PARTICLE IMAGE VELOCIMETRY

Georges QUÉNOT, Jaroslaw PAKLEZA, Tomasz A. KOWALEWSKI*,

Object: This project takes place inside an inter-department (MECA/ DT - CHM/ IMM) cooperation and also involves the Center of Mechanics of the Polish Academy of Sciences (IPPT PAN). Its goal is to explore the possibility to use an optical flow technique for Particle Image Velocimetry (PIV, which consist in measuring quantitatively velocities inside fluid flows through direct observation of tracer particles. The optical flow method offers new approach to analyze flow images. It largely improves spatial accuracy and minimizes number of spurious vectors. Application of the method may help in quantitative analyses of several challenging problems of fluid mechanics as well as in full plane validation of their numerical counterparts.

Description: Optical flow computation consists in extracting a dense velocity field from an image sequence assuming that intensity (or color) is conserved during displacement. Several techniques have been developed for the computation of optical flow. In a survey and a comparative performance study, Barron, Fleet and Beauchemin classify them in four categories: differential, correlation based, energy based, and phase based. Not all of them are well suited for the PIV problem. Many of them require long image sequence that are not easily available experimentally and/or do not perform very well on the particle image texture (especially multi-resolution methods). We chose an Optical Flow Computation technique based on the use of dynamic programming [1]. Compared with other optical flow approaches or to classical correlation based PIV, it has the following advantages:

It can be used with sequence of several images,
It performs a global image match by propagating continuity and regularity constraints. This helps in ambiguous or low particle density regions,
Local correlation is iteratively searched on regions whose shape is modified by the flow instead of being searched on rigid blocks. This greatly improves the accuracy in regions with strong velocity gradient,
It is able to operate on multiband images.

Results and Prospects: An optical flow computation technique based on the use of Dynamic Programming has been successfully applied to Particle Image Velocimetry yielding a significant increase in the accuracy and spatial resolution of the velocity field [2]. Results have been obtained for calibrated synthetic sequences and for real sequences from a liquid freezing experiment. The average accuracy is below 0.5 pixel/frame for two-image sequences and below 0.2 pixel/frame for four-image sequences even with a 10% noise level and a 10% rate of appearance and disappearance of particles. A velocity vector is obtained for every pixel of the image. Figure 1 (postscript, 1968667 bytes) shows the obtained velocity field from a couple of particle images. Though calculation time is rather long (comparing with classical PIV), the high accuracy and high spatial resolution of Optical Flow PIV allows to use it for code validations. All the sequences used, along with an evaluation procedure for PIV techniques on them, have been installed on the laboratory server. They are available at the address: ftp://ftp.limsi.fr/pub/quenot/opflow/testdata/
Future work will be conducted in three directions:

Better characterization of the result quality: statistical estimation of the accuracy of the velocity field from the particle density (or texture), the smoothness of the extracted field and the reconstruction error.
Improvement of measure process: optimal choice of average velocity value (through time interval between images) and the particle density to minimize the relative error.
Direct search for three-dimensional velocity field for which Dynamic Programming based Optical Flow search is very well suited.

References:
[1] Georges M. Quénot, Computation of Optical Flow Using Dynamic Programming [1536721 bytes], IAPR Workshop on Machine Vision Applications, Tokyo, Japan, 12-14 nov 1996. Abstract.
[2] Georges M. Quénot, Jaroslaw Pakleza and Tomasz A. Kowalewski, Particle Image Velocimetry with Optical Flow, To appear in Experiments in fluids. Abstract.

* Polish Academy of Sciences, Center of Mechanics.