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Experiments in Fluids

, Volume 45, Issue 2, pp 257–266 | Cite as

Analysis of velocity interpolation schemes for image deformation methods in PIV

  • T. Astarita
Research Article

Abstract

The spatial resolution of PIV can be increased significantly by using an image deformation method (IDM) and very small grid distance (i.e. the final distance between vectors), therefore, also increasing the processing time. By using an interpolation scheme with a good spectral response, in the dense predictor step of the algorithm, it is possible to increase the grid distance without decreasing the spatial resolution therefore decreasing the total processing time.

Keywords

Modulation Transfer Function Interpolation Scheme Interrogation Window Total Processing Time Dense Predictor 
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.

Abbreviations

FFT

Fast Fourier transform

IDM

Image deformation method

IS

Interpolation scheme

MTF

Modulation transfer function

PIV

Particle image velocimetry

WW

Weighting window

List of symbols

a

modulation factor associated to the correlation step of the algorithm, dimensionless

b

modulation factor associated to the weighted average step of the algorithm, dimensionless

c

modulation factor associated to the dense predictor step of the algorithm, dimensionless

E21

power spectra, pixels2

k

iteration number, dimensionless

mk

modulation factor at iteration k, dimensionless

n

random noise level, dimensionless

N

number of measurement points, dimensionless

r

displacement field, pixels

rc

corrector displacement field, pixels

rp

dense predictor displacement field, pixels

rk

displacement field at iteration k, pixels

\( \overline{{\varvec{r}^{{k - 1}}_{p} }} \)

weighted average of the dense predictor displacement field, pixels

te

percentage time needed to perform the dense predictor step, dimensionless

v

vertical displacement, pixels

vi

local measured displacement, pixels

Wa

interrogation window linear dimension, pixels

Wb

linear dimension of the weighting window used in the weighted average step of the algorithm, pixels

Wc

grid distance, pixels

x

horizontal image coordinate, pixels

y

vertical image coordinate, pixels

δ

total error, pixels

λ

spatial wavelength, pixels

ω

normalised spatial frequency (W a /λ), dimensionless

References

  1. Astarita T (2006) Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution. Exp Fluids 40:977–987CrossRefGoogle Scholar
  2. Astarita T (2007) Analysis of weighting windows for image deformation methods in PIV. Exp Fluids 43:859–872CrossRefGoogle Scholar
  3. Astarita T, Cardone G (2005) Analysis of interpolation schemes for image deformation methods in PIV. Exp Fluids 38:233–243CrossRefGoogle Scholar
  4. Blu T, Thévenaz P, Unser M (2004) Linear interpolation revitalized. IEEE Trans Image Process 13(5):710–719CrossRefMathSciNetGoogle Scholar
  5. Carlomagno GM, Nese FG, Cardone G , Astarita T (2004) Thermo-fluid-dynamics of a complex fluid flow. Infrared Phys Technol 46:31–39CrossRefGoogle Scholar
  6. Huang HT, Fiedler HE, Wang JJ (1993) Limitation and improvement of PIV. 2. Particle image distortion, a novel technique. Exp Fluids 15:263–273Google Scholar
  7. Jambunathan K, Ju XY, Dobbins BN, Ashforth-Frost S (1995) An improved cross correlation technique for particle image velocimetry. Meas Sci Technol 6:507–514CrossRefGoogle Scholar
  8. Kim BJ, Sung HJ (2006) A further assessment of interpolation schemes for window deformation in PIV. Exp Fluids 41:499–511CrossRefGoogle Scholar
  9. Nogueira J, Lecuona A, Rodriguez PA (1999) Local field correction PIV: on the increase of accuracy of digital PIV systems. Exp Fluids 27:107–116CrossRefGoogle Scholar
  10. Nogueira J, Lecuona A, Rodríguez PA (2005a) Limits on the resolution of correlation PIV iterative methods. Fundamentals. Exp Fluids 39:305–313CrossRefGoogle Scholar
  11. Nogueira J, Lecuona A, Rodríguez PA, Alfaro JA, Acosta A (2005b) Limits on the resolution of correlation PIV iterative methods. Practical implementation and design of weighting functions. Exp Fluids 39:314–321CrossRefGoogle Scholar
  12. Scarano F (2002) Iterative image deformation methods in PIV. Meas Sci Technol 13:R1–R19CrossRefGoogle Scholar
  13. Scarano F, Schrijer FFJ (2005) Effect of predictor filtering on the stability and spatial resolution of iterative PIV interrogation. In: Proceedings of the 6th international symposium on particle image velocimetry, Pasadena, CaliforniaGoogle Scholar
  14. Stanislas M, Okamoto K, Kähler C (2003) Main results of the first international PIV Challenge2003. Meas Sci Technol 14:R63–R89CrossRefGoogle Scholar
  15. Stanislas M, Okamoto K, Kähler CJ, Westerweel J (2005), Main results of the second international PIV challenge. Exp Fluids 39:170–191CrossRefGoogle Scholar
  16. Unser M (1999), Splines: a perfect fit for signal and image processing. IEEE Signal Process Mag 16(6):22–38CrossRefGoogle Scholar
  17. Utami T, Blackwelder RF, Ueno T (1991) A cross-correlation technique for velocity field extraction from particulate visualization. Exp Fluids 10:213–223CrossRefGoogle Scholar
  18. Westerweel J, Scarano F (2005) Universal outlier detection for PIV data. Exp Fluids 39:1096–1100CrossRefGoogle Scholar
  19. Willert CE, Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10:181–193CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.University of Naples Federico IINaplesItaly

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