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 shapes:solid 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 55 points (25 function evaluations)

Separable 2-D interpolation using 55 points (25=10 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.

Acknowledgments

References

[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