Optical flow for particle images with optimization based on a priori knowledge of the flow

Abstract This paper proposes a new Optical Flow method for particle image velocimetry applications.
The proposed method is based on the use of an a priori sparse knowledge of the flow. 
A particular insight is given to the optimization derivation based on an image-independent method.
Two alternatives are introduced. The first one uses particle-tracking velocimetry (PTV) estimates as subpixel information to describe the finest velocity scales. The expected true displacements related to the motion of the individual particles are used as anchors for the optimization procedure when the density of the particles is large enough. Alternatively, the second method solves the well-known median problem based on new image-independent functions in areas of low particle density.
Studies have been carried out on synthetic images to characterize the error and analyze the impact of image parameters (particle density, particle size, or noise) on the methods. The new methods are compared with a reference method against synthetic data: two Lamb-Oseen vortex rings and a 3D Turbulent Homogeneous and Isotropic flow.
The results show that the performances of the new method exceed those of the reference method in almost all tested cases, except for images with particles of relatively small size. It is notably shown that the new method is less dependent on the particle density and the noise embedded in the images than other optical flow estimators.