Abstract
This paper formulates the optic flow problem as a set of over-determined simultaneous linear equations. It then introduces and studies two new robust optic flow methods. The first technique is based on using the Least Median of Squares (LMedS) to detect the outliers. Then, the inlier group is solved using the least square technique. The second method employs a new robust statistical method named the Least Median of Squares Orthogonal Distances (LMSOD) to identify the outliers and then uses total least squares to solve the optic flow problem. The performance of both methods are studied by experiments on synthetic and real image sequences. These methods outperform other published methods both in accuracy and robustness.
Similar content being viewed by others
References
Bab-Hadiashar, A. 1996. Least squares and closest point problem in optic flow estimation: The duality or the confusion. Technical Report MECSE 96-2, Monash University, Clayton, 3168, Australia, available at: http://batman.eng.monash.edu.au/ali/.
Barron, J.L., Fleet, D.J., and Beauchemin, S.S. 1994. Systems and experiment performance of optical flow techniques. Intern. J. Comput. Vis., 12:43-77.
Bergen, J.R., Anandan, P., Hana, K.J., and Hingorani, R. 1992. Hierarchical model-based motion estimation. In Proc. Secd. Europ. Conf. Comp. Vis., ECCV-92, Springer-Verlag, pp. 237-252.
Bergen, J.R., Burt, P.J., Hana, K.J., Hingorani, R., Jeanne, P., and Peleg, S. 1991. Dynamic multiple motion estimation. Artif. Inte. Comp. Vis. Proc. Israeli Conf., North Holland, pp. 147-156.
Black, M.J. 1994. Recursive non-linear estimation of discontinous flowfield. In Proc. of Third Europ. Conf. on Comp. Vis., ECCV-94, Springer-Verlag, pp. 138-145.
Black, M.J. and Anandan, P. 1991. Robust dynamic motion estimation over time. In Proc. of Computer Vision and Pattern Recognition, CVPR-91, Maui, HI, pp. 296-302.
Black, M.J. and Anandan, P. 1993. A framework for the robust estimation of optical flow. In Proc. Int. Conf. on Computer Vision, ICCV-93, Berlin, pp. 231-236.
Black, M.J. and Anandan, P. 1996. The robust estimation of multiple motion: Parametric and piecewise-smooth flow fields. Computer Vision and Image Understanding, 63(1):75-104.
Black, M.J. and Jepson, A.D. 1994. Estimating multiple independent motions in segmented images using parametric models with local deformations. Workshop on Motion of Non-rigid and Articulated Objects, Austin, pp. 220-227.
Bober, M. and Kittler, J. 1994a. Estimation of complex multimodal motion: An approach based on robust statistics and hough transform. Image and Vision Computing, 12(10):661-668.
Bober, M. and Kittler, J. 1994b. Robust motion analysis. In Proc. of Computer Vision and Pattern Recognition, CVPR-94, Seattle, pp. 947-952.
Burt, P.J., Bergen, J.R., Hingorani, R., Kolczynski, R., Lee, W.A., Leung, A., Lubin, J., and Shvaytser, H. 1989. Object tracking with a moving camera: An application of dynamic motion analysis. In Proc. of the Workshop on Visual Motion, Irvin, CA, pp. 2-12.
Cafforio, C. and Rocca, F. 1976. Methods for measuring small displacement of television images. IEEE Trans. Inform. Theory, IT-22:573-579.
Chaudhuri, S. and Chatterjee, S. 1991. Performance analysis of total least squares method in three-dimensional motion estimation. IEEE Trans. on Robotics and Automation, 7(5):707-714.
Chu, C.H. and Delp, E.J. 1989. Estimating displacement vector form an image sequence. J. Opt. Soc. Am. A, 6(6):871-878.
Darrell, T. and Pentland, A. 1991. Robust estimation of a multilayered motion representation. IEEE Proc. of Workshop on Visual Motion, Princeton, NJ, pp. 173-178.
Edelsbrunner, H. and Souvaine, D.L. 1990. Computing least median of squares regression lines and guided topological sweep. J. of the American Statistical Association, 85(409):115-119.
Fennema, C. and Thompson, W. 1979. Velocity determination in scenes containing several moving objects. Comput. Graph. Image Process, 9:301-315.
Fleet, D.J. and Jepson, A.D. 1990. Computation of component image velocity from local phase information. Intern. J. Comput. Vis., 5:77-104.
Giachetti, A. and Torre, V. 1996. Refinement of optical flow estimation and detection of motion edges. In Proc. of Fourth Europ. Conf. on Comp. Vis., ECCV-96, Springer-Verlag, pp. 151-160.
Hampel, F.R., and Ronchetti, E.M., Rousseeuw, P.J., and Stahel, W.A. 1986. Robust Statistics: The Approach Based on Influence Functions. John Wiley: New York.
Heeger, D. 1997. Private correspondence.
Horn, B.K.P. 1986. Robot Vision. MIT Press: Cambridge.
