Experiments in Fluids

, Volume 38, Issue 2, pp 233–243 | Cite as

Analysis of interpolation schemes for image deformation methods in PIV

  • T. Astarita
  • G. Cardone


Image deformation methods in particle image velocimetry are becoming more and more accepted by the scientific community but some aspects have not been thoroughly investigated neither theoretically nor with the aid of simulations. A fundamental step in this type of algorithm is reconstruction of the deformed images that requires the use of an interpolation scheme. The aim of this paper is to examine the influence of this aspect on the accuracy of the PIV algorithm. The performance assessment has been conducted using synthetic images and the results show that both the systematic and total errors are strongly influenced by the interpolation scheme used in the reconstruction of the deformed images. Time performances and the influence of particle diameter are also analysed.


Particle Image Velocimetry Total Error Interpolation Scheme Bias Error Interrogation Window 
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.



interpolation scheme based on the B-spline of order M


fast Fourier transform


interpolation scheme based on the shift theorem of the Fourier transform using M xM points


image deformation methods


iterative discrete window offset


interpolation scheme(s)


particle image distortion


particle image velocimetry


interpolation scheme based on the sinc formula using M xM points

List of symbols


particle diameter, pixels


grey intensity of the first image, dimensionless


grey intensity of the second image, dimensionless


horizontal image coordinate (integer value), pixels


vertical image coordinate (integer value), pixels


horizontal shift, pixels


vertical shift, pixels


number of measurement points, dimensionless


number of particles per interrogation window, dimensionless


displacement field, pixels

r c

corrector displacement field, pixels

r w

displacement field averaged over the interrogation window, pixels


time needed to perform deformation of the images, seconds


mean measured displacement, pixels


imposed displacement, pixels

u i

local measured displacement, pixels


interrogation window linear dimension, pixels


horizontal image coordinate, pixels


vertical image coordinate, pixels

\( \overline{\beta } \)

mean bias error, pixels


bias error, pixels

\( \overline{\sigma } \)

mean total error, pixels


total error, pixels


mean operator

ϕ lm

cross-correlation coefficient, dimensionless


random error, pixels



iteration counter, dimensionless


  1. Gui L, Wereley ST (2002) A correlation-based continuous window-shift technique to reduce the peak-locking effect in digital PIV image evaluation. Exp Fluids 32:506–517CrossRefGoogle Scholar
  2. Hart DP (2000) Super-resolution PIV by recursive local-correlation. J Visual 3(2):187–194Google Scholar
  3. Huang HT, Fiedler HE, Wang JJ (1993) Limitation and improvement of PIV, part 2. Particle image distortion, a novel technique. Exp Fluids 15:263–273Google Scholar
  4. Jambunathan K, Ju XY, Dobbins BN, Ashforth-Frost S (1995) An improved cross correlation technique for particle image velocimetry. Meas Sci Technol 6:507–514Google Scholar
  5. Keane RD, Adrian RJ (1993) Theory of cross correlation analysis of PIV images. In: Nieuwstadt FTM (ed) Flow visualization and image analysis. pp 1–25Google Scholar
  6. Lecordier B, Demare D, Vervisch LMJ, Rèveillon J, Trinitè M (2001) Estimation of the accuracy of PIV treatments for turbulent flow studies by direct numerical simulation of multi-phase flow. Meas Sci Technol 12:1382–1391Google Scholar
  7. Meunier P, Leweke T (2003) Analysis and treatment of errors due to high velocity gradients in particle image velocimetry. Exp Fluids 35:408–421Google Scholar
  8. Nogueira J, Lecuona A, Rodriguez PA (1999) Local field correction PIV: on the increase of accuracy of digital PIV systems. Exp Fluids 27:107–116Google Scholar
  9. Nogueira J, Lecuona A, Rodriguez PA (2001) Local field correction PIV, implemented by means of simple algorithms, and multigrid versions. Meas Sci Technol 12:1911–1921Google Scholar
  10. Raffel M, Willert CE, Kompenhans J (1998) Particle image velocimetry: a practical guide. Springer, Berlin Heidelberg New YorkGoogle Scholar
  11. Scarano F (2002) Iterative image deformation methods in PIV. Meas Sci Technol 13:R1–R19CrossRefGoogle Scholar
  12. Scarano F (2004) A super-resolution particle image velocimetry interrogation approach by means of velocity second derivatives correlation. Meas Sci Technol 15:475–486Google Scholar
  13. Scarano F, Riethmuller ML (1999) Iterative multigrid approach in PIV image processing with discrete window offset. Exp Fluids 26:513–523CrossRefGoogle Scholar
  14. Scarano F, Riethmuller ML (2000) Advances in iterative multigrid PIV image processing. Exp Fluids S51–S60Google Scholar
  15. Soria J (1996) An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp Therm Fluid Sci 12:221–233CrossRefGoogle Scholar
  16. Unser M (1999) Splines: a perfect fit for signal and image processing. IEEE Signal Proc Mag 16(6):22–38Google Scholar
  17. Unser M, Aldroubi A, Eden M (1993a) B-spline signal processing: part I—theory. IEEE T Signal Proces 41(2):821–832Google Scholar
  18. Unser M, Aldroubi A, Eden M (1993b) B-spline signal processing: part II—efficient design and applications. IEEE T Signal Proces 41(2):834–848Google Scholar
  19. Utami T, Blackwelder RF, Ueno T (1991) A cross-correlation technique for velocity field extraction from particulate visualization. Exp Fluids 10:213–223Google Scholar
  20. Wereley ST, Meinhart CD (2001) Second-order accurate particle image velocimetry. Exp Fluids 31:258–268CrossRefGoogle Scholar
  21. Westerweel J (1993) Digital particle image velocimetry—theory and applications. PhD Thesis, Delft University of Technology, The NetherlandsGoogle Scholar
  22. Westerweel J (2000) Theoretical analysis of the measurement precision in particle image velocimetry. Exp Fluids 29:S3–S12CrossRefGoogle Scholar
  23. Westerweel J, Dabiri D, Gharib M (1997) The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings. Exp Fluids 23:20–28CrossRefGoogle Scholar
  24. Willert CE, Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10:181–193Google Scholar
  25. Yaroslavsky LP (1996) Signal sinc-interpolation: a fast computer algorithm. Bioimaging 4:225–231Google Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.University of Naples Federico II, DETECNaplesItaly

Personalised recommendations