Abstract
Estimating the fundamental matrix from a pair of stereo images is one of the central problems in stereo vision. Typically, this estimation is based on a sparse set of point correspondences that has been obtained by a matching of characteristic image features. In this paper, however, we propose a completely different strategy: Motivated by the high precision of recent variational methods for computing the optic flow, we investigate the usefulness of their dense flow fields for recovering the fundamental matrix. To this end, we consider the state-of-the-art optic flow method of Brox et al. (ECCV 2004). Using non-robust and robust estimation techniques for determining the fundamental matrix, we compare the results computed from its dense flow fields to the ones estimated from a RANSAC method that is based on a sparse set of SIFT-matches. Scenarios for both converging and ortho-parallel camera settings are considered. In all cases, the computed results are significantly better than the ones obtained by the RANSAC method – even without the explicit removal of outliers.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Black, M.J., Anandan, P.: Robust dynamic motion estimation over time. In: Proc. 1991 IEEE Conference on Computer Vision and Pattern Recognition, Maui, HI, June 1991, pp. 292–302. IEEE Computer Society Press, Los Alamitos (1991)
Brox, T., Bruhn, A., Papenberg, N., Weickert, J.: High Accuracy Optical Flow Estimation Based on a Theory for Warping. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 25–36. Springer, Heidelberg (2004)
Bruhn, A., Weickert, J., Kohlberger, T., Schnörr, C.: A multigrid platform for real-time motion computation with discontinuity-preserving variational methods. International Journal of Computer Vision 70(3), 257–277 (2006)
Chaterjee, S., Hadi, A.: Sensitivity Analysis in Linear Regression. Wiley, New York (1988)
Faugeras, O., Luong, Q.-T., Papadopoulo, T.: The Geometry of Multiple Images. MIT Press, Cambridge (2001)
Fischler, M., Bolles, R.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM 24, 381–385 (1981)
Frahm, J.-M., Pollefeys, M.: RANSAC for (quasi-) degenerate data (QDEGSAC). In: Proc. 2006 IEEE Conference on Computer Vision and Pattern Recognition, June 2006, pp. 453–460. IEEE Computer Society Press, New York (2006)
Harris, C.G., Stephens, M.: A combined corner and edge detector. In: Proc. Fourth Alvey Vision Conference, Manchester, England, August 1988, pp. 147–152 (1988)
Hartley, R.: In defense of the eight-point algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 19, 580–593 (1997)
Horn, B., Schunck, B.: Determining optical flow. Artificial Intelligence 17, 185–203 (1981)
Huber, P.J.: Robust Statistics. Wiley, New York (1981)
Lehmann, S., Bradley, A.P., Clarkson, V.L., Williams, J., Kootsookos, P.J.: Correspondence free determination of the affine fundamental matrix. IEEE Transactions on Pattern Analysis and Machine Intelligence 29(1), 82–97 (2007)
Longuet-Higgins, H.C.: A computer algorithm for reconstructing a scene from two projections. Nature 293, 133–135 (1981)
Lowe, D.G.: Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision 60(2), 91–110 (2004)
Luong, Q.-T., Faugeras, O.D.: The fundamental matrix: theory, algorithms, and stability analysis. International Journal of Computer Vision 17(1), 43–75 (1996)
Nir, T., Kimmel, R., Bruckstein, A.: Over-parameterized variational optical flow. International Journal of Computer Vision 76(2), 205–216 (2008)
Rousseeuw, P., Leroy, A.: Robust Regression and Outlier Detection. Wiley, Chichester (1987)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)
Scharstein, D., Szeliski, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. International Journal of Computer Vision 47(1-3), 7–42 (2002)
Torr, P., Murray, D.: The development and comparison of robust methods for estimating the fundamental matrix. International Journal of Computer Vision 24(3), 271–300 (1997)
Weng, J., Huang, T., Ahuja, N.: Motion and structure from two perspecitve views: algorithms, error analysis and error estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(5), 451–476 (1989)
Zhang, Z., Deriche, R., Faugeras, O., Luong, Q.-T.: A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. Artificial Intelligence 78, 87–119 (1995)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mainberger, M., Bruhn, A., Weickert, J. (2008). Is Dense Optic Flow Useful to Compute the Fundamental Matrix?. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2008. Lecture Notes in Computer Science, vol 5112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69812-8_62
Download citation
DOI: https://doi.org/10.1007/978-3-540-69812-8_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69811-1
Online ISBN: 978-3-540-69812-8
eBook Packages: Computer ScienceComputer Science (R0)