Horn, B.K.P. and Schunck, B.G. 1981. Determining optical flow. Artificial Intelligence, 17:185-204.
Iu, S.L. 1995. Robust estimation of motion vector field with discontinuity and occlusion using local outliers rejection. J. of Visual Communication and Image Representation, 6(2):132-141.
Jähne, B. 1993. Spatio-Temporal Image Processing, Theory and Scientific Applications. Springer-Verlag: New York.
Jepson, A.D. and Black, M.J. 1993. Mixture models for optical flow computation. In Proc. of Compu. Vision and Pattern Recognition, CVPR-93, New York, pp. 760-761.
Jepson, A.D. and Black, M.J. 1995. Mixture models for optical flow computation. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 19, pp. 271-286.
Ju, S.X., Black, M.J., and Jepson, A.D. 1996. Skin and Bones: Multilayer, locally affine, optical flow and regularaization with transparency. In Proc. of Computer Vision and Pattern Recognition, CVPR-96, San Francisco, pp. 307-314.
Kvalseth, T.O. 1985. Cautionary note about R 2. The American Statistician, 39(4):279-285.
Limb, J.O. and Murphy, J.A. 1975. Measuring the speed of moving objects from television signals. IEEE Trans. on Communications, 23(4):474-478.
Liu, H., Hong, T., Herman, M., and Chellappa, R. 1996. Accuracy vs. efficiency trade-offs in optical flow algorithms. In Proc. of Fourth Europ. Conf. on Comp. Vis., ECCV-96, Springer-Verlag, pp. 174-183.
Meer, P., Mintz, D., Rosenfeld, A., and Kim, D.Y. 1991. Robust regression methods for computer vision: A review. Intern. J. Comput. Vis., 6(1):59-70.
Mitiche, A. 1994. Computational Analysis of Visual Motion. Plenum: New York.
Nagel, H.H. 1987. On the estimation of optical flow. Artificial Intelligence, 33:299-324.
Nagel, H.H. 1995. Optical flow estimation and the interaction between measurement errors at adjacent pixel positions. Intern. J. Comput. Vis., 15:271-288.
Nesi, P., Del Bimbo, A., and Ben-Tzvi, D. 1995. A robust algorithm for optical flow estimation. Computer Vision and Image Understanding, 62(1):59-68.
Odobez, J.M. and Bouthemy, P. 1995. Robust multiresolution estimation of parametric motion models. J. of Visual Communication and Image Representation, 6(4):348-365.
Otte, M. and Nagel, H.H. 1994. Optical flow estimation: Advances and comparisons. In Proc. of Third Europ. Conf. on Comp. Vis., ECCV-94, Springer-Verlag, pp. 51-60.
Rousseeuw, P.J. 1984. Least median of squares regression. Journal of the American Statistical Association, 79:871-880.
Rousseeuw, P.J. and Leroy, A.M. 1987. Robust Regression and Outlier Detection. John Wiley: New York.
Schunck, B.G. 1989. Image flow segmentation and estimation by constraint line clustering. IEEE Trans. on Pattern Anal. and Mach. Intell., PAMI, 11(10):1010-1027.
Shi, J. and Tomasi, C. 1994. Good features to track. In Proc. of Computer Vision and Pattern Recognition, CVPR-94, Seattle, pp. 593-600.
Steele, J.M. and Steiger, W.L. 1986. Algorithms and complexity for least median of squares regression. Discrete. Appl. Math., 14:93-100.
Stewart, C. 1996. Bias in robust estimation caused by discontinuities and multiple structures. Technical Report, Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York TR-12180-3590.
Szeliski, R. and Coughlan, J. 1994. Hierarchical spline-based image registration. In Proc. of Computer Vision and Pattern Recognition, CVPR-94, Seattle, pp. 194-201.
VanHuffel, S. and Vandewalle, J. 1991. The Total Least Squares Problem: Computational Aspects and Analysis. 1st edition, SIAM: Philadelphia.
Van Mieghlem, J.A., Avi-Itzhak, H.I., and Melen, R.D. 1995. Straight line extraction using iterative total least squares method. J. of Visual Communication and Image Representation, 6(1):59-68.
Wang, S., Markandey, V., and Reid, A. 1992. Total least squares fitting spatiotemporal derivatives to smooth optical flow field. In Proc. of the SPIE: Signal and Data Processing of Small Targets, vol. 1698, pp. 42-55.
Weber, J. and Malik, J. 1993. Robust computation of optical flow in a multi-scale differential framework. In Proc. of Int. Conf. on Computer Vision, ICCV-93, Berlin, pp. 12-20.
Weber, J. and Malik, J. 1995. Robust computation of optical flow in a multi-scale differential framework. Intern. J. Comput. Vis., 14:67-81.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bab-Hadiashar, A., Suter, D. Robust Optic Flow Computation. International Journal of Computer Vision 29, 59–77 (1998). https://doi.org/10.1023/A:1008090730467
Issue Date:
DOI: https://doi.org/10.1023/A:1008090730467