Abstract
This paper presents a new framework for particle tracking based on a Gaussian Mixture Model (GMM). It is an extension of the state-of-the-art iterative reconstruction of individual particles by a continuous modeling of the particle trajectories considering the position and velocity as coupled quantities. The proposed approach includes an initialization and a processing step. In the first step, the velocities at the initial points are determined after iterative reconstruction of individual particles of the first four images to be able to generate the tracks between these initial points. From there on, the tracks are extended in the processing step by searching for and including new points obtained from consecutive images based on continuous modeling of the particle trajectories with a Gaussian Mixture Model. The presented tracking procedure allows to extend existing trajectories interactively with low computing effort and to store them in a compact representation using little memory space. To demonstrate the performance and the functionality of this new particle tracking approach, it is successfully applied to a synthetic turbulent pipe flow, to the problem of observing particles corresponding to a Brownian motion (e.g., motion of cells), as well as to problems where the motion is guided by boundary forces, e.g., in the case of particle tracking velocimetry of turbulent Rayleigh–Bénard convection.
Highlights
In many areas of science, theories and experiments are in constant interaction
We suggest using a probabilistic prediction based on the Gaussian Mixture Model (GMM) instead of the extrapolation used in [57]
A new framework approach for particle tracking based on a Gaussian Mixture Model (GMM) is presented
Summary
In many areas of science, theories and experiments are in constant interaction. Theories are based on experimental designs and the insights gained with experiments can change theories or create new ones. The second application belongs to the domain of experimental fluid mechanics, where methods like PIV and PTV are the most prominent flow field measurement techniques yielding velocity vectors within observation planes or volumes They have in common that the velocity vectors in a moving fluid are determined from the displacement of seeding particles transported by the flow during a prescribed time interval. Mikheev and Zubtsov [32] propose to improve the tracking procedure by proper pre-conditioning of the particle displacement which is realized in the time-resolved 3D tracking method of the commercially distributed Shake-The-Box (STB) software With the latter, particle positions in subsequent images are predicted by extrapolating trajectories generated using former images with a third-order polynomial [45]. In contrast to the STB software, the here presented probabilistic particle tracking approach does not rely on a tomographic PIV evaluation for initialization or a Particle-Space Correlation as used for multi-pulse applications [37]
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