Abstract
In this paper we define a complete framework for processing large image sequences for a global monitoring of short range oceanographic and atmospheric processes. This framework is based on the use of a non quadratic regularization technique for optical flow computation that preserves flow discontinuities. We also show that using an appropriate tessellation of the image according to an estimate of the motion field can improve optical flow accuracy and yields more reliable flows. This method defines a non uniform multiresolution approach for coarse to fine grid generation. It allows to locally increase the resolution of the grid according to the studied problem. Each added node refines the grid in a region of interest and increases the numerical accuracy of the solution in this region. We make use of such a method for solving the optical flow equation with a non quadratic regularization scheme allowing the computation of optical flow field while preserving its discontinuities. The second part of the paper deals with the interpretation of the obtained displacement field. For this purpose a phase portrait model used along with a new formulation of the approximation of an oriented flow field allowing to consider arbitrary polynomial phase portrait models for characterizing salient flow features. This new framework is used for processing oceanographic and atmospheric image sequences and presents an alternative to complex physical modeling techniques.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barron, J.L., Fleet, D.J., and Beauchemin, S.S. 1994. Performance of optical flowtechniques. International Journal of Computer Vision, 12(1):43–77.
Berroir, J.-P., Herlin, I.L., and Cohen, I. 1995. Tracking highly deformable structures: a surface model applied to vortex evolution within satellite oceanographic images. EOS-SPIE Satellite Remote Sensing II.
Black, M.J. 1994. Recursive non-linear estimation of discontinuous flow fields. In Third European Conference on Computer Vision, Springer-Verlag: Sweden, pp. 138–145.
Black, M.J. and Anandan, P. 1991. Robust dynamic motion estimation over time. In IEEE Proceedings of Computer Vision and Pattern Recognition, pp. 296–302.
Ciarlet, P.G. 1987. The Finite Element Methods for Elliptic Problems. North-Holland: Amsterdam.
Cohen, I. and Herlin, I. 1996. Optical flow and phase portrait methods for environmental satellite image sequences. In Proceedings of the Fourth European Conference on Computer Vision 1996, Cambridge.
Cohen, I. and Herlin, I. 1998. Tracking meteorological structures through curves matching using geodesic paths. In IEEE Proceedings of the Sixth International Conference on Computer Vision, Bombay, India, pp. 396–401.
Cohen, I. and Herlin, I. 1998a. Curves matching using geodesic paths. In IEEE Proceedings of Computer Vision and Pattern Recognition, Santa Barbara.
Ford, R.M. and Strickland, R.N. 1993. Nonlinear phase portrait models for oriented textures. In IEEE Proceedings of Computer Vision and Pattern Recognition, New York, pp. 644–645.
Ford, R.M., Strickland, R.N., and Thomas, B.A. 1994. Image models for 2-D flow visualization and compression. CVGIP: Graphical Models and Image Processing, 56(1):75–93.
Glowinski, R. 1984. Numerical Methods for Nonlinear Variational Problems. Springer-Verlag: New York. Springer Series in Computational Physics.
Golub, G.H. and Van Loan, C.F. 1989. Matrix Computations. 2nd edition, The Johns Hopkins University Press: London.
Herlin, I., Cohen, I., and Bouzidi, S. 1996. Image processing for sequence of oceanographic images. The Journal of Visualization and Computer Animation, to appear.
Horn, B.K.P. and Schunck, G. 1981. Determining optical flow. Arti-ficial Intelligence, 17:185–203.
Irani, M., Rousso, B., and Peleg, S. 1992. Detecting and tracking multiple moving objects using temporal integration. In Proceedings of the Second European Conference on Computer Vision 1992, pp. 282–287.
Kimia, B.B. and Siddiqi, K. 1994. Geometric heat equation and nonlinear diffusion of shapes and images. In IEEE Proceedings of Computer Vision and Pattern Recognition, pp. 113–120.
Lefschetz, S. 1976. Differential Equations: Geometric Theory. 2nd edition, New York: Dover Publications.
Lions, P.L., Morel, J.M., and Alvarez, L. 1990. Image selective smoothing and edge detection by nonlinear diffusion. Technical Report 9046, CEREMADE, U.R.A. CNRS 749, Université Paris IX-Dauphine. Cahiers de Mathématiques de la Décision.
Mémin, E. and Perez, P. 1998. A multigrid approach for hierarchical motion estimation. In IEEE Proceedings of the Sixth International Conference on Computer Vision, Bombay, India, pp. 933–938.
Muller, J.R., Anandan, P., and Bergen, J.R. 1994. Adaptive-complexity registration of images. In IEEE Proceedings of Computer Vision and Pattern Recognition, pp. 953–957.
Nagel, H.H. and Enkelmann, W. 1986. An investigation of smoothness constraints for the estimation of displacement vector fields from image sequence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(5):565–593.
Nemytskii, V.V. and Stepanov, V.V. 1989. Qualitative Theory of Differential Equations. Dover Publications: New York.
Niessen, W.J. and Florack, L.M.J., Salden, A.H., Romeny, B.M. 1994. Nonlinear diffusion of scalar images using well-posed differential operators. In IEEE Proceedings of Computer Vision and Pattern Recognition, pp. 92–97.
Otte, M. and Nagel, H.-H. 1994. Optical flow estimation: Advances and comparisons. In Proceedings of the Third European Conference on Computer Vision 1994, pp. 51–60.
Rao, A.R. and Jain, R.C. 1992. Computerized flow field analysis: Oriented textures fields. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(7):693–709.
Rosen, J.B. 1960. The gradient projection method for nonlinear programming. Part I: Linear constraints. J. Soc. Indust. Appl. Math., 8(1):181–217.
Rudin, L.I., Osher, S., and Fatemi, E. 1992. Nonlinear total variation based noise removal algorithms. In Ecoles CEA-EDF-INRIA; Problèmes Non Linéaires Appliqués: Modélisation Mathématique pour le traitement d'images, pp. 149–179.
Samet, H. 1989. The Design and Analysis of Spatial Data Structures. Addison-Wesley.
Schnorr, C. 1992. Computation of discontinuous optical flow by domain decomposition and shape optimization. IJCV, 8(2):153–165.
Shu, C.-F. and Jain, R.C. 1992. Vector field analysis for oriented patterns. In IEEE Proceedings of Computer Vision and Pattern Recognition, Urbana Champaign: Illinois, pp. 673–676.
Szeliski, R. and Shum, H.Y. 1995. Motion estimation with quadtree splines. Technical report, DEC Cambridge Research Lab.
Vasilescu, M. and Terzopoulos, D. 1992. Adaptive meshes and shells: Irregular triangulation, discontinuities, and hierarchical subdivision. In IEEE Proceedings of Computer Vision and Pattern Recognition, pp. 829–832.
Verri, A. and Poggio, T. 1989. Motion field and optical flow: Qualitative properties. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(5):490–498.
Yahia, H., Herlin, I., and Vogel, L. 1995. Temporal tracking with implicit templates. Technical Report 2701, INRIA Rocquencourt.
Zhong, J., Huang, T.S., and Adrian, R.J. 1994. Salient structure analysis of fluid flow. In IEEE Proceedings of Computer Vision and Pattern Recognition, pp. 310–315, Seattle, Washington.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cohen, I., Herlin, I. Non Uniform Multiresolution Method for Optical Flow and Phase Portrait Models: Environmental Applications. International Journal of Computer Vision 33, 29–49 (1999). https://doi.org/10.1023/A:1008161130332
Issue Date:
DOI: https://doi.org/10.1023/A:1008161130332