A spatio-temporal matching algorithm for 3D particle tracking velocimetry

Abstract

3D-Particle Tracking Velocimetry (PTV) is one of the most flexible techniques for flow measurement, which allows the determination of three-dimensional velocity fields. Research activities in this field performed by the Institute of Geodesy and Photogrammetry at ETH Zurich for more than a decade have reached a status of an operational and reliable measurement method used in hydrodynamics and space applications. The method is based on the visualization of a flow with small, neutrally buoyant particles and recording of particle image sequences with 3-4 CCD cameras. In cooperation with the Institute of Hydromechanics and Water Resources Management at ETH Zurich further progress has been achieved in the improvement of the existing hardand software solutions. Regarding the algorithmic aspect of the method a new spatiotemporal matching method was developed, implemented and tested on different data sets. In former implementations the determination of the 3D particle positions was separated from the tracking of each particle, while the new method uses a combination of image and object space based information to establish spatio-temporal correspondences between particle positions of consecutive time steps. A system based on 4 CCD cameras is capable of tracking up to 1000 particles at video frequency (25Hz) with a relative accuracy of the velocity vectors of approximately 1:4000 of the field of view. The latest developments of the algorithmic aspects of 3D PTV are described and some examples of the successful application of the method are given in this paper. INTRODUCTION The 3D PTV is a technique for the determination of 3D velocity fields in flows. The existing 3D PTV solution developed at the Institute of Geodesy and Photogrammetry applying a object space based tracking algorithm should be improved in a way that the redundant information in image and object space is exploited more efficiently. The use of image and object space based information in combination with a prediction of the particle motion was thought to lead to enhanced results in the velocity field determination. The most important result to be expected from this work is a substantial increase of the tracking rate in 3D PTV. This is of importance mainly in the context of a Lagrangian analysis of particle trajectories, which can be considered the actual domain of the technique. Long trajectories are an absolute requisite for a Lagrangian flow analysis, as integral time and length scales can only be determined if long correlation lengths have been recorded. In addition, the number of simultaneous trajectories should be large enough to form a sufficient basis for a statistical analysis. Due to interruptions of particle trajectories caused by unsolved ambiguities the number of long trajectories decreases exponentially with the trajectory length. Very long trajectories over hundred and more time instances can so far only be determined if the probability of ambiguities is reduced by a low seeding density, thus concurrently reducing the spatial resolution of the system and the basis for a statistical analysis. A reduction of the trajectory interruptions due to unsolved ambiguities can multiply the yield of long trajectories and thus the usefulness of the results of 3D PTV, which further enlarges the application potential of the technique. Within the framework of a research project of the Swiss National Science Foundation a new spatio-temporal matching algorithm was developed and implemented. The technique has reached a status of an operational and reliable measurement tool used in hydrodynamics and space applications (Becker et al, 1995, Maas et al, 1997, Willneff and Maas, 2000). NOMENCLATURE XO,YO, ZO: 3D coordinates of projective center O Xi,Yi, Zi: 3D coordinates of object point Pi xi, yi: Image coordinates of Pi c: Principle distance of the camera xh, yh: Coordinates of the principle point ω, φ, κ: Rotation angles of the direction of the optical axis Drot: Rotation matrix as function of the rotation angles ω, φ, κ aij: Elements of 3x3 rotation matrix ti: Time step of image sequence