Correlation Tracking: Using simulations to interpolate highly correlated particle tracks

Ella M. King, Zizhao Wang, David A. Weitz, Frans Spaepen, and Michael P. Brenner

Phys. Rev. E 105, 044608 – Published 25 April 2022

Abstract

Despite significant advances in particle imaging technologies over the past two decades, few advances have been made in particle tracking, i.e., linking individual particle positions across time series data. The state-of-the-art tracking algorithm is highly effective for systems in which the particles behave mostly independently. However, these algorithms become inaccurate when particle motion is highly correlated, such as in dense or strongly interacting systems. Accurate particle tracking is essential in the study of the physics of dense colloids, such as the study of dislocation formation, nucleation, and shear transformations. Here, we present a method for particle tracking that incorporates information about the correlated motion of the particles. We demonstrate significant improvement over the state-of-the-art tracking algorithm in simulated data on highly correlated systems.

Received 25 January 2022
Accepted 6 April 2022

DOI:https://doi.org/10.1103/PhysRevE.105.044608

Physics Subject Headings (PhySH)

Diffusion Interactions & forces Rheology

Condensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

Authors & Affiliations

Ella M. King ¹, Zizhao Wang², David A. Weitz^1,2, Frans