A deep neural network architecture for reliable 3D position and size determination for Lagrangian particle tracking using a single camera

Abstract

Microfluidic flows feature typically fully three-dimensional velocity fields. However, often the optical access for measurements is limited. Astigmatism or defocus particle tracking velocimetry is a technique that enables the 3D position determination of individual particles by the analysis of astigmatic/defocused particle images. The classification and position determination of particles is a task well suited to deep neural networks (DNNs). In this work, two DNNs are used to extract the class and in-plane position (object detection) as well as the depth position (regression network). The performance of both DNNs is assessed by the position uncertainties as well as the precision of the size classes and the amount of recalled particles. The DNNs are evaluated on a synthetic dataset and establish a new benchmark of DNNs in defocus tracking applications. The recall is higher than compared to classic methods and the in-plane errors are always subpixel accurate. The relative uncertainty in the depth position is below \SI{1}{\percent} for all examined particle seeding concentrations. Additionally, the performance on experimental images, using four different particle sizes, ranging from 1.14 to \SI{5.03}{\micro\meter} is analyzed. The particle images are systematically rearranged to produce comprehensive datasets of varying particle seeding concentrations. The distinction between particles of similar size is more challenging but the DNNs still show very good results. A precision above \SI{96}{\percent} is reached with a high recall above \SI{95}{\percent}. The error in the depth position remains below \SI{1}{\percent} and the in-plane errors are subpixel accurate with respect to the labels. The work shows that first, DNNs can be trained with artificially rearranged data sets based on individual experimental images and are therefore easily adaptable to various experimental setups and applicable by non experts. Second, the DNNs can be successfully adapted to determine additional variables as in this case the size of the suspended particles.

Interplay of acoustophoresis and dielectrophoresis in a standing surface acoustic wave field: from spherical to non-spherical particles

“…Here, I sum refers to the summed intensity within the detected particle contour and I ex to a particle contour extended by a factor of 1.25. A similar approach was employed in previous studies to exclude overlapping particle images [63][64][65]. An uncertainty estimation based on synthetic particle images revealed subpixel accuracy in the determination of the x-and y-positions of the particles as well as a mean absolute error of 0.03 • for the in-plane angle φ [47].…”