Fig. 2

Accuracy and performance evaluations of quickPIV. a–d Mean biases (red lines) and random errors (green error bars) of unnormalized PIV applied to synthetic data containing particles shifted by homogeneous translations. a PIV errors are reduced by increasing interrogation size. As illustrated under the 2D examples, the intensity patterns contained in small interrogation areas (5\(\times\)5 pixels) display unspecific structures, and are more susceptible to out-of-frame loss. The 2D analyses were performed on 200\(\times\)200 pixel images containing 5k particles, and 3D analyses on 200\(\times\)200\(\times\)200 voxel volumes with 100k particles. b Particle densities of around 15 particles per interrogation region minimize PIV errors. Low particle count are susceptible to out-of-frame loss, while high particle densities degrade PIV accuracies by producing uniform intensity patterns. Interrogation size during this evaluation was 10\(\times\)10 pixels and 10\(\times\)10\(\times\)10 voxels. c Particle sizes of 1-2 pixels achieve optimal PIV accuracies. The 2D examples show that large particle radii blur the intensity pattern inside the interrogation regions, reducing the pattern complexity. d Top, PIV accuracy under non-integer translations oscillates between 0.0 and 0.5. Bottom, with 3-point Gaussian interpolation, errors are reduced by an order of magnitude. The leftmost figures show a slight loss of accuracy due to out-of-frame loss as the translation strength increases. Adding a search margin greater than the translation strength completely compensates for this effect. e Left, execution times distribution of 1000 FFT computations on input images of \(40 \times 40\) pixels. Background processes sporadically slow down FFT execution. Right, comparison of 2D FFT performance between Julia, C++ and Python for increasing input sizes. Julia and C++ calls of FFTW are equally fast, while the FFT implementation in NumPy is approximately three times slower. The execution time of FFT spikes when the input sizes are prime numbers, e.g. 23, 29 or 43