Optical flow: A curve evolution approach

IEEE Transactions on Image Processing

Volumn 5, Issue 4, 1996, Pages 598-610

  Kumar, Arun ^a   Tannenbaum, Allen R ^a   Balas, Gary J ^a  

^a University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; CONSTRAINT THEORY; DIFFERENTIAL EQUATIONS; FINITE DIFFERENCE METHOD; IMAGE SEGMENTATION; LAGRANGE MULTIPLIERS; LIGHT SOURCES; OPTICAL SYSTEMS; THREE DIMENSIONAL; VARIATIONAL TECHNIQUES;

EDGE INFORMATION; EULER-LAGRANGE DIFFERENTIAL EQUATIONS; OPTICAL FLOW CONSTRAINT; SPATIOTEMPORAL DIFFERENTIATION METHOD; STATIC CAMERA;

OPTICAL FLOWS;

EID: 0030128710     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.491336     Document Type: Article

References (63)

1. U. Abresch and J. Langer, "The normalized curve shortening flow and homothetic solutions," J. Diff. Geom., vol. 23, p. 175-196, 1986.
2. L. Alvarez, F. Guichard, and J. M. Morel, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numerical Anal., vol. 29, pp 845-866, 1992.
3. L. Alvarez, F. Guichard, P. L. Lions, and J. M. Morel, "Axiomatization et nouveaux operateurs de la morphologie mathematique," C. R. Acad. Sci. Paris, vol. 315, pp. 265-268, 1992.
4. _, "Axiomes et equations fondamentales du traitement d'images," C. R. Acad. Sci. Paris, vol. 315, p. 135-138, 1992.
5. S. Angenent, "Parabolic equations for curves on surfaces, I: Curves with p-integrable curvature," Ann. Math., vol. 133, pp. 451-483, 1990.
6. _, "Parabolic equations for curves on surfaces, II: Intersections, blow-up, and generalized solutions," Ann. Math., vol. 133, pp. 171-215, 1991.
7. J. L. Barron, D. J. Fleet, and S. S. Beauchemin, "Performance of optical flow techniques," Int. J. Comput. Vision, vol. 12, pp. 43-77, 1994.
8. A. D. Bimbo, P. Nesi, and J. L. C. Sanz, "Optical flow computation using extended constraints," Tech. Rep., Dept. Syst. Informatics, Univ. of Florence, 1992.
9. C. Cafforio and F. Rocca, "Tracking moving objects in television images," Signal Processing, vol. 1, pp. 133-140, 1979.
10. M. Campani and A. Verri, "Computing optical flow from an overconstrained system of linear algebraic equations," in Proc. Third IEEE Int. Conf. Comput. Vision (ICCV), Osaka, Japan, 1990, pp. 22-26.
11. V. Caselles, F. Catte, T. Coll, and F. Dibos, "A geometric model for active contours in image processing," AMS, vol. 29, pp. 1-10, 1993.
12. M. G. Crandall, H. Ishii, and P. L. Lions, "Users guide to viscosity solutions of second order partial linear differential equations," Bull. Amer. Math. Soc., vol. 27, pp. 1-67, 1992.
13. C. L. Epstein and M. Gage, "The curve shortening flow," Wave Motion: Theory, Modeling, and Computation, A. Chorin and A. Majda, Eds. New York: Springer-Verlag, 1987.
14. L. C. Evans, "Estimates for smooth absolutely minimizing Lipschitz extensions," Electron. J. Diff. Eq., vol. 1, pp. 1-9, 1993.
15. L. C. Evans and J. Spruck, "Motion of level sets by mean curvature, I," J. Diff. Geom., vol. 33, pp. 635-681, 1991.
16. L. Florack, "The syntactical structure of scalar images," Ph.D. Dissertation, Univ. Utrecht, The Netherlands, Nov. 1993.
17. M. Gage and R. S. Hamilton, "The heat equation shrinking convex plane curves," J. Diff. Geom, vol. 23, pp. 285-314, 1986.
18. M. Grayson, "The heat equation shrinks embedded plane curves to round points," J. Diff. Geom., vol. 26, pp. 285-314, 1987.
19. _, "Shortening embedded curves," Ann. Math, vol. 129, pp. 71-111, 1989.
20. R. M. Haralick and J. S. Lee, "The facet approach to optical flow," in Proc. Image Understanding Workshop (Science Applications), Arlington, VA, Dec. 1983.
21. E. C. Hildreth, "Computations underlying the measurement of visual motion," Artif. Intell., vol. 23, pp. 309-354, 1984.
22. B. K. P. Horn and B. G. Schunck, "Determining optical flow," Artif. Intell., vol. 23, pp. 185-203, 1981.
23. B. K. P. Horn, Robot Vision. Cambridge, MA: MIT Press, 1986.
24. R. Jain, W. N. Martin, and J. K. Aggarwal, "Segmentation through the detection of changes due to motion," Comput. Graphics Image Processing, vol. 11, no. 1, pp. 13-34, 1979.
25. R. Jain, D. Militzer, and H.-H. Nagel, "Separating nonstationary from stationary scene components in a sequence of real world TV-images," in Proc. 5th Int. Joint Conf. Artificial Intell., Aug. 1979, pp. 612-618.
26. R. Jain and H.-H. Nagel. "On the analysis of accumulative difference pictures from image sequences of real world scenes," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-1, no. 2, pp. 206-214, 1979.
27. B. B. Kimia, "Toward a computational theory of shape," Ph.D. dissertation, McGill Univ., Dept. Elect. Eng., Aug. 1990.
28. B. B. Kimia, A. Tannenbaum, and S. W. Zucker, "Shapes, shocks and deformations-I," Int. J. Comput. Vision, vol. 15, pp. 189-224, 1996.
29. _, "Toward a computational theory of shape: An overview," in Lecture Notes in Computer Science, vol. 427. New York: Springer-Verlag, 1990, pp. 402-407.
30. _, "On the evolution of curves via a function of curvature-I: The classical case," J. Math Anal. Applications, vol. 163, pp. 438-458, 1992.
31. J. J. Koenderink, "The structure of images," Biol. Cybern., vol. 50, pp. 363-370, 1984.
32. _, Solid Shape. Cambridge, MA: MIT Press, 1990.
33. J. Konrad and E. Dubois, "Multigrid Bayesian estimation of the image motion fields using stochastic relaxation," in Proc. Second IEEE Int. Conf. Comput. Vision ICCV, Tampa, FL, 1988, pp. 354-362.
34. N. V. Krylov, Nonlinear Elliptic and Parabolic Equations of the Second Order. Boston, MA: Kluwer, 1987.
35. 1 minimization," in preparation.
36. R. J. LeVeque, Numerical Method for Conservation Laws. Boston, MA: Birkhauser, 1992.
37. C. Longuet-Higgins and K. Prazdny, "The interpretation of a moving retinal image," in Proc. Royal Soc. London B, vol. 208, pp. 385-397, 1980.
38. M. Luettgen, W. C. Karl, and A. Willsky, "Efficient multiscale regularization with applications to the computation of optical flow," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-3, pp. 41-63, 1984.
39. R. Malladi, J. A. Sethian, and B. C. Vemuri, "Shape modeling with front propagation: a level set approach," IEEE Trans. Patt. Anal. Machine Intell., to be published.
40. V. Markandey and B. E. Flichbaugh, "Multispectral constraints for optical flow compulation," in Proc. Third IEEE Int. Conf. Comput. Vision ICCV, Osaka, Japan, Dec. 1990, pp. 38-41.
41. A. Mitiche, Y. F. Wang, and J. K. Aggarwal, "Experiments in computing optical flow with the gradient-based multiconstraint method," Patt. Recogn., vol. 20, no. 2, pp. 173-179, 1987.
42. F. Mokhatarian and A. Mackworth, "A theory of multiscale, curvature-based shape representation for planar curves," IEEE Trans. Patt. Anal. Machine Intell., vol. 14, pp. 789-805, 1992.
43. H.-H. Nagel and W. Enkelmann, "An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, no. 5, pp. 565-593, 1986.
44. S. J. Osher and J. A. Sethian, "Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys., vol. 79, pp. 12-49, 1988.
45. P. Perona and J. Malik, "Scale space and edge detection using anisotropic diffusion," IEEE Trans. Patt. Anal. Machine Intell., vol. 12, pp. 629-639, 1990.
46. T. Poggio, V. Torre, and C. Koch, "Computational vision and regularization theory," Nature, vol. 317, no. 26, pp. 314-319, Sept. 1985.
47. K. Prazdny, "On the information in optical flows," Comput. Vision, Graphics, Image Processing, vol. 23, pp. 239-259, 1983.
48. J. G. Rosen, "The gradient projection method for nonlinear programming, II: Nonlinear constraints," J. Soc. Indust. Appl. Math, vol. 9, pp. 514-532, 1961.
49. L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D, vol. 60, pp. 259-268, 1993.
50. G. Sapiro and A. Tannenbaum, "Area and length preserving geometric invariant scale-spaces," IEEE Trans. Patt. Anal. Machine Intell., vol. 17, pp. 67-72, 1995.
51. _, "Affine invariant scale-space," Int. J. Comput. Vision, vol. 11, no. 1, pp. 25-44, 1993.
52. _, "On affine plane curve evolution," J. Functional Anal., vol. 119, no. 1, pp. 79-120, 1994.
53. B. G. Schunck, "The motion constraints equation for optical flow," in Proc. Seventh IEEE Int. Conf. Patt. Recogn., 1984, pp. 20-22.
54. J. A. Sethian, "An analysis of flame propagation," Ph.D. Dissertation, Univ. of California, Berkeley, June 1982.
55. _, "Curvature and the evolution of fronts," Commun. Math. Phys., 101, pp. 487-499, 1985.
56. _, "A review of recent numerical algorithms for hypersurfaces moving with curvature dependent speed," J. Diff. Geom., vol. 31, pp. 131-161, 1989.
57. J. A. Sethian and J. Strain, "Crystal growth and dendritic solidification," J. Computat. Phys., vol. 98, 1992.
58. M. Spivak, A Comprehensive Introduction to Differential Geometry. Berkeley, CA: Publish or Perish, 1979.
59. O. Tretiak and L. Pastor, "Velocity estimation from image sequences with second order differential operators," in Proc. Seventh IEEE Int. Conf. Patt. Recogn., 1984, pp. 16-29, 1984.
60. A. Verri and T. Poggio, "Motion field and optical flow: Qualitative properties," IEEE Trans. Patt. Anal. Machine Intell., vol. 11, pp. 490-498, 1989.
61. B. White, "Some recent developments in differential geometry," Math. Intelligencer, vol. 11, pp. 41-47, 1989.
62. A. P. Witkin, "Scale-space filtering," in Int. Joint. Conf. Artificial Intell., 1983, pp. 1019-1021.
63. R. J. Woodham, "Multiple light source optical flow," in Proc. Third IEEE Int. Conf. Comput. Vision (ICCV), Osaka, Japan, Dec. 1990, pp. 42-46.