iccv iccv2013 iccv2013-138 iccv2013-138-reference knowledge-graph by maker-knowledge-mining
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Author: Avishek Chatterjee, Venu Madhav Govindu
Abstract: In this paper we address the problem of robust and efficient averaging of relative 3D rotations. Apart from having an interesting geometric structure, robust rotation averaging addresses the need for a good initialization for largescale optimization used in structure-from-motion pipelines. Such pipelines often use unstructured image datasets harvested from the internet thereby requiring an initialization method that is robust to outliers. Our approach works on the Lie group structure of 3D rotations and solves the problem of large-scale robust rotation averaging in two ways. Firstly, we use modern ?1 optimizers to carry out robust averaging of relative rotations that is efficient, scalable and robust to outliers. In addition, we also develop a twostep method that uses the ?1 solution as an initialisation for an iteratively reweighted least squares (IRLS) approach. These methods achieve excellent results on large-scale, real world datasets and significantly outperform existing methods, i.e. the state-of-the-art discrete-continuous optimization method of [3] as well as the Weiszfeld method of [8]. We demonstrate the efficacy of our method on two large- scale real world datasets and also provide the results of the two aforementioned methods for comparison.
[1] E. Candes and J. Romberg. L1-magic : recovery of sparse signals via convex programming. http : //users . ece . gat e ch . edu / ˜ j ust in/ l 1magi c.
[2] E. Candes and T. Tao. Decoding by linear programming. IEEE Transactions on Information Theory, 51(12), 2005.
[3] D. J. Crandall, A. Owens, N. Snavely, and D. Huttenlocher. Discrete-continuous optimization for large-scale structure from motion. In CVPR, 2011.
[4] J. Fredriksson and C. Olsson. Simultaneous multiple rotation averaging using lagrangian duality. In ACCV, 2012.
[5] V. M. Govindu. Combining two-view constraints for motion estimation. In CVPR, 2001.
[6] V. M. Govindu. Lie-algebraic averaging for globally consistent motion estimation. In CVPR, 2004.
[7] V. M. Govindu. Robustness in motion averaging. In ACCV, 2006.
[8] R. Hartley, K. Aftab, and J. Trumpf. L1 rotation averaging using the weiszfeld algorithm. In CVPR, 2011.
[9] R. Hartley, J. Trumpf, Y. Dai, and H. Li. Rotation averaging. IJCV, 103(3), 2013. IJCV,
[10] P. W. Holland and R. E. Welsch. Robust regression using it- eratively reweighted least-squares. Commun. Statist. Theory Methods, 9, 1977. Methods,
[11] C. Olsson and O. Enqvist. Stable structure from motion for unordered image collections. In SCIA, 2011.
[12] S. N. Sinha, D. Steedly, and R. Szeliski. A multi-stage linear approach to structure from motion. In RMLE 2010 Workshop, 2010.
[13] N. Snavely, S. M. Seitz, and R. Szeliski. Photo tourism: Exploring photo collections in 3d. In SIGGRAPH, 2006.
[14] R. Szeliski. Computer Vision: Algorithms and Applications. Springer-Verlag, 2010.
[15] B. Triggs, P. McLauchlan, R. Hartley, and A. Fitzgibbon. Bundle adjustment – a modern synthesis. In Vision Algorithms: Theory and Practice, 2000.
[16] R. Tron and R. Vidal. Distributed computer vision algorithms through distributed averaging. In CVPR, 2011.
[17] R. Tron, R. Vidal, and A. Terzis. Distributed pose averaging in camera networks via consensus on SE(3). In ICDSC, 2008.
[18] C. Zach, M. Klopschitz, and M. Pollefeys. Disambiguating visual relations using loop constraints. In CVPR, 2010. 528