Abstract
Multiple rotation averaging is an important problem in computer vision. The problem is challenging because of the nonlinear constraints required to represent the set of rotations. To our knowledge no one has proposed any globally optimal solution for the case of simultaneous updates of the rotations. In this paper we propose a simple procedure based on Lagrangian duality that can be used to verify global optimality of a local solution, by solving a linear system of equations. We show experimentally on real and synthetic data that unless the noise levels are extremely high this procedure always generates the globally optimal solution.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Nistér, D.: An efficient solution to the five-point relative pose problem. Trans. Pattern Analysis and Machine Intelligence (2004)
Tardif, J.P., Bartoli, A., Trudeau, M., Guilbert, N., Roy, S.: Algorithms for batch matrix factorization with application to structure-from-motion. In: Conf. Computer Vision and Pattern Recognition (2007)
Gherardi, R., Farenzena, M., Fusiello, A.: Improving the efficiency of hierarchical structure-and-motion. In: Conf. Computer Vision and Pattern Recognition (2010)
Crandall, D., Owens, A., Snavely, N., Huttenlocher, D.P.: Discrete-continuous optimization for large-scale structure from motion. In: Proc. IEEE Conf. on Computer Vision and Pattern Recognition (2011)
Enqvist, O., Kahl, F., Olsson, C.: Non-sequential structure from motion. In: Workshop on Omnidirectional Vision, Camera Networks and Non-Classical Cameras, Barcelona, Spain (2011)
Govindu, V.: Combining two-view constraints for motion estimation. In: Conf. Computer Vision and Pattern Recognition (2001)
Govindu, V.: Lie-algebraic averaging for globally consistent motion estimation. In: Conf. Computer Vision and Pattern Recognition, Washington DC, USA, vol. I, pp. 684–691 (2004)
Govindu, V.M.: Robustness in Motion Averaging. In: Narayanan, P.J., Nayar, S.K., Shum, H.-Y. (eds.) ACCV 2006. LNCS, vol. 3852, pp. 457–466. Springer, Heidelberg (2006)
Martinec, D., Pajdla, T.: Robust rotation and translation estimation in multiview reconstruction. In: Conf. Computer Vision and Pattern Recognition (2007)
Hartley, R., Aftab, K., Trumpf, J.: L1 rotation averaging using the weiszfeld algorithm. In: Conf. Computer Vision and Pattern Recognition, Colorado Springs, USA (2011)
Hartley, R., Trumpf, J., Dai, Y.: Rotation averaging and weak convexity. In: International Symposium on Mathematical Theory of Networks and Systems, Piscataway, USA (2010)
Dai, Y., Trumpf, J., Li, H., Barnes, N., Hartley, R.: Rotation Averaging with Application to Camera-Rig Calibration. In: Zha, H., Taniguchi, R.-i., Maybank, S. (eds.) ACCV 2009, Part II. LNCS, vol. 5995, pp. 335–346. Springer, Heidelberg (2010)
Zach, C., Klopschitz, M., Pollefeys, M.: Disambiguating visual relations using loop constraints. In: Conf. Computer Vision and Pattern Recognition (2010)
Sharp, G., Lee, S., Wehe, D.: Multiview registration of 3d scenes by minimizing error between coordinate frames. Trans. Pattern Analysis and Machine Intelligence 26, 1037–1050 (2004)
Hartley, R., Seo, Y.: Verifying global minima for L 2 minimization problems. In: Conf. Computer Vision and Pattern Recognition, Anchorage, USA (2008)
Sorensen, D.: Minimization of a large-scale quadratic fuction subject to a spherical constraint. SIAM J. Optim. 7, 141–161 (1997)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)
Daubechies, I., DeVore, R., Fornasier, M., Güntürk, C.S.: Iteratively reweighted least squares minimization for sparse recovery. Communications on Pure and Applied Mathematics 63, 1–38 (2010)
Bube, K.P., Langan, R.T.: Hybrid l1 / l2 minimization with applications to tomography. Geophysics 62, 1183–1195 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fredriksson, J., Olsson, C. (2013). Simultaneous Multiple Rotation Averaging Using Lagrangian Duality. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds) Computer Vision – ACCV 2012. ACCV 2012. Lecture Notes in Computer Science, vol 7726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37431-9_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-37431-9_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37430-2
Online ISBN: 978-3-642-37431-9
eBook Packages: Computer ScienceComputer Science (R0)