Particle Image Velocimetry using Feature Tracking and Delaunay tessellation

This work presents YATS (Yet Another Tracking Software), an application of Feature Tracking (FT) and Computational Geometry techniques to the measure of fluid flows. From a general point of view, FT can be considered as a correlation based method, working on interrogation windows, for tracking features inside high, medium and low seeded images. FT defines its best correlation measure as the minimum of the Sum of Squared Differences (SSD) of intensity values of pixels between the interrogation windows in two consecutive frames. The implemented algorithm is able to extract interrogation window displacement and deformations from frame to frame adopting, in consecutive steps, two different models of motion for the window itself: a pure translational model, in which a rigid motion hypothesis is adopted, and an affine one, in which first order window deformation parameters are taken into account, allowing the interrogation spot to be translated, rotated, scaled and sheared. For small motions, a linearization of the image intensity leads to solve the SSD minimization problem in a Newton-Raphson style. Velocity computation is performed where the solution of FT linear system exists, i.e. where image intensity gradients are not null both in x and y directions (features). Velocity and velocity gradients are obtained, in a lagrangian fashion, along the trajectory of each feature. As a result, high-density-in-space lagrangian measurements are gained, in terms of fluid velocity and velocity spatial derivatives. Lagrangian information is then embedded into a Delaunay tessellation, which is uniquely defined by the spatial relative positions of the features tracked from time t to t+1: the Eulerian fields of velocity and velocity spatial derivatives are obtained by applying the Natural Neighbours (NN) interpolation algorithm on the Delaunay tessellation itself, for an arbitrary sized grid. In NN method the support for data interpolation is not defined by the same measure in all directions, but is allowed to be non isotropic: support size in r direction is not given by an L2 metric but is a consequence of the geometric construct that defines the region of interaction between the features. Results obtained for two kinds of synthetic images are shown: array of vortices and Std. set of the Visualization Society of Japan. The accuracy of the method is highlighted both in Lagrangian and Eulerian framework. 0 50 100 150 200 250 0