Abstract
It has been observed previously that the number of iterations required to derive good model parameter values used by RANSAC-like model estimators is too optimistic. We present the derivation of an analytical formula that allows the calculation of the sufficient limit of iterations needed to obtain good parameter values with the prescribed probability for any number of model parameters. It explains the values that had been found experimentally for certain numbers of model parameters by others very well. Furthermore, the improvement that our approach of SUfficient Random SAmple Coverage (SURSAC) offers, in comparison to the original RANSAC algorithm as well as to its adaptive modification by Hartley and Zisserman, is demonstrated with synthetic data for the case of a non-linear model function over a wide range of outlier fractions and different ratios of inlier and outlier densities.
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References
Chum, O., & Matas, J. (2005). Matching with PROSAC—progressive sample consensus. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1, 220–226.
Chum, O., Matas, J., & Kittler, J. (2003). Locally optimized RANSAC. In B. Michaelis, & G. Krell (Eds.), Lecture notes in computer science. Proceedings of the 25th DAGM symposium on pattern recognition (pp. 236–243). Berlin: Springer.
Chum, O., Matas, J., & Obdrz̆álek, S. (2004). Enhancing RANSAC by generalized model optimization. In Proceedings Asian conference on computer vision (ACCV) (Vol. 2, pp. 812–817), January 2004.
Fischler, M. A., & Bolles, R. C. (1981). Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6), 381–395.
Huber, P. J. (1985). Robust statistics. New York: Wiley.
Hartley, R., & Zisserman, A. (2003). Multiple view geometry in computer vision (2nd ed.). New York: Cambridge University Press.
Lacey, A. J., Pinitkarn, N., & Thacker, N. A. (2000). An evaluation of the performance of RANSAC algorithms for stereo camera calibration. In Proceedings British machine vision conference (pp. 646–655).
Matas, J., & Chum, O. (2004). Randomized RANSAC with t d,d test. Image and Vision Computing, 22(10), 837–842.
Meer, P. (2004). Robust techniques for computer vision. Emerging topics in computer vision. New York: Prentice Hall. Chapter 4.
Meer, P., Mintz, D., Rosenfeld, A., & Kim, D. Y. (1991). Robust regression methods for computer vision: a review. International Journal of Computer Vision, 6, 59–70.
Michaelsen, E., von Hansen, W., Kirchhof, M., Meidow, J., & Stilla, U. (2006). Estimating the essential matrix: GOODSAC versus RANSAC. In Symposium on photogrammetric computer vision.
Nistér, D. (2003). Preemptive RANSAC for live structure and motion estimation. In 9th IEEE international conference on computer vision (ICCV’03) (Vol. 1, pp. 199–206), October 2003.
Rousseeuw, P. J., & Leroy, A. M. (1987). Robust regression and outlier detection. New York: Wiley.
Stewart, C. V. (1999). Robust parameter estimation in computer vision. SIAM Review, 41(3), 513–537.
Torr, P. H. S., & Murray, D. W. (1997). The development and comparison of robust methods for estimating the fundamental matrix. International Journal of Computer Vision, 24(3), 271–300.
Tordoff, B., & Murray, D. W. (2002). Guided sampling and consensus for motion estimation. In Proceedings 7th European conference on computer vision (ECCV) (Vol. 1, pp. 82–98), Copenhagen, 2002. Berlin: Springer.
Tordoff, B. J., & Murray, D. W. (2005). Guided-MLESAC: faster image transform estimation by using matching priors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(10), 1523–1535.
Torr, P. H. S., & Zisserman, A. (2000). MLESAC: a new robust estimator with application to estimating image geometry. Computer Vision and Image Understanding, 78, 138–156.
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Scherer-Negenborn, N., Schaefer, R. Model Fitting with Sufficient Random Sample Coverage. Int J Comput Vis 89, 120–128 (2010). https://doi.org/10.1007/s11263-010-0329-7
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DOI: https://doi.org/10.1007/s11263-010-0329-7