  Particle image velocimetry (PIV) is essential in experimental fluid dynamics.
In the current work, we propose a new velocity field estimation paradigm, which
achieves a synergetic combination of the deep learning method and the
traditional cross-correlation method. Specifically, the deep learning method is
used to optimize and correct a coarse velocity guess to achieve a
super-resolution calculation. And the cross-correlation method provides the
initial velocity field based on a coarse correlation with a large interrogation
window. As a reference, the coarse velocity guess helps with improving the
robustness of the proposed algorithm. This fully convolutional network with
embedded cross-correlation is named as CC-FCN. CC-FCN has two types of input
layers, one is for the particle images, and the other is for the initial
velocity field calculated using cross-correlation with a coarse resolution.
Firstly, two pyramidal modules extract features of particle images and initial
velocity field respectively. Then the fusion module appropriately fuses these
features. Finally, CC-FCN achieves the super-resolution calculation through a
series of deconvolution layers to obtain the single-pixel velocity field. As
the supervised learning strategy is considered, synthetic data sets including
ground-truth fluid motions are generated to train the network parameters.
Synthetic and real experimental PIV data sets are used to test the trained
neural network in terms of accuracy, precision, spatial resolution and
robustness. The test results show that these attributes of CC-FCN are further
improved compared with those of other tested PIV algorithms. The proposed model
could therefore provide competitive and robust estimations for PIV experiments.
