Advances in iterative multigrid PIV image processing
F. Scarano, M. L. Riethmuller
Abstract An image-processing technique is proposed,
which performs iterative interrogation of particle image
velocimetry (PIV) recordings. The method is based on
cross-correlation, enhancing the matching performances
by means of a relative transformation between the in-
terrogation areas. On the basis of an iterative prediction
of the tracers motion, window offset and deformation
are applied, accounting for the local deformation of the
¯uid continuum. In addition, progressive grid re®ne-
ment is applied in order to maximise the spatial reso-
lution. The performances of the method are analysed
and compared with the conventional cross correlation
with and without the effect of a window discrete offset.
The assessment of performance through synthetic PIV
images shows that a remarkable improvement can be
obtained in terms of precision and dynamic range.
Moreover, peak-locking effects do not affect the method
in practice. The velocity gradient range accessed with the
application of a relative window deformation (linear
approximation) is signi®cantly enlarged, as con®rmed in
the experimental results.
The application of digital analysis to particle image
velocimetry (PIV) (Willert and Gharib1991) shows an
increasing number of successful investigations in this
decade. As a consequence, the interest from the user
community in investigating challenging ¯ows stimulates
theoretical studies to gain a deeper understanding of the
A literature survey yields a considerable number of
studies related to the image analysis methods with the
cross correlation, which provide a mathematical back-
ground for evaluating the performances and establishing
some limitations of this matching operator (Adrian et al.
1991; Westerweel 1993). Furthermore, several works based
on the analysis of synthetic images (Monte Carlo simula-
tions) of particle tracers associated to reference ¯ow ®elds
represent a numerical approach to study the interrogation
performances (Willert and Gharib1991; Fincham and
Spedding 1997; Huang et al. 1997; Raffel et al. 1998 and
The investigation focuses upon the measurable velocity
u and velocity gradient
ru ranges, the spatial resolution
Dr and the con®dence level of the technique.
A general agreement is observed concerning the fol-
lowing arguments related to conventional cross-correla-
1. The velocity dynamic range is in con¯ict with the spa-
tial resolution due to the in-plane out of pattern motion,
leading to loss-of-pairs (Adrian 1991).
2. A velocity underestimate occurs due to the ®nite extent
of the interrogation windows, resulting into a trade-off
between accuracy and spatial resolution.
3. The fractional displacement estimate is affected by a
bias error with a periodic pattern of one pixel wave-
length causing a measurement bias towards integer
values (peak locking).
4. The correlation signal/noise ratio decreases in high
gradient regions. A discontinuous response is observed
in some cases, which introduces a severe corruption of
The remainder of the work discusses the above prob-
lems, analysing the main sources of error, and proposes a
strategy to solve or compensate for such effects.
The idea of image deformation is not new in the ®eld of
image processing and in problems of visual motion anal-
ysis, more speci®cally, in the applications concerning
seeded ¯uid ¯ows and ®nally in PIV.
Huang et al. (1993a) propose the particle image
distortion (PID) technique as intended to improve the
robustness and the accuracy of conventional cross-
correlation analysis with respect to ¯ows with high velocity
gradients. The method is based on the iterative application
of cross-correlation analysis on ®xed-size windows, when
the images are deformed. The process starts with a con-
ventional cross-correlation interrogation and terminates
when a convergence criterion is satis®ed. The results of
each interrogation step are validated, ®ltered and used to
shift and deform the two images to compensate for the
signal loss due to out-of-pattern motion. From this work,
it appears that the PID technique allows access to larger
Experiments in Fluids [Suppl.] S51±S60 Ó Springer-Verlag 2000
F. Scarano (&)
, M. L. Riethmuller
Department of Environmental and Applied Fluid Dynamics
n Institute for Fluid Dynamics
72 ch. de Waterloo, 1640 Rhode-Saint Gene
Department of Aerospace Engineering
Delft University of Technology
Kluyverweg 1, 2629 HS Delft, The Netherlands
This research was supported by the European Commission
through the Marie Curie research and training program (contract
no. ERBFMBICT 983141).