Optical flow: a curve evolution approach

A novel approach for the computation of optical flow based on an L (1) type minimization is presented. It is shown that the approach has inherent advantages since it does not smooth the flow-velocity across the edges and hence preserves edge information. A numerical approach based on computation of evolving curves is proposed for computing the optical flow field. Computations are carried out on a number of real image sequences in order to illustrate the theory as well as the numerical approach.

[1]  Steven Haker,et al.  Stereo Disparity and L1 Minimization , 1997 .

[2]  H. C. Longuet-Higgins,et al.  The interpretation of a moving retinal image , 1980, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[3]  Tomaso Poggio,et al.  Computational vision and regularization theory , 1985, Nature.

[4]  J. Sethian,et al.  Crystal growth and dendritic solidification , 1992 .

[5]  S. Zucker,et al.  Toward a computational theory of shape: an overview , 1990, eccv 1990.

[6]  M. Grayson Shortening embedded curves , 1989 .

[7]  Ellen C. Hildreth,et al.  Computations Underlying the Measurement of Visual Motion , 1984, Artif. Intell..

[8]  J. Sethian Curvature and the evolution of fronts , 1985 .

[9]  Andrew P. Witkin,et al.  Scale-space filtering: A new approach to multi-scale description , 1984, ICASSP.

[10]  G. Sapiro,et al.  On affine plane curve evolution , 1994 .

[11]  Robert J. Woodham Multiple light source optical flow , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[12]  J. B. Rosen The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints , 1960 .

[13]  Allen Tannenbaum,et al.  Stereo disparity and L/sup 1/ minimization , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[14]  Brian White,et al.  Some recent developments in differential geometry , 1989 .

[15]  M. Grayson The heat equation shrinks embedded plane curves to round points , 1987 .

[16]  J. Sethian AN ANALYSIS OF FLAME PROPAGATION , 1982 .

[17]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

[18]  Vishal Markandey,et al.  Multispectral constraints for optical flow computation , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[19]  Nicolai V. Krylov,et al.  Nonlinear Elliptic and Parabolic Equations of the Second Order Equations , 1987 .

[20]  Farzin Mokhtarian,et al.  A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[21]  M. Gage,et al.  The Curve Shortening Flow , 1987 .

[22]  M. Gage,et al.  The heat equation shrinking convex plane curves , 1986 .

[23]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[24]  Yuan-Fang Wang,et al.  Experiments in computing optical flow with the gradient-based, multiconstraint method , 1987, Pattern Recognit..

[25]  J. Sethian Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws , 1990 .

[26]  Jorge L. C. Sanz,et al.  Optical flow computation using extended constraints , 1996, IEEE Trans. Image Process..

[27]  W. Clem Karl,et al.  Efficient multiscale regularization with applications to the computation of optical flow , 1994, IEEE Trans. Image Process..

[28]  Guillermo Sapiro,et al.  Area and Length Preserving Geometric Invariant Scale-Spaces , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[29]  U. Abresch,et al.  The normalized curve shortening flow and homothetic solutions , 1986 .

[30]  J. B. Rosen The gradient projection method for nonlinear programming: Part II , 1961 .

[31]  Benjamin B. Kimia,et al.  On the evolution of curves via a function of curvature , 1992 .

[32]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[33]  Ramesh C. Jain,et al.  On the Analysis of Accumulative Difference Pictures from Image Sequences of Real World Scenes , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[34]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[35]  Hans-Hellmut Nagel,et al.  An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[36]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[37]  Tomaso A. Poggio,et al.  Motion Field and Optical Flow: Qualitative Properties , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[38]  V. Caselles,et al.  A geometric model for active contours in image processing , 1993 .

[39]  K. Prazdny,et al.  On the information in optical flows , 1983, Comput. Vis. Graph. Image Process..

[40]  C. Cafforio,et al.  Tracking moving objects in television images , 1979 .

[41]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[42]  David J. Fleet,et al.  Performance of optical flow techniques , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[43]  M. Spivak A comprehensive introduction to differential geometry , 1979 .

[44]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[45]  L. Evans,et al.  Motion of level sets by mean curvature. II , 1992 .

[46]  B KimiaBenjamin,et al.  Shapes, shocks, and deformations I , 1995 .

[47]  Jake K. Aggarwal,et al.  Segmentation through the detection of changes due to motion , 1979 .

[48]  S. Angenent Parabolic equations for curves on surfaces Part I. Curves with $p$-integrable curvature , 1990 .

[49]  S. Angenent Parabolic equations for curves on surfaces Part II. Intersections, blow-up and generalized solutions , 1991 .

[50]  Alessandro Verri,et al.  Computing optical flow from an overconstrained system of linear algebraic equations , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[51]  Eric Dubois,et al.  Multigrid Bayesian Estimation Of Image Motion Using Stochastic Relaxation , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[52]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[53]  Lawrence C. Evans Estimates for smooth absolutely minimizing Lipschitz extensions. , 1993 .