Globally Optimal Inlier Set Maximization with Unknown Rotation and Focal Length

  • Jean-Charles Bazin
  • Yongduek Seo
  • Richard Hartley
  • Marc Pollefeys
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8690)


Identifying inliers and outliers among data is a fundamental problem for model estimation. This paper considers models composed of rotation and focal length, which typically occurs in the context of panoramic imaging. An efficient approach consists in computing the underlying model such that the number of inliers is maximized. The most popular tool for inlier set maximization must be RANSAC and its numerous variants. While they can provide interesting results, they are not guaranteed to return the globally optimal solution, i.e. the model leading to the highest number of inliers. We propose a novel globally optimal approach based on branch-and-bound. It computes the rotation and the focal length maximizing the number of inlier correspondences and considers the reprojection error in the image space. Our approach has been successfully applied on synthesized data and real images.


Consensus set maximization branch-and-bound inlier detection RANSAC 


  1. 1.
    Agarwal, S., Snavely, N., Simon, I., Seitz, S.M., Szeliski, R.: Building Rome in a day. In: ICCV (2009)Google Scholar
  2. 2.
    Bazin, J.-C., Seo, Y., Pollefeys, M.: Globally optimal consensus set maximization through rotation search. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds.) ACCV 2012, Part II. LNCS, vol. 7725, pp. 539–551. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Bouguet, J.Y.: Camera calibration toolbox for MatlabGoogle Scholar
  4. 4.
    Brown, M., Hartley, R., Nister, D.: Minimal solutions for panoramic stitching. In: CVPR (2007)Google Scholar
  5. 5.
    Brown, M., Lowe, D.: Automatic panoramic image stitching using invariant features. IJCV (2007)Google Scholar
  6. 6.
    Choi, K., Lee, S., Seo, Y.: A branch-and-bound algorithm for globally optimal camera pose and focal length. Image and Vision Computing (2010)Google Scholar
  7. 7.
    Chum, O., Matas, J.: Optimal randomized RANSAC. TPAMI (2008)Google Scholar
  8. 8.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM (1981)Google Scholar
  9. 9.
    Hartley, R., Kahl, F.: Global optimization through rotation space search. IJCV (2009)Google Scholar
  10. 10.
    Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press (2004)Google Scholar
  11. 11.
    Horst, R., Tuy, H.: Global optimization: deterministic approaches. Springer (2006)Google Scholar
  12. 12.
    Kahl, F., Agarwal, S., Chandraker, M., Kriegman, D., Belongie, S.: Practical global optimization for multiview geometry. IJCV (2008)Google Scholar
  13. 13.
    Li, H.: Consensus set maximization with guaranteed global optimality for robust geometry estimation. In: ICCV (2009)Google Scholar
  14. 14.
    Lowe, D.: Distinctive image features from scale-invariant keypoints. IJCV (2003)Google Scholar
  15. 15.
    McCormick, G.: Computability of global solutions to factorable nonconvex programs: part I - convex underestimating problems. Mathematical Programming (1976)Google Scholar
  16. 16.
    Moor, R.: Interval Analysis. Prentice-Hall (1966)Google Scholar
  17. 17.
    Nistér, D.: Preemptive RANSAC for live structure and motion estimation. In: ICCV (2003)Google Scholar
  18. 18.
    Olsson, C., Enqvist, O., Kahl, F.: A polynomial-time bound for matching and registration with outliers. In: CVPR (2008)Google Scholar
  19. 19.
    Raguram, R., Frahm, J.-M., Pollefeys, M.: A comparative analysis of RANSAC techniques leading to adaptive real-time random sample consensus. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol. 5303, pp. 500–513. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Snavely, N., Seitz, S.M., Szeliski, R.: Photo tourism: Exploring photo collections in 3D. In: SIGGRAPH (2006)Google Scholar
  21. 21.
    Sun, M., Telaprolu, M., Lee, H., Savarese, S.: An efficient branch-and-bound algorithm for optimal human pose estimation. In: CVPR (2012)Google Scholar
  22. 22.
    Torr, P., Zisserman, A.: MLESAC: A new robust estimator with application to estimating image geometry. Computer Vision and Image Understanding (2000)Google Scholar
  23. 23.
    Yang, J., Li, H., Jia, Y.: Go-ICP: solving 3D registration efficiently and globally optimally. In: ICCV (2013)Google Scholar
  24. 24.
    Yu, C., Seo, Y., Lee, S.W.: Global optimization for estimating a BRDF with multiple specular lobes. In: CVPR (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jean-Charles Bazin
    • 1
  • Yongduek Seo
    • 2
  • Richard Hartley
    • 3
  • Marc Pollefeys
    • 1
  1. 1.Department of Computer ScienceETH ZurichSwitzerland
  2. 2.Department of Media TechnologySogang UniversitySouth Korea
  3. 3.Australian National University and NICTACanberraAustralia

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