Development and application of a hierarchical system for digital particle image velocimetry to free-surface turbulence

A method for particle image velocimetry (PIV) is presented which improves upon the accuracy, computational efficiency and dynamic range (i.e., the difference between the largest and smallest resolvable particle displacement vectors) of conventional PIV techniques. The technique is applied to free-surface turbulence to resolve energy spectra for motions with a wide dynamic range. The methodology-based on multi-grid image processing algorithms for rigid body motion analysis, estimates the displacement vectors at discrete particle locations. The essence of this technique is to estimate large scale motions from image intensity patterns of low spatial frequencies and small scale motions from intensity patterns of high spatial frequencies. Cross-correlation between a pair of time separated particle images is implemented by the hierarchical computational scheme of Burt ["Fast filter transforms for image processing," Int. J. Comput. Vision 16, 20 (1981)]. Each image is convolved with a series of band-pass filters and subsampled to obtain a set of images progressively decreasing in resolution and size. A coarse estimate of the displacement field obtained from pairs of lower resolution images are used to obtain more accurate estimates at the next (finer) level. Processing starts at the level of lowest resolution and stops at the highest resolution level, which contains the original image pair. Due to subsampling of low resolution images, the match template size can be kept constant for all stages of computation, thus eliminating the dependence of the largest resolvable displacement on the size of match template. In the present work, the search area at each level is kept constant at 3 X 3 pixels and the match template size at 5 X 5 pixels for all levels of computation. The algorithm has been implemented using simple thresholding based on the confidence level of an estimated displacement vector, as suggested by Anandan ["A computational framework and an algorithm for measurement of visual motion," Int. J. Comput. Vision, 2, 283, (1987)]. However, the confidence-level-based smoothing technique for rigid body motions (continuous velocity fields) could not be applied to displacement estimates obtained at discrete points i.e., the particle locations. Instead, smoothing was performed over the area covered by each particle. The algorithm has been tested against direct numerical simulations of turbulent flows when the flow field is known and particle images have been generated from these with the addition of noise. Both the accuracy of motion estimation and the computation time are seen to improve as compared to conventional PIV methods. Finally, video images taken of particle motion on the free-surface of a channel flow have been used to determine the capabilities of the technique in an experimental study. The resulting spectra show a quasi-two-dimensional character of the free-surface turbulent flow field, which corresponds well with the direct numerical simulations. (C) 1998 American Institute of Physics.