Abstract
Variational methods for optic flow computation have the reputation of producing good results at the expense of being too slow for real-time applications. We show that real-time variational computation of optic flow fields is possible when appropriate methods are combined with modern numerical techniques. We consider the CLG method, a recent variational technique that combines the quality of the dense flow fields of the Horn and Schunck approach with the noise robustness of the Lucas–Kanade method. For the linear system of equations resulting from the discretised Euler–Lagrange equations, we present a fast full multigrid scheme in detail. We show that under realistic accuracy requirements this method is 175 times more efficient than the widely used Gauß-Seidel algorithm. On a 3.06 GHz PC, we have computed 27 dense flow fields of size 200 × 200 pixels within a single second.
Our research is partly funded by the DFG project SCHN 457/4-1. Andrés Bruhn thanks Ulrich Rüde and Mostafa El Kalmoun for interesting multigrid discussions.
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
Barron, J.L., Fleet, D.J., Beauchemin, S.S.: Performance of optical flow techniques. International Journal of Computer Vision 12(1), 43–77 (1994)
Brandt, A.: Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation 31(138), 333–390 (1977)
Briggs, W.L., Henson, V.E., McCormick, S.F.: A Multigrid Tutorial, 2nd edn. SIAM, Philadelphia (2000)
Bruhn, A., Weickert, J., Schnörr, C.: Combining the advantages of local and global optic flow methods. In: Van Gool, L. (ed.) DAGM 2002. LNCS, vol. 2449, pp. 454–462. Springer, Heidelberg (2002)
Enkelmann, W.: Investigation of multigrid algorithms for the estimation of optical flow fields in image sequences. Computer Vision, Graphics and Image Processing 43, 150–177 (1987)
Galvin, B., McCane, B., Novins, K., Mason, D., Mills, S.: Recovering motion fields: an analysis of eight optical flow algorithms. In: Proc. 1998 British Machine Vision Conference, Southampton, England (September 1998)
Ghosal, S., Vaněk, P.Č.: Scalable algorithm for discontinuous optical flow estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(2), 181–194 (1996)
Horn, B., Schunck, B.: Determining optical flow. Artificial Intelligence 17, 185–203 (1981)
Lucas, B., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: Proc. Seventh International Joint Conference on Artificial Intelligence, Vancouver, Canada, August 1981, pp. 674–679 (1981)
Nagel, H.-H.: Constraints for the estimation of displacement vector fields from image sequences. In: Proc. Eighth International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany, August 1983, vol. 2, pp. 945–951 (1983)
Terzopoulos, D.: Image analysis using multigrid relaxation. IEEE Transactions on Pattern Analysis and Machine Intelligence 8(2), 129–139 (1986)
Weickert, J., Schnörr, C.: A theoretical framework for convex regularizers in PDE-based computation of image motion. International Journal of Computer Vision 45(3), 245–264 (2001)
Young, D.M.: Iterative Solution of Large Linear Systems. Academic Press, New York (1971)
Zini, G., Sarti, A., Lamberti, C.: Application of continuum theory and multigrid methods to motion evaluation from 3D echocardiography. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 44(2), 297–308 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bruhn, A., Weickert, J., Feddern, C., Kohlberger, T., Schnörr, C. (2003). Real-Time Optic Flow Computation with Variational Methods. In: Petkov, N., Westenberg, M.A. (eds) Computer Analysis of Images and Patterns. CAIP 2003. Lecture Notes in Computer Science, vol 2756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45179-2_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-45179-2_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40730-0
Online ISBN: 978-3-540-45179-2
eBook Packages: Springer Book Archive