Adaptive Structure from Motion with a Contrario Model Estimation

  • Pierre Moulon
  • Pascal Monasse
  • Renaud Marlet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7727)


Structure from Motion (SfM) algorithms take as input multi-view stereo images (along with internal calibration information) and yield a 3D point cloud and camera orientations/poses in a common 3D coordinate system. In the case of an incremental SfM pipeline, the process requires repeated model estimations based on detected feature points: homography, fundamental and essential matrices, as well as camera poses. These estimations have a crucial impact on the quality of 3D reconstruction. We propose to improve these estimations using the a contrario methodology. While SfM pipelines usually have globally-fixed thresholds for model estimation, the a contrario principle adapts thresholds to the input data and for each model estimation. Our experiments show that adaptive thresholds reach a significantly better precision. Additionally, the user is free from having to guess thresholds or to optimistically rely on default values. There are also cases where a globally-fixed threshold policy, whatever the threshold value is, cannot provide the best accuracy, contrary to an adaptive threshold policy.


Fundamental Matrix Adaptive Threshold Bundle Adjustment Structure From Motion Visual Odometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agarwal, S., Snavely, N., Simon, I., Seitz, S., Szeliski, R.: Building Rome in a day. In: 12th IEEE International Conference on Computer Vision (ICCV), pp. 72–79 (2009)Google Scholar
  2. 2.
    Frahm, J.-M., Fite-Georgel, P., Gallup, D., Johnson, T., Raguram, R., Wu, C., Jen, Y.-H., Dunn, E., Clipp, B., Lazebnik, S., Pollefeys, M.: 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
  3. 3.
    Kahl, F.: Multiple view geometry and the L  ∞ -norm. In: ICCV, pp. 1002–1009 (2005)Google Scholar
  4. 4.
    Dalalyan, A., Keriven, R.: L 1-penalized robust estimation for a class of inverse problems arising in multiview geometry. In: NIPS, pp. 441–449 (2009)Google Scholar
  5. 5.
    Furukawa, Y., Ponce, J.: Accurate, dense, and robust multiview stereopsis. IEEE Transactions on Pattern Analysis and Machine Intelligence 32, 1362–1376 (2010)CrossRefGoogle Scholar
  6. 6.
    Hiep, V., Keriven, R., Labatut, P., Pons, J.: Towards high-resolution large-scale multi-view stereo. In: CVPR, pp. 1430–1437 (2009)Google Scholar
  7. 7.
    Zach, C., Klopschitz, M., Pollefeys, M.: Disambiguating visual relations using loop constraints. In: CVPR, pp. 1426–1433 (2010)Google Scholar
  8. 8.
    Aanæs, H., Dahl, A., Steenstrup Pedersen, K.: Interesting interest points. International Journal of Computer Vision 97, 18–35 (2012)CrossRefGoogle Scholar
  9. 9.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision (IJCV) 60, 91–110 (2004)CrossRefGoogle Scholar
  10. 10.
    Bay, H., Tuytelaars, T., Van Gool, L.: SURF: Speeded Up Robust Features. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, pp. 404–417. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Lourakis, M.I.A., Argyros, A.A.: SBA: A software package for generic sparse bundle adjustment. ACM Transactions on Mathematical Software (TOMS) 36 (2009)Google Scholar
  12. 12.
    Wu, C., Agarwal, S., Curless, B., Seitz, S.M.: Multicore bundle adjustment. In: CVPR, pp. 3057–3064 (2011)Google Scholar
  13. 13.
    Snavely, N., Seitz, S.M., Szeliski, R.: Photo tourism: exploring photo collections in 3D. ACM Transactions on Graphics (TOG) 25, 835–846 (2006)CrossRefGoogle Scholar
  14. 14.
    Gherardi, R., Farenzena, M., Fusiello, A.: Improving the efficiency of hierarchical structure-and-motion. In: CVPR, pp. 1594–1600 (2010)Google Scholar
  15. 15.
    Havlena, M., Torii, A., Knopp, J., Pajdla, T.: Randomized structure from motion based on atomic 3D models from camera triplets. In: CVPR, pp. 2874–2881 (2009)Google Scholar
  16. 16.
    Scaramuzza, D., Fraundorfer, F.: Visual odometry: Part I - the first 30 years and fundamentals. IEEE Robot. Automat. Mag. 18 (2011)Google Scholar
  17. 17.
    Fraundorfer, F., Scaramuzza, D.: Visual odometry: Part II - matching, robustness, and applications. IEEE Robot. Automat. Mag. 19 (2012)Google Scholar
  18. 18.
    Martinec, D., Pajdla, T.: Robust rotation and translation estimation in multiview reconstruction. In: CVPR (2007)Google Scholar
  19. 19.
    Govindu, V.M.: Combining two-view constraints for motion estimation. In: CVPR, vol. 2, pp. II.218–II.225 (2001)Google Scholar
  20. 20.
    Govindu, V.M.: Robustness in Motion Averaging. In: Narayanan, P.J., Nayar, S.K., Shum, H.-Y. (eds.) ACCV 2006. LNCS, vol. 3852, pp. 457–466. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. 21.
    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 (CACM) 24, 381–395 (1981)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Desolneux, A., Moisan, L., Morel, J.M.: From Gestalt theory to image analysis: a probabilistic approach, 1st edn. Springer (2007)Google Scholar
  23. 23.
    Moisan, L., Moulon, P., Monasse, P.: Automatic homographic registration of a pair of images, with a contrario elimination of outliers. Image Processing On Line (2012),
  24. 24.
    Moisan, L., Stival, B.: A probabilistic criterion to detect rigid point matches between two images and estimate the fundamental matrix. Int. J. of Computer Vision (IJCV) 57, 201–218 (2004)CrossRefGoogle Scholar
  25. 25.
    Rabin, J., Delon, J., Gousseau, Y., Moisan, L.: MAC-RANSAC: a robust algorithm for the recognition of multiple objects. In: Proc. of 3DPTV 2010, Paris (2010)Google Scholar
  26. 26.
    Nistér, D.: An efficient solution to the five-point relative pose problem. In: CVPR, vol. 2, pp. II.195–II.202 (2003)Google Scholar
  27. 27.
    Lepetit, V., Moreno-Noguer, F., Fua, P.: EPnP: an accurate O(n) solution to the PnP problem. International Journal of Computer Vision (IJCV) 81, 155–166 (2009)CrossRefGoogle Scholar
  28. 28.
    Strecha, C., von Hansen, W., Van Gool, L.J., Fua, P., Thoennessen, U.: On benchmarking camera calibration and multi-view stereo for high resolution imagery. In: CVPR, pp. 1–8 (2008)Google Scholar
  29. 29.
    Haralick, R.M., Shapiro, L.G.: Computer and Robot Vision, 1st edn. Addison-Wesley Longman Publishing Co., Inc., Boston (1992)Google Scholar
  30. 30.
    Rabin, J., Delon, J., Gousseau, Y.: A statistical approach to the matching of local features. SIAM J. Imaging Sciences 2, 931–958 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  31. 31.
    Sabater, N., Almansa, A., Morel, J.M.: Meaningful matches in stereovision. IEEE Transactions on Pattern Analysis and Machine Intelligence 99 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pierre Moulon
    • 1
    • 2
  • Pascal Monasse
    • 1
  • Renaud Marlet
    • 1
  1. 1.LIGM (UMR CNRS), Center for Visual Computing, ENPCUniversité Paris-EstMarne-la-ValléeFrance
  2. 2.Mikros Image.Levallois-PerretFrance

Personalised recommendations