Experiments in Fluids

, Volume 42, Issue 1, pp 61–78 | Cite as

Optical Stokes flow estimation: an imaging-based control approach

Research Article


We present an approach to particle image velocimetry based on optical flow estimation subject to physical constraints. Admissible flow fields are restricted to vector fields satifying the Stokes equation. The latter equation includes control variables that allow to control the optical flow so as to fit to the apparent velocities of particles in a given image pair. We show that when the real unknown flow observed through image measurements conforms to the physical assumption underlying the Stokes equation, the control variables allow for a physical interpretation in terms of pressure distribution and forces acting on the fluid. Although this physical interpretation is lost if the assumptions do not hold, our approach still allows for reliably estimating more general and highly non-rigid flows from image pairs and is able to outperform cross-correlation based techniques.



The authors thank Johan Carlier (Cemagref) for providing the turbulent image pairs and Rainer Hain (TU Braunschweig) for providing the cross-correlation estimates. Support by the Deutsche Forschungsgemeinschaft (DFG, SCHN 457/6) within the priority programme “Bildgebende Messverfahren in der Strömungsmechanik” (www.spp1147.tu-berlin.de) and by the EU project “Fluid Image Analysis and Description” (http://www.//fluid.irisa.fr/) is gratefully acknowledged.


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer ScienceUniversity of MannheimMannheimGermany

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