Abstract
How hard are geometric vision problems with outliers? We show that for most fitting problems, a solution that minimizes the number of outliers can be found with an algorithm that has polynomial time-complexity in the number of points (independent of the rate of outliers). Further, and perhaps more interestingly, other cost functions such as the truncated L2-norm can also be handled within the same framework with the same time complexity.
We apply our framework to triangulation, relative pose problems and stitching, and give several other examples that fulfill the required conditions. Based on efficient polynomial equation solvers, it is experimentally demonstrated that these problems can be solved reliably, in particular for low-dimensional models. Comparisons to standard random sampling solvers are also given.
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References
Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with application to image analysis and automated cartography. Commun. Assoc. Comp. Mach. (1981)
Chum, O., Matas, J.: Optimal randomized ransac. Trans. Pattern Analysis and Machine Intelligence (2008)
Hartley, R., Sturm, P.: Triangulation. Computer Vision and Image Understanding (1997)
Kahl, F., Hartley, R.: Multiple view geometry under the L ∞ -norm. Trans. Pattern Analysis and Machine Intelligence (2008)
Ke, Q., Kanade, T.: Quasiconvex optimization for robust geometric reconstruction. Trans. Pattern Analysis and Machine Intelligence (2007)
Sim, K., Hartley, R.: Removing outliers using the L ∞ -norm. In: Conf. Computer Vision and Pattern Recognition (2006)
Olsson, C., Eriksson, A., Hartley, R.: Outlier removal using duality. In: Conf. Computer Vision and Pattern Recognition (2010)
Yu, J., Eriksson, A., Chin, T.J., Suter, D.: An adversarial optimization approach to efficient outlier removal. In: Int. Conf. Computer Vision (2011)
Breuel, T.: Implementation techniques for geometric branch-and-bound matching methods. Computer Vision and Image Understanding (2003)
Li, H.: Consensus set maximization with guaranteed global optimality for robust geometry estimation. In: Int. Conf. Computer Vision (2009)
Cass, T.: Polynomial-time geometric matching for object recognition. Int. Journal of Computer Vision (1999)
Li, H.: A practical algorithm for L ∞ triangulation with outliers. In: Conf. Computer Vision and Pattern Recognition (2007)
Olsson, C., Enqvist, O., Kahl, F.: A polynomial-time bound for matching and registration with outliers. In: Conf. Computer Vision and Pattern Recognition (2008)
Bazaraa, M., Sherali, H., Shetty, C.: Nonlinear Programming: Theory and Algorithms. Wiley (1993)
Byröd, M., Josephson, K., Åström, K.: Fast and stable polynomial equation solving and its application to computer vision. Int. Journal of Computer Vision (2009)
Källén, H., Ardö, H., Enqvist, O.: Tracking and reconstruction of vehicles for accurate position estimation. In: W. on Applications of Computer Vision (2011)
Hartley, R., Kahl, F.: Global optimization through rotation space search. Int. Journal of Computer Vision (2009)
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Enqvist, O., Ask, E., Kahl, F., Åström, K. (2012). Robust Fitting for Multiple View Geometry. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds) Computer Vision – ECCV 2012. ECCV 2012. Lecture Notes in Computer Science, vol 7572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33718-5_53
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DOI: https://doi.org/10.1007/978-3-642-33718-5_53
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