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A probabilistic analysis of a common RANSAC heuristic

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Abstract

Random Sample Consensus (RANSAC) is an iterative algorithm for robust model parameter estimation from observed data in the presence of outliers. First proposed by Fischler and Bolles back in 1981, it still is a very popular algorithm in the computer vision community. The primary objective of their paper was to find an effective strategy for excluding outliers from estimation process, but it did not consider the presence of noise among the inliers. A common practice among implementations of RANSAC is to take a few samples extra than the minimum required for estimation problem, but implications of this heuristic are lacking in the literature. In this paper, we present a probabilistic analysis of this common heuristic and explore the possibility of finding an optimal size for the randomly sampled data points per iteration of RANSAC. We also improve upon the lower bound for the number of iterations of RANSAC required to recover the model parameters. On the basis of this analysis, we propose an improvement in the hypothesis step of RANSAC algorithm. Since this step is shared (unchanged) by many of the variants of RANSAC, their performance can also be improved upon. The paper also presents the improvements achieved by incorporating the findings of our analysis in two of the popular variants of RANSAC.

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References

  1. 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)

    Article  MathSciNet  Google Scholar 

  2. Chum, O., Matas, J., Kittler, J.: Locally Optimized RANSAC, Pattern Recognition, pp. 236–243. Springer, Berlin (2003)

    Book  Google Scholar 

  3. Torr, P.H.S., Zisserman, A.: MLESAC: a new robust estimator with application to estimating image geometry. Comput. Visi. Image Underst. 78, 138 (2000)

    Article  Google Scholar 

  4. Lebeda, K., Matas, J., Chum, O.: Fixing the locally optimized RANSAC. In: British Machine Vision Conference, vol. 95.1–95.11 (2012)

  5. Choi, S., Kim, T., Yu, W.: Performance evaluation of RANSAC family. In: British Machine Vision Conference (2009)

  6. Raguram, R., Frahm, J.-M., Pollefeys, M.: A comparative analysis of RANSAC techniques leading to adaptive real-time random sample consensus. In: Proceedings of the 10th European Conference on Computer Vision: Part II, vol. 500–513 (2008)

  7. Huber, P.J.: Robust Statistics. Wiley, London (1981)

    Book  MATH  Google Scholar 

  8. Tordoff, B.J., Murray, D.W.: Guided-MLESAC: faster image transform estimation by using matching priors. IEEE Trans. Pattern Anal. Mach. Intell. 27(10), 15231535 (2005)

    Article  Google Scholar 

  9. Chum, O., Matas, J.: Matching with PROSAC progressive sample consensus. In: IEEE Conference on Computer Vision and Pattern Recognition (2005)

  10. Matas, J, Chum, O.: Randomized RANSAC. In: British Machine Vision Conference, vol. 49–58. Vienna University of Technology (2002)

  11. Matas, J., Chum, O.: Randomized RANSAC with sequential probability ratio test. In: IEEE International Conference on Computer Vision (2005)

  12. Nistr, D., Nistr, D.: Preemptive RANSAC for live structure and motion estimation. Proc. IEEE Int. Conf. Comput. Vis. 1, 199–206 (2003)

    Article  Google Scholar 

  13. Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore (1996)

    MATH  Google Scholar 

  14. Umeyama, S.: Least-squares estimation of transformation parameters between two point patterns. IEEE Trans. Pattern Anal. Mach. Intell. 13, 376–380 (1991)

    Article  Google Scholar 

  15. Hemanth Kumar, S., Ramakrishnan, K.R.: Improved motion vector compression using 3D-warping. In: 2014 Data Compression Conference, vol. 424–424 (2014, March)

  16. Hemanth Kumar, S., Suraj, K., Ramakrishnan, K.R.: An efficient depth estimation using temporal 3D-warping. In: 2014 International Conference on 3D Imaging (IC3D) (2014, Dec)

  17. Sturm, J., Engelhard, N., Endres, F., Burgard, W., Cremers, D.: A benchmark for the evaluation of RGB-D SLAM systems, book. In: Proceedings of the International Conference on Intelligent Robot Systems (IROS) (2012 Oct)

  18. Oxford Visual Geometry Group Affine Covariant Regions Datasets. http://www.robots.ox.ac.uk/~vgg/data/data-aff.html

  19. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60, 91–110 (2004)

    Article  Google Scholar 

  20. Oh, K., Yea, S., Vetro, A., Ho, Y.: Virtual view synthesis method and self evaluation metrics for free viewpoint television and 3D video. Int. J. Imaging Syst. Technol. 20, 378–390 (2010)

    Article  Google Scholar 

  21. Bay, H., Ess, A., Tuytelaars, T., Van Gool, L.: Speeded-up robust features (SURF). Comput. Vis. Image Underst. 110, 346–359 (2008)

    Article  Google Scholar 

  22. Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  23. Julier, S.J., Uhlmann, J.K.: A new extension of the Kalman filter to nonlinear systems, book. In: Proceedings of the Aerosense, vol. 82–193 (1997)

  24. Sanjeev Arulampalam, M., Maskell, S., Gordon, N.: A tutorial on particle fillters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 50, 174–188 (2002)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Science (IISc), Bangalore, India

    Hemanth Kumar Sangappa & K. R. Ramakrishnan

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  1. Hemanth Kumar Sangappa
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  2. K. R. Ramakrishnan
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Correspondence to Hemanth Kumar Sangappa.

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Sangappa, H.K., Ramakrishnan, K.R. A probabilistic analysis of a common RANSAC heuristic. Machine Vision and Applications 30, 71–89 (2019). https://doi.org/10.1007/s00138-018-0973-4

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  • DOI: https://doi.org/10.1007/s00138-018-0973-4

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