Efficient Two-View Geometry Classification

  • Johannes L. Schönberger
  • Alexander C. Berg
  • Jan-Michael Frahm
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9358)


Typical Structure-from-Motion systems spend major computational effort on geometric verification. Geometric verification recovers the epipolar geometry of two views for a moving camera by estimating a fundamental or essential matrix. The essential matrix describes the relative geometry for two views up to an unknown scale. Two-view triangulation or multi-model estimation approaches can reveal the relative geometric configuration of two views, e.g., small or large baseline and forward or sideward motion. Information about the relative configuration is essential for many problems in Structure-from-Motion. However, essential matrix estimation and assessment of the relative geometric configuration are computationally expensive. In this paper, we propose a learning-based approach for efficient two-view geometry classification, leveraging the by-products of feature matching. Our approach can predict whether two views have scene overlap and for overlapping views it can assess the relative geometric configuration. Experiments on several datasets demonstrate the performance of the proposed approach and its utility for Structure-from-Motion.



This material is based upon work supported by the National Science Foundation under Grant No. IIS-1252921, IIS-1349074, IIS-1452851, CNS-1405847, and by the US Army Research, Development and Engineering Command Grant No. W911NF-14-1-0438.


  1. 1.
    Agarwal, S., Furukawa, Y., Snavely, N., Simon, I., Curless, B., Seitz, S., Szeliski, R.: Building rome in a day. In: ICCV (2009)Google Scholar
  2. 2.
    Baarda, W., Netherlands Geodetic Commission, et al.: Statistical concepts in geodesy, vol. 2(4). Rijkscommissie voor Geodesie (1967)Google Scholar
  3. 3.
    Breiman, L.: Random forests. Mach. Learn. 45, 5–32 (2001)CrossRefzbMATHGoogle Scholar
  4. 4.
    Bron, C., Kerbosch, J.: Algorithm 457: finding all cliques of an undirected graph. ACM Commun. 16, 48–50 (1973)CrossRefzbMATHGoogle Scholar
  5. 5.
    Cazals, F., Karande, C.: A note on the problem of reporting maximal cliques. Theoret. Comput. Sci. 407(1), 564–568 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chum, O., Matas, J.: Matching with prosac-progressive sample consensus (2005)Google Scholar
  7. 7.
    Chum, O., Matas, J., Obdrzalek, S.: Enhancing ransac by generalized model optimization. In: ACCV (2004)Google Scholar
  8. 8.
    Crandall, D., Owens, A., Snavely, N., Huttenlocher, D.P.: Discrete-continuous optimization for large-scale structure from motion. In: CVPR (2011)Google Scholar
  9. 9.
    Criminisi, A.: Accurate Visual Metrology from Single and Multiple Uncalibrated Images. Springer, London (2001)CrossRefzbMATHGoogle Scholar
  10. 10.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. ACM Commun. 24(6), 381–395 (1981)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Förstner, W.: Uncertainty and projective geometry. In: Corrochano, E.B. (ed.) Handbook of Geometric Computing, pp. 493–534. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Frahm, J.M., Pollefeys, M.: RANSAC for (quasi-) degenerate data (QDEGSAC). In: CVPR (2006)Google Scholar
  13. 13.
    Frahm, J.-M., Fite-Georgel, P., Gallup, D., Johnson, T., Raguram, R., Wu, C., Jen, Y.-H.: Building rome on a cloudless day. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part IV. LNCS, vol. 6314, pp. 368–381. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  14. 14.
    Hartley, R., Schaffalitzky, F.: \(L_\infty \) minimization in geometric reconstruction problems. In: CVPR (2004)Google Scholar
  15. 15.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  16. 16.
    Hartmann, W., Havlena, M., Schindler, K.: Predicting matchability. In: CVPR (2014)Google Scholar
  17. 17.
    Kanatani, K.: Statistical Optimization for Geometric Computation: Theory and Practice. Elsevier Science, Amsterdam (1996)zbMATHGoogle Scholar
  18. 18.
    Kanatani, K., Morris, D.D.: Gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy. IEEE Trans. Inf. Theor. 47(5), 2017–2028 (2001)Google Scholar
  19. 19.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. IJCV 60(2), 91–110 (2004)CrossRefGoogle Scholar
  20. 20.
    Nister, D.: An efficient solution to the five-point relative pose problem. In: CVPR (2003)Google Scholar
  21. 21.
    Nister, D., Stewenius, H.: Scalable recognition with a vocabulary tree. In: CVPR (2006)Google Scholar
  22. 22.
    Oliva, A., Torralba, A.: Modeling the shape of the scene: a holistic representation of the spatial envelope. IJCV 42(3), 145–175 (2001)CrossRefzbMATHGoogle Scholar
  23. 23.
    Raguram, R., Chum, O., Pollefeys, M., Matas, J., Frahm, J.: Usac: a universal framework for random sample consensus. IEEE PAMI 35(8), 2022–2038 (2013)CrossRefGoogle Scholar
  24. 24.
    Raguram, R., Frahm, J.M., Pollefeys, M.: Arrsac: adaptive real-time random sample consensus. In: ECCV (2008)Google Scholar
  25. 25.
    Raguram, R., Tighe, J., Frahm, J.M.: Improved geometric verification for large scale landmark image collections. In: BMVC (2012)Google Scholar
  26. 26.
    Raguram, R., Wu, C., Frahm, J.M., Lazebnik, S.: Modeling and recognition of landmark image collections using iconic scene graphs. IJCV 95(3), 213–239 (2011)CrossRefGoogle Scholar
  27. 27.
    Schönberger, J.L., Berg, A.C., Frahm, J.M.: Paige: pairwise image geometry encoding for improved efficiency in structure-from-motion. In: CVPR (2015)Google Scholar
  28. 28.
    Tomita, E., Tanaka, A., Takahashi, H.: The worst-case time complexity for generating all maximal cliques and computational experiments. Theoret. Comput. Sci. 363(1), 28–42 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Torr, P.H.: An assessment of information criteria for motion model selection. In: CVPR (1997)Google Scholar
  30. 30.
    Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle adjustment – a modern synthesis. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) ICCV-WS 1999. LNCS, vol. 1883, pp. 298–372. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  31. 31.
    Wu, C.: Towards linear-time incremental structure from motion. In: 3DV (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Johannes L. Schönberger
    • 1
  • Alexander C. Berg
    • 1
  • Jan-Michael Frahm
    • 1
  1. 1.The University of North Carolina at Chapel HillChapel HillUSA

Personalised recommendations