Experiments in Fluids

, Volume 38, Issue 4, pp 511–515 | Cite as

Two-dimensional Gaussian regression for sub-pixel displacement estimation in particle image velocimetry or particle position estimation in particle tracking velocimetry



An explicit solution of two-dimensional Gaussian regression for the estimation of particle displacement from the correlation function in particle image velocimetry (PIV) or particle position from the images in particle tracking velocimetry (PTV) with sub-pixel accuracy is introduced. The accuracy and the ability of the methods to avoid pixel locking due to non-axially orientated, elliptically shaped particle images or correlation peaks are investigated using simulated and experimentally obtained images.



The financial support of the Deutsche Forschungsgemeinschaft under grant Tr 194/21 and of the Finnish National Technology Agency, TEKES are gratefully acknowledged.


  1. Adrian RJ, Yao CS (1985) Pulsed laser technique application to liquid and gaseous flows and the scattering power of seed materials. Appl Opt 24(1):44–52Google Scholar
  2. Alexander BF, Ng KC (1991) Elimination of systematic error in sub-pixel accuracy centroid estimation. Opt Eng 30:1320–1331Google Scholar
  3. Huang H, Dabiri D, Gharib M (1997) On error of digital particle image velocimetry. Meas Sci Technol 8:1427–1440Google Scholar
  4. Keane RD, Adrian RJ (1992) Theory of cross-correlation analysis of PIV images. Appl Sci Res 49:191–215Google Scholar
  5. Lindken R, Merzkirch W (2002) A novel PIV technique for measurements in multiphase flows and its application to two-phase bubbly flows. Exp Fluids 33:814–825Google Scholar
  6. Lourenco I, Krothapalli A (1995) On the accuracy of velocity and vorticity measurements with PIV. Exp Fluids 18:421–428Google Scholar
  7. Marxen M, Sullivan PE, Loewen MR, Jähne B (2000) Comparison of Gaussian particle center estimators and the achievable measurement density for particle tracking velocimetry. Exp Fluids 29:145–153Google Scholar
  8. Morgan JS, Slater DC, Timothy JG, Jenkins EB (1989) Centroid position measurements and subpixel sensitivity variations with the MAMA detector. Appl Opt 28(6):1178–1192Google Scholar
  9. Nobach H, Damaschke N, Tropea C (2004) High-precision sub-pixel interpolation in PIV/PTV image processing. In: Proceedings of the 12th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, July 2004, paper 24.1Google Scholar
  10. Prasad AK, Adrian RJ, Landreth CC, Offutt PW (1992) Effect of resolution on the speed and accuracy of particle image velocimetry interrogation. Exp Fluids 13:105–116Google Scholar
  11. Roesgen T (2003) Optimal subpixel interpolation in particle image velocimetry. Exp Fluids 35:252–256Google Scholar
  12. Ronneberger O, Raffel M, Kompenhans J (1998) Advanced evaluation algorithms for standard and dual plane particle image velocimetry. In: Proceedings of the 9th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, July 1998, paper 10.1Google Scholar
  13. Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8:1379–1392Google Scholar
  14. Willert C (1996) The fully digital evaluation of photographic PIV recordings. Appl Sci Res 56(2–3):79–102Google Scholar
  15. Willert CE, Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10:181–193Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Fachgebiet Strömungslehre und AerodynamikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Energy and Process EngineeringTampere University of TechnologyTampereFinland

Personalised recommendations