognit. 2, 2161–2168 (2006)
Pless, R.: Using many cameras as one. Comput. Vis. Pattern Recognit. 2, 587–593 (2003)
Quan, L., Lan, Z.D.: Linear n-point camera pose determination. Pattern Anal. Mach. Intell. 21, 774–780 (1999)
Schweighofer, G., Pinz, A.: Globally optimal o(n) solution to the pnp problem for general camera models. In: British Machine Vision Conference, pp. 1–10 (2008)
Tariq, S., Dellaert, F.: A multi-camera 6-dof pose tracker. In: International Symposim on Mixed and Augmented Reality, pp. 296–297 (2004)
Acknowledgments
This work is supported in part by the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant #269916 (v-charge) and 4DVideo ERC Starting Grant Nr. 210806.
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Hee Lee, G., Li, B., Pollefeys, M., Fraundorfer, F. (2016). Minimal Solutions for Pose Estimation of a Multi-Camera System. In: Inaba, M., Corke, P. (eds) Robotics Research. Springer Tracts in Advanced Robotics, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-28872-7_30
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DOI: https://doi.org/10.1007/978-3-319-28872-7_30
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