Using optical flow equation for particle detection and velocity prediction in particle tracking Luca Shindler ⇑ , Monica Moroni, Antonio Cenedese DICEA, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy article info Keywords: Particle detection Particle tracking velocimetry Image processing Feature extraction Optical flow abstract A new algorithm of particle identification suitable for particle tracking technique in fluid mechanics is proposed and tested with synthetic images specifically developed with differ- ent particle parameters. The new approach is based on the solution of the optical flow equation via a sum-of-squared-difference method. Particles are detected through the iden- tification of corner features, where image intensity gradients are not null in two orthogonal directions. It is thus possible to identify low intensity and overlapped particles. Further- more, the feature selection criterion is optimal by construction because it is based on the optical flow solution and therefore a good feature is the one that can be tracked well. This leads to the second advantage of the method, which is the possibility to obtain the local velocity, given by the approximate solution of the optical flow equation, that can be used as a predictor for the subsequent particle pairing step. The proposed algorithm is tested using synthetically generated and experimental images and demonstrates its abil- ity to detect a great number of particles with high reliability in different cases analysed. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction Particle tracking velocimetry (PTV) is a widely used image analysis technique that is able to describe the properties of fluid flows via the reconstruction of particle paths. These are obtained by tracking tracer particles seeding the fluid under investigation. The particles are illuminated with an appropriate light source, such as lasers, and the scattered light is re- corded with high quality digital cameras. PTV differs from cross-correlation techniques, in its ability to provide a Lagrangian description of motion, which is of fundamental importance for understanding turbulent mixing and scalar dispersion [1,2]. Once the single-exposure images recording the fluid motion are acquired, the two-dimensional PTV procedure involves three consecutive steps: 1. identification of each particle in the image space of the camera; 2. calculation of barycentre coordinates for each detected particle; 3. temporal matching of particle positions, so as to generate particle trajectories. Moreover, in three-dimensional analysis the reconstruction of particle position in the object space is usually required [3,4]. Although these different phases are all of fundamental importance, the steps of particle identification and the subsequent barycentre calculation will crucially influence the accuracy and precision of the whole particle tracking system. 0096-3003/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2012.02.030 ⇑ Corresponding author. E-mail address: luca.shindler@uniroma1.it (L. Shindler). Applied Mathematics and Computation 218 (2012) 8684–8694 Contents lists available at SciVerse ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc