PIV Challenge 2003

1
Worldwide PIV Challenge 2003 German Aerospace
Center (DLR)
Busan, Korea September 19-20, 2003
www.pivchallenge.org
Image distortion PIV based on B-Splines
) or YAPA Yet Another PIV Algorithm
Chris WillertInstitute of Propulsion Technology,
DLR, 51170 Köln, Germany
Algorithm
Overview
AbstractThe algorithm used by DLR for the
PIV-Challenge is a combination of pyramid-based
grid refinement (multi-grid, see e.g. Willert,
1997) and full-field image deformation which is
intended to give second-order accurate
displacement data. At its core a standard
FFT-based correlation algorithm provides local
image shift data. Special emphasis was placed on
striking a balance between accuracy, robustness
and processing speed. The specific
characteristics of this algorithm, whose
flowchart is shown on the right, will be given in
the following sections. Image Pre-Processing The
images from Cases A and C both benefit from image
enhancement prior to correlation processing.
High-pass filtering and/or dynamic histogram
equalization reduce background noise and thereby
increase correlation peak visibility. Multi-Grid-P
rocessing A typical processing pyramid may look
as follows 1st pass 96 ? 96 win, 48 ? 48
step (50 overlap) 2nd pass 64 ? 64 win, 32
? 32 step (50 overlap) 3rd pass 32 ? 32
win, 16 ? 16 step (50 overlap) 4th pass 16 ?
16 win, 8 ? 8 step (50 overlap) Final pass 16
? 16 win, 8 ? 8 step (50 overlap) One unique
feature here involves down-sampling the image
instead of using larger interrogation windows.
This down-sampling is performed by summing up the
intensities of neighboring pixels without
clipping the result that is, image intensities
are preserved at a reduced spatial resolution.
In effect small and fast interrogation windows
(typ. 32?32 px) then may be re-used throughout
the first iterations. Aside from speeding up the
processing with smaller windows the same
validation criteria (e.g. correlation peak search
area, median filtering, etc.) may be used
throughout. After validation the new displacement
data is projected onto the next finer resolution
using bilinear interpolation. For added
stability the intermediate data is smoothed with
a 3?3 kernel. To improve convergence, the
interrogation at the final resolution is once
repeated. Peak Detection Generally the three
highest correlation peaks are located from a
limited region of interest in the correlation
plane. In the final processing passes, a
Levenberg-Marquardt nonlinear least-squares fit
to the correlation peak is performed for
sub-pixel peak location using 7?7 values. The
procedure is described by Ronneberger et al.
(1998).
Image Samples
Grid RefinementPyramid
Processing Flow Chart
(taken from Case Bnear bottom edge)
Start
64?64
32?32
16?16
16?16 (Final Pass)
64 pixels
Note that images are shifted toward each other
using half the displacement for each.
2
How to increase speed
Image interpolation
After each interrogation pass the displacement
data is used to deform the image data by applying
half the local shift to each image in opposite
directions. Bi-linear interpolation is used to
sample the displacement data which gives room for
further improvement.Unique here is the use of
B-splines (B basis or basic) for the
interpolation of the displaced images which was
found to give superior performance with respect
to polynomial or cardinal sinc interpolation. One
side effect in high gradient particle image data
is that the interpolated image may take on
negative values or overshoot (ringing). The
effect increases for under-sampled images.

• apply image deformation to entire image rather
  than to each interrogation window
• delay precision peak detection until final pass
• detect only strongest correlation peak during
  initial passes
• limit correlation peak search area
• delay image deformation until final pass
• image down-sampling to reduce correlation window
  size
• employ dimensional separability of many image
  operations (use 2? 1-D in place of 2-D)
• use FFTs whenever possible
• take advantage of Fourier transform symmetry
  properties (i.e. real-to-complex FFTs)
• re-use spline coefficients (e.g. need only be
  calculated once for original images)
• use bilinear image interpolation for intermediate
  passes
• (choose a processing platform with large CPU
  cache and fast memory access as full frame image
  deformation is more memory intensive than
  localized image deformation)

Interpolation function shapessolid line cubic
B-Splinedotted linear interpolator
Generalized interpolation(ßn(x) synthesis
function)For linear interpolation c(k) image
samplesand For cubic B-spline
Equivalent interpolant of cubic B-spline
Note Here c(k) are coefficients, not image
samples! These are calculated a-proiri for the
original images using a forward-backward
recursive filter which requires 2 additions and 2
multiplications per coefficient (e.g. fast
computation).(Thévenanz et al., 2002)
Non-separable 2-D interpolation using 5?5 points
(25 function evaluations)
Separable 2-D interpolation using 5?5 points
(2?510 function evaluations)
(Figures in part from Thévenaz et al., 2000)
Conclusions

• Improvement possibilities / open issues
• The potentials of B-splines for PIV processing
  have not yet been fully exploited.
• Further work may include
• improved displacement field interpolation schemes
  during the image distortion steps
• use of B-splines to artificially increase image
  resolution (Fincham Delerce, 2000)
• quantify the performance of the different image
  interpolation schemes. (It was observed that a
  5th order B-spline sometimes produced noisier
  results than a 3rd order B-spline)
• improved intermediate data validation (to
  increase robustness to image quality)

Processing of all three data sets was performed
with the same algorithm with slight variations in
image pre-processing, peak-detection ROI and
validation parameters. The results provided for
the PIV-Challenge were intended to strike an
optimum between high-spatial resolution and high
validation rates on the one hand, and reasonable
noise levels and processing speed on the other. A
higher spatial resolution would have been
possible but at the cost of increased noise.
Alternatively, the noise could have been further
reduced through massively over-sampled PIV
interrogation which significantly increases
processing times. Finally, image interpolation
based on B-splines was found outperform
traditional techniques (i.e. polynominal or
sinc-based interpolation) both in terms of speed
and precision.
References
Acknowledgments
1 C. Willert (1997), Stereoscopic digital PIV
for application in wind tunnel flows,
Measurement Science and Technology, vol. 8, pp.
1465-1479. 2 O. Ronneberger, M. Raffel, J.
Kompenhans (1998), Advanced evaluation
algorithms for standard and dual plane PIV,
Proc. 9th Intl. Symp. on Appl. of Laser
Techniques to Fluid Mechanics, Lisbon, Pt, July
13-16. 3 P. Thévenaz, T. Blu, M. Unser (2000),
Interpolation revisited, IEEE Transaction on
Medical Imaging, vol. 19, no. 7, pp.
739-758. 4 A. Fincham, G. Delerce (2000),
Advanced optimization of correlation imaging
velocimetry algorithms, Experiments in Fluids,
vol. 29, no. 7, pp. S13-S22.
The PIV-Challenge image data sets were entirely
processed with the PIVview software package
(PIVTEC GmbH, Germany). PIVTEC is a DLR
out-sourcing enterprise founded in 2001 and is
dedicated to making PIV-related developments of
DLR commercially available. A demo version of
PIVview may be downloaded from www.pivtec.com
Göttingen Germany