Fig. 1

QuickPIV pipeline The PIV analysis starts by subdividing the input volumes, \(V_{t}\) and \(V_{t+1}\), into a grid of cubic interrogation, IV, and search volumes, SV. Cross-correlation is performed between each IV[i, j, k] and SV[i, j, k] pair, and a displacement vector, (u[i, j, k], v[i, j, k], w[i, j, k]), is computed from each cross-correlation matrix through the position of the maximum peak relative to the center of the cross-correlation matrix. The computed vector components are added to the U, V and W matrices. Optionally, signal-to-noise ratios are computed from each cross-correlation matrix and added to SN. If multi-pass is used, the cross-correlation analysis is repeated at progressively lower scales, which is achieved by scaling down the interrogation size, overlap and search margin parameters at each iteration. During multi-pass, previously computed displacements offset the sampling of the search volumes, effectively refining the computed displacements at each iteration. In order to post-process the PIV-computed vector fields, quickPIV currently implements: signal-to-noise and vector magnitude filtering, space-time averaging, divergence maps, velocity maps, collectiveness maps, pseudo-trajectories and unit conversion. (a) Left, two \(60\times 50 \times 50\) voxel volumes are overlaid, with particles in \(V_t\) shown in red, and particles in \(V_{t+1}\) in blue. Interrogation volume size of \(16 \times 16 \times 16\) voxels leads to \(3\times 3 \times 3\) subdivision of non-overlapping interrogation and search volumes. Right, with 50% overlap the grid subdivision size is \(6 \times 5 \times 5\). (b) Example of 3D cross-correlation between IV[2, 2, 2] and SV[2, 2, 2]. The use of a search margin of 5 voxels is illustrated, enlarging the search volume by 5 voxels in all directions. (c) Example of displacement computation. For clarity, this example portrays low particle densities and big particle radii, which results in sub-optimal accuracy of the 3-point Gaussian sub-voxel approximation