Experiments in Fluids

, Volume 40, Issue 6, pp 977–987 | Cite as

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

  • T. Astarita
Research Article


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).


Particle Image Velocimetry Total Error Modulation Transfer Function Interpolation Scheme Local Approach 
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


Image deformation method


Iterative discrete window offset


Interpolation scheme


Modulation transfer function


Particle image velocimetry


Top hat moving average

List of symbols


modulation factor associated to the predictor displacement field, dimensionless


modulation factor at iteration k, dimensionless


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


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


iteration number, dimensionless


horizontal shift, pixels


vertical shift, pixels


random noise level, dimensionless


number of measurement points, dimensionless


percentage of lost particles, dimensionless


displacement field, pixels


corrector displacement field, pixels


interpolated predictor displacement field, pixels


displacement field averaged over the interrogation window, pixels


mean measured displacement, pixels


imposed displacement, pixels


local measured displacement, pixels


amplitude of the sinusoidal displacement field, pixels


weighting function, dimensionless


interrogation window linear dimension, pixels


horizontal image coordinate, pixels


vertical image coordinate, pixels


bias error, pixels

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

mean total error, pixels


total error, pixels


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


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


spatial wavelength, pixels


mean operator


cross-correlation coefficient, dimensionless


normalised spatial frequency (W/λ), dimensionless


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.University of Naples Federico II, DETECNaplesItaly

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