Nonlinear Variational Method for Optical Flow Computation

We present a new method for optical flow computation based on the minimization of a non-quadratic functional. The solution of the obtained nonlinear differential equations is done with a time dependent approach leading to the successive solutions of linear systems. This new method allows to compute optical flow fields while insuring a unique solution and preserving the flow discontinuities. This method seems to be more appropriate since it does not enforce the optical flow to be smooth in the boundaries of moving objects and reconstruct the optical flow discontinuities without any specific processing of these points. We have applied the model on synthetical and real image sequences which illustrate the properties of this approach. Finally we give an interesting application which merges optical flow field and snake models for boundaries tracking.

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

[2]  R. Glowinski.  Lectures on Numerical Methods for Non-Linear Variational Problems , 1981 .

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

[4]  J. W. Eastwood,et al.  Springer series in computational physics Editors: H. Cabannes, M. Holt, H.B. Keller, J. Killeen and S.A. Orszag , 1984 .

[5]  B. G. Schunck.  The image flow constraint equation , 1986 .

[6]  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.

[7]  Janet Aisbett,et al.  Optical Flow with an Intensity-Weighted Smoothing , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Laurent D. Cohen,et al.  A finite element method applied to new active contour models and 3D reconstruction from cross sections , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[9]  Joachim Dengler,et al.  Estimation of discontinuous displacement vector fields with the minimum description length criterion , 1990, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[10]  Michael J. Black,et al.  Robust dynamic motion estimation over time , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

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

[12]  ISAAC COHEN,et al.  Using deformable surfaces to segment 3-D images and infer differential structures , 1992, CVGIP Image Underst..

[13]  Nicholas Ayache,et al.  Features extraction and analysis methods for sequences of ultrasound Images , 1992, Image Vis. Comput..

[14]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[15]  David J. Fleet,et al.  Performance of optical flow techniques , 1994, International Journal of Computer Vision.