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Analysis of interpolation schemes for image deformation methods in PIV

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Abstract

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.

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Notes

  1. In many previous works this point is not described in detail, so it is difficult to clearly understand who was the first to propose the two approaches.

  2. Of course the time t is a function of the computer used during the simulation so it should be regarded as a relative measurement.

Abbreviations

BSPLM:

interpolation scheme based on the B-spline of order M

FFT:

fast Fourier transform

FFTM:

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

IDM:

image deformation methods

IDWO:

iterative discrete window offset

IS:

interpolation scheme(s)

PID:

particle image distortion

PIV:

particle image velocimetry

SINCM:

interpolation scheme based on the sinc formula using M xM points

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

l :

horizontal shift, pixels

m :

vertical shift, pixels

N :

number of measurement points, dimensionless

N I :

number of particles per interrogation window, dimensionless

r :

displacement field, pixels

r c :

corrector displacement field, pixels

r w :

displacement field averaged over the interrogation window, pixels

t :

time needed to perform deformation of the images, seconds

ū :

mean measured displacement, pixels

u :

imposed displacement, pixels

u i :

local measured displacement, pixels

W :

interrogation window linear dimension, pixels

x :

horizontal image coordinate, pixels

y :

vertical image coordinate, pixels

\( \overline{\beta } \) :

mean bias error, pixels

β :

bias error, pixels

\( \overline{\sigma } \) :

mean total error, pixels

δ :

total error, pixels

μ :

mean operator

ϕ lm :

cross-correlation coefficient, dimensionless

σ :

random error, pixels

k :

iteration counter, dimensionless

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

    T. Astarita & G. Cardone

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  1. T. Astarita
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  2. G. Cardone
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Correspondence to T. Astarita.

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Astarita, T., Cardone, G. Analysis of interpolation schemes for image deformation methods in PIV. Exp Fluids 38, 233–243 (2005). https://doi.org/10.1007/s00348-004-0902-3

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