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Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution

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Abstract

As testified by a previous article (Astarita and Cardone in Exp Fluids 38:233–243, 2005), a critical point that can influence significantly the accuracy of image deformation methods (IDM) for particle image velocimetry (PIV) is the interpolation scheme (IS) used in the reconstruction of deformed images. In the cited paper the effect of noise has been neglected and for this reason in this follow-up paper the influence of the IS, in the presence of noise, on both accuracy and spatial resolution is studied. Performance assessment is conducted using synthetic images with particles of Gaussian shape and with constant and sinusoidal displacement fields. Both the local and the top hat moving average approaches are investigated and the modulation transfer function, the total and bias errors have been used to evaluate the performances of IDMs for PIV applications. The results show that, when a high noise level is present in the images, the influence of the IS is less relevant than what was shown by Astarita and Cardone (Exp Fluids 38:233–243, 2005).

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Abbreviations

BSPLM :

Interpolation scheme based on the B-spline of order M

FFT:

Fast Fourier transform

IDM:

Image deformation method

IDWO:

Iterative discrete window offset

IS:

Interpolation scheme

MTF:

Modulation transfer function

PIV:

Particle image velocimetry

THMA:

Top hat moving average

a :

modulation factor associated to the predictor displacement field, dimensionless

a k :

modulation factor at iteration k, dimensionless

b :

modulation factor associated with steps 2 and 5 of the algorithm, dimensionless

D :

particle diameter, pixels

f :

grey intensity of the first image, dimensionless

g :

grey intensity of the second image, dimensionless

i :

horizontal image coordinate (integer value), pixels

j :

vertical image coordinate (integer value), pixels

k :

iteration number, dimensionless

l :

horizontal shift, pixels

m :

vertical shift, pixels

n :

random noise level, dimensionless

N :

number of measurement points, dimensionless

p :

percentage of lost particles, dimensionless

r :

displacement field, pixels

r c :

corrector displacement field, pixels

r i :

interpolated predictor displacement field, pixels

r w :

displacement field averaged over the interrogation window, pixels

\(\ifmmode\expandafter\bar\else\expandafter\=\fi{u}\) :

mean measured displacement, pixels

u :

imposed displacement, pixels

u i :

local measured displacement, pixels

U :

amplitude of the sinusoidal displacement field, pixels

w :

weighting function, dimensionless

W :

interrogation window linear dimension, pixels

x :

horizontal image coordinate, pixels

y :

vertical image coordinate, pixels

β :

bias error, pixels

\(\ifmmode\expandafter\bar\else\expandafter\=\fi{\delta }\) :

mean total error, pixels

δ :

total error, pixels

δ n :

total error associated to a random noise equal to n, pixels

δ e n :

estimated total error associated to a random noise equal to n, pixels

λ :

spatial wavelength, pixels

μ :

mean operator

φ lm :

cross-correlation coefficient, dimensionless

ω :

normalised spatial frequency (W/λ), dimensionless

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  1. University of Naples Federico II, DETEC, P.le Tecchio 80, 80125, Naples, Italy

    T. Astarita

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  1. T. Astarita
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Astarita, T. Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution. Exp Fluids 40, 977–987 (2006). https://doi.org/10.1007/s00348-006-0139-4

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  • DOI: https://doi.org/10.1007/s00348-006-0139-4

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