Skip to main content
Log in

Reliable and Efficient Computation of Optical Flow

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

In this paper, we present two very efficient and accurate algorithms for computing optical flow. The first is a modified gradient-based regularization method, and the other is an SSD-based regularization method. For the gradient-based method, to amend the errors in the discrete image flow equation caused by numerical differentiation as well as temporal and spatial aliasing in the brightness function, we propose to selectively combine the image flow constraint and a contour-based flow constraint into the data constraint by using a reliability measure. Each data constraint is appropriately normalized to obtain an approximate minimum distance (of the data point to the linear flow equation) constraint instead of the conventional linear flow constraint. These modifications lead to robust and accurate optical flow estimation. We propose an incomplete Cholesky preconditioned conjugate gradient algorithm to solve the resulting large and sparse linear system efficiently. Our SSD-based regularization method uses a normalized SSD measure (based on a similar reasoning as in the gradient-based scheme) as the data constraint in a regularization framework. The nonlinear conjugate gradient algorithm in conjunction with an incomplete Cholesky preconditioning is developed to solve the resulting nonlinear minimization problem. Experimental results on synthetic and real image sequences for these two algorithms are given to demonstrate their performance in comparison with competing methods reported in literature.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anandan, P. 1989. A computational framework and an algorithm for the measurement of visual motion. International Journal of Computer Vision, 2:283-310.

    Google Scholar 

  • Barron, J.L., Fleet, D.J., and Beauchemin, S.S. 1994. Performance of optical flowtechniques. International Journal of Computer Vision, 12(1):43-77.

    Google Scholar 

  • Black, M. and Anandan, P. 1996. The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields. Computer Vision and Image Understanding, 63(1):75-104.

    Article  Google Scholar 

  • Black, M. and Jepson, A. 1996. Estimating optical flowin segmented images using variable-order parametric models with local deformations. IEEE Trans. Patt. Anal. Mach. Intell., 18(10):972-986.

    Article  Google Scholar 

  • Duncan, J.H. and Chou, T.-C. 1992. On the detection of motion and the computation of optical flow. IEEE Trans. Patt. Anal. Mach. Intell., PAMI-14(3):346-352.

    Article  Google Scholar 

  • Elman, H.C. 1986. A stability analysis of incomplete LU factorizationss. Mathematics of Computation, 47(175):191-217.

    Google Scholar 

  • Gill, P.E., Murray, W., and Wright, M.H. 1981. Practical Optimization. Academic Press: London, New York.

    Google Scholar 

  • Golub, G.H. and Van Loan, C.F. 1989. Matrix Computations. 2nd edition, The Johns Hopkins University Press.

  • Heitz, F. and Bouthemy, P. 1993. Multimodal estimation of discontinuous optical flow using Markov random fields. IEEE Trans. Patt. Anal. Mach. Intell., PAMI-15:1217-1232.

    Article  Google Scholar 

  • Hildreth, E.C. 1984. Computations underlying the measurement of visual motion. Artificial Intelligence, 23:309-354.

    Article  Google Scholar 

  • Horn, B.K.P. and Schunck, B.G. 1981. Determining optical flow. Artificial Intelligence, 17:185-203.

    Article  Google Scholar 

  • Ju, S., Black, M., and Jepson, A. 1996. Skin and bones: Multi-layer, locally affine, optical flowand regularization with transparency. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, CA, pp. 307-314.

  • Kumar, A., Tannenbaum, A., and Balas, G. 1996. Optical-flow: A curve evolution approach. IEEE Trans. Image Processing, 5(4):598-610.

    Article  Google Scholar 

  • Lai, S.-H. and Vemuri, B.C. 1997. Physically based adaptive preconditioning for early vision. IEEE Trans. Patt. Anal. Mach. Intel., 19:594-607.

    Article  Google Scholar 

  • Lucas, B. and Kanade, T. 1981. An iterative image registration technique with an application to stereo vision. In Proc. DARPA Image Understanding Workshop, pp. 121-130.

  • Marr, D. 1982. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. Freeman.

  • Meijerink, J.A. and van der Vorst, H.A. 1977. An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Mathematics of Computation, 31(137):148- 162.

    Google Scholar 

  • Nagel, H.-H. 1983. Constraints for the estimation of displacement vector fields from image sequences. In Proc. IJCAI83, Karlsruhe, Germany, pp. 945-951.

  • Nagel, H. and Enkelmann, W. 1986. An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences. IEEE Trans. Patt. Anal. Mach. Intell., PAMI-8(5):565-593.

    Google Scholar 

  • Negahdaripour, S. and Yu, C. 1993. A generalized brightness change model for computing optical flow. In Proc. International Conference on Computer Vision, Berlin, Germany, pp. 2-11.

  • Rudin, L., Osher, S., and Fatemi, E. 1993. Nonlinear total variation based noise removal algorithms. Physica D, 60:259-268.

    Google Scholar 

  • Szeliski, R. and Coughlan, J. 1994. Hierarchical spline-based image registration. In Proc. IEEE Conference on Computer Vision Pattern Recognition, Seattle, Washington, pp. 194-201.

  • Szeliski, R. and Shum, H. 1995. Motion estimation with quadtree splines. In Proc. International Conference on Computer Vision, Cambrige, MA, pp. 757-763.

  • Terzopoulos, D. 1986. Regularization of inverse visual problems involving discontinuities. IEEE Trans. Patt. Anal. Mach. Intell., PAMI-8(4):413-424.

    Google Scholar 

  • Uras, S., Girosi, F., Verri, A., and Torre, V. 1988. A computational approach to motion perception. Biol. Cybern., 60:79-87.

    Article  Google Scholar 

  • Verri, A. and Poggio, T. 1989. Motion field and optical flow: Qualitative properties. IEEE Trans. Patt. Anal. Mach. Intell., 11(5):490- 498.

    Article  Google Scholar 

  • Waxman, A. and Wohn, K. 1985. Contour evolution, neighborhood deformation, and global image flow: Planner surfaces in motion. International Journal of Robotics Research, 4:95-108.

    Google Scholar 

  • Weber, J. and Malik, J. 1995. Robust computation of optical flow in a multiscale differential framework. International Journal of Computer Vision, 14(1):67-81.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lai, SH., Vemuri, B.C. Reliable and Efficient Computation of Optical Flow. International Journal of Computer Vision 29, 87–105 (1998). https://doi.org/10.1023/A:1008005509994

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008005509994

Navigation