Experiments in Fluids

, Volume 44, Issue 2, pp 291–304 | Cite as

Variational second order flow estimation for PIV sequences

  • L. AlvarezEmail author
  • C. A. Castaño
  • M. García
  • K. Krissian
  • L. Mazorra
  • A. Salgado
  • J. Sánchez
Research Article


We present in this paper a variational approach to accurately estimate simultaneously the velocity field and its derivatives directly from PIV image sequences. Our method differs from other techniques that have been presented in the literature in the fact that the energy minimization used to estimate the particles motion depends on a second order Taylor development of the flow. In this way, we are not only able to compute the motion vector field, but we also obtain an accurate estimation of their derivatives. Hence, we avoid the use of numerical schemes to compute the derivatives from the estimated flow that usually yield to numerical amplification of the inherent uncertainty on the estimated flow. The performance of our approach is illustrated with the estimation of the motion vector field and the vorticity on both synthetic and real PIV datasets.


Vorticity Particle Image Velocimetry Particle Image Velocimetry Image Motion Vector Field Average Angular Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work has been funded by the European Commission under the Specific Targeted Research Project FLUID (contract no. FP6-513663). We acknowledge the Research Institute CEMAGREF (Rennes, France) for providing to us the synthetic PIV image and the real PIV sequence we have used in the experiments.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • L. Alvarez
    • 1
    Email author
  • C. A. Castaño
    • 1
  • M. García
    • 1
  • K. Krissian
    • 1
  • L. Mazorra
    • 1
  • A. Salgado
    • 1
  • J. Sánchez
    • 1
  1. 1.Departamento de Informática y SistemasUniversidad de Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain

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