Experiments in Fluids

, Volume 38, Issue 2, pp 233–243

Analysis of interpolation schemes for image deformation methods in PIV

Original

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.

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

List of symbols

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

Superscript

k

iteration counter, dimensionless

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.University of Naples Federico II, DETECNaplesItaly

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