Skip to main content

Efficient Two-View Geometry Classification

  • Conference paper
  • First Online:
Pattern Recognition (DAGM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9358))

Included in the following conference series:

Abstract

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 is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  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. Baarda, W., Netherlands Geodetic Commission, et al.: Statistical concepts in geodesy, vol. 2(4). Rijkscommissie voor Geodesie (1967)

    Google Scholar 

  3. Breiman, L.: Random forests. Mach. Learn. 45, 5–32 (2001)

    Article  Google Scholar 

  4. Bron, C., Kerbosch, J.: Algorithm 457: finding all cliques of an undirected graph. ACM Commun. 16, 48–50 (1973)

    Article  Google Scholar 

  5. Cazals, F., Karande, C.: A note on the problem of reporting maximal cliques. Theoret. Comput. Sci. 407(1), 564–568 (2008)

    Article  MathSciNet  Google Scholar 

  6. Chum, O., Matas, J.: Matching with prosac-progressive sample consensus (2005)

    Google Scholar 

  7. Chum, O., Matas, J., Obdrzalek, S.: Enhancing ransac by generalized model optimization. In: ACCV (2004)

    Google Scholar 

  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. Criminisi, A.: Accurate Visual Metrology from Single and Multiple Uncalibrated Images. Springer, London (2001)

    Book  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  11. Förstner, W.: Uncertainty and projective geometry. In: Corrochano, E.B. (ed.) Handbook of Geometric Computing, pp. 493–534. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Frahm, J.M., Pollefeys, M.: RANSAC for (quasi-) degenerate data (QDEGSAC). In: CVPR (2006)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  14. Hartley, R., Schaffalitzky, F.: \(L_\infty \) minimization in geometric reconstruction problems. In: CVPR (2004)

    Google Scholar 

  15. Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  16. Hartmann, W., Havlena, M., Schindler, K.: Predicting matchability. In: CVPR (2014)

    Google Scholar 

  17. Kanatani, K.: Statistical Optimization for Geometric Computation: Theory and Practice. Elsevier Science, Amsterdam (1996)

    Google Scholar 

  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. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. IJCV 60(2), 91–110 (2004)

    Article  Google Scholar 

  20. Nister, D.: An efficient solution to the five-point relative pose problem. In: CVPR (2003)

    Google Scholar 

  21. Nister, D., Stewenius, H.: Scalable recognition with a vocabulary tree. In: CVPR (2006)

    Google Scholar 

  22. Oliva, A., Torralba, A.: Modeling the shape of the scene: a holistic representation of the spatial envelope. IJCV 42(3), 145–175 (2001)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  24. Raguram, R., Frahm, J.M., Pollefeys, M.: Arrsac: adaptive real-time random sample consensus. In: ECCV (2008)

    Google Scholar 

  25. Raguram, R., Tighe, J., Frahm, J.M.: Improved geometric verification for large scale landmark image collections. In: BMVC (2012)

    Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  29. Torr, P.H.: An assessment of information criteria for motion model selection. In: CVPR (1997)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  31. Wu, C.: Towards linear-time incremental structure from motion. In: 3DV (2013)

    Google Scholar 

Download references

Acknowledgment

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Johannes L. Schönberger .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Schönberger, J.L., Berg, A.C., Frahm, JM. (2015). Efficient Two-View Geometry Classification. In: Gall, J., Gehler, P., Leibe, B. (eds) Pattern Recognition. DAGM 2015. Lecture Notes in Computer Science(), vol 9358. Springer, Cham. https://doi.org/10.1007/978-3-319-24947-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24947-6_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24946-9

  • Online ISBN: 978-3-319-24947-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics