Defocus particle tracking: a comparison of methods based on model functions, cross-correlation, and neural networks

Abstract

Defocus particle tracking (DPT) has gained increasing importance for its use to determine particle trajectories in all three dimensions with a single-camera system, as typical for a standard microscope, the workhorse of today's ongoing biomedical revolution. DPT methods derive the depth coordinates of particle images from the different defocusing patterns that they show when observed in a volume much larger than the respective depth of field. Therefore it has become common for state-of-the-art methods to apply image recognition techniques. Two of the most commonly and widely used DPT approaches are the application of (astigmatism) particle image model functions (MF methods) and the normalized cross-correlations between measured particle images and reference templates (CC methods). Though still young in the field, the use of neural networks (NN methods) is expected to play a significant role in future and more complex defocus tracking applications. To assess the different strengths of such defocus tracking approaches, we present in this work a general and objective assessment of their performances when applied to synthetic and experimental images of different degrees of astigmatism, noise levels, and particle image overlapping. We show that MF methods work very well in low-concentration cases, while CC methods are more robust and provide better performance in cases of larger particle concentration and thus stronger particle image overlap. The tested NN methods generally showed the lowest performance, however, in comparison to the MF and CC methods, they are yet in an early stage and have still great potential to develop within the field of DPT.

On the acoustically induced fluid flow in particle separation systems employing standing surface acoustic waves – Part I

“…Particle images with an Euclidean distance of less than 7.5 pixel to the calibration function in the ( ax , ay ) plane were considered as valid particle detections. 60 For particle tracking a simple nearest-neighbor algorithm was applied. 61 With the estimated displacement vector d and the time interval Δ t , the individual particle velocity vectors were determined by u = d /Δ t .…”

On the acoustically induced fluid flow in particle separation systems employing standing surface acoustic waves – Part II

“…59 Any detected particle with a Euclidean distance smaller than 7.5 pixels to the calibration function in the ( ax , ay ) plane, where ax and ay are the lengths of the semi axes of the elliptical particle images, was declared as valid. 60 After determining the particle positions in the double frame images, the displacement vector d was obtained using a nearest-neighbor algorithm. 61 Based on the time interval Δ t , the velocity vector of a single particle was derived according to u = d /Δ t .…”

From rectangular to diamond shape: on the three-dimensional and size-dependent transformation of patterns formed by single particles trapped in microfluidic acoustic tweezers

“…Therefore, the effect of ξ on the 3D pattern formation and transformation was studied experimentally, employing two SAW devices with two different wavelengths λ SAW , in which particles of different diameters d p were trapped. To measure the three-dimensional trapping locations of the particles and to characterize the geometrical features of the patterns formed within the micro chambers, astigmatism particle tracking velocimetry (APTV) 21,22 was applied. The experimental setup, measurement procedures and obtained results will be described in detail as follows.…”