Fast 3D PIV with direct sparse cross-correlations

The extension of the well-assessed high-accuracy algorithms for two-dimensional-two components particle image velocimetry (PIV) to the case of three-dimensional (3D) data involves a considerable increase of the computational cost. Tomographic PIV is strongly affected by this issue, relying on 3D cross-correlation to estimate the velocity field. In this study, a number of solutions are presented, enabling a more efficient calculation of the velocity field without any significant loss of accuracy. A quick estimation of the predictor displacement field is proposed, based on voxels binning in the first steps of the process. The corrector displacement field is efficiently computed by restricting the search area of the correlation peak. In the initial part of the process, the calculation of a reduced cross-correlation map by using Fast Fourier Transform on blocks is suggested, in order to accelerate the processing by avoiding redundant calculations in case of overlapping interrogations windows. Eventually, direct cross-correlations with a search radius of only 1 pixel in the neighborhood of the estimated peak are employed; the final iterations are consistently faster, since direct correlations can better enjoy the sparsity of the distributions, reducing the number of operations to be performed. Furthermore, three different approaches to reduce the number of redundant calculations for overlapping windows are presented, based on pre-calculations of the contributions to the cross-correlations coefficients along segments, planes or blocks. The algorithms are tested both on synthetic and real images, showing that a potential speed-up of up to 800 times can be obtained, depending on the complexity of the flow field to be analyzed. The challenging application on a real swirling jet results in a speed-up of an order of magnitude.