Particle-Image Velocimetry and the Assignment Problem

The Particle-Image Velocimetry (PIV) is a standard optical contactless measurement technique to determine the velocity field of a fluid flow for example around an obstacle such as an airplane wing. Tiny density neutral and light-reflecting particles are added to the otherwise invisible fluid flow. Then two consecutive images (A and B) of a thin laser illuminated light sheet are taken by a CCD camera with a time-lag of a few milliseconds. From these two images one tries to estimate the local shift of the particles, for which it is common to use a cross-correlation function. Based on the displacement of the tracers and the time-lag, the local velocities can be determined. This method requires a high level of experience by its user, fine tuning of several parameters, and multiple pre- and post-processing steps of the data in order to obtain meaningful results. We present a new approach that is based on the matching problem in bipartite graphs. Ideally, each particle in image A is assigned to exactly one particle in image B, and in an optimal assignment, the sum of shift distances of all particles in A to particles in B is minimal. However, the real-world situation is far from being ideal, because of inhomogeneous particle sizes and shapes, inadequate illumination of the images, or particle losses due to a divergence out of the two-dimensional light sheet area into the surrounding three-dimensional space, to name just a few sources of imperfection. Our new method is implemented in MATLAB with a graphical user interface. We evaluate and compare it with the cross-correlation method using real measured data. We demonstrate that our new method requires less interaction with the user, no further post-processing steps, and produces less erroneous results. This article is based on the master thesis [5], written by the first coauthor, and supervised by all other coauthors.