International Journal of Computer Vision

, Volume 39, Issue 1, pp 41–56 | Cite as

Reliable Estimation of Dense Optical Flow Fields with Large Displacements

  • Luis Alvarez
  • Joachim Weickert
  • Javier Sánchez


In this paper we show that a classic optical flow technique by Nagel and Enkelmann (1986, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 8, pp. 565–593) can be regarded as an early anisotropic diffusion method with a diffusion tensor. We introduce three improvements into the model formulation that (i) avoid inconsistencies caused by centering the brightness term and the smoothness term in different images, (ii) use a linear scale-space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima, and (iii) create an energy functional that is invariant under linear brightness changes. Applying a gradient descent method to the resulting energy functional leads to a system of diffusion–reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an efficient linear implicit numerical scheme in detail. Our method creates flow fields with 100 % density over the entire image domain, it is robust under a large range of parameter variations, and it can recover displacement fields that are far beyond the typical one-pixel limits which are characteristic for many differential methods for determining optical flow. We show that it performs better than the optical flow methods with 100 % density that are evaluated by Barron et al. (1994, Int. J. Comput. Vision, Vol. 12, pp. 43–47). Our software is available from the Internet.

image sequences optical flow differential methods anisotropic diffusion linear scale-space regularization finite difference methods performance evaluation 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Luis Alvarez
    • 1
  • Joachim Weickert
    • 2
  • Javier Sánchez
    • 1
  1. 1.Departamento de Informática y SistemasUniversidad de Las PalmasLas PalmasSpain
  2. 2.Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer ScienceUniversity of MannheimMannheimGermany

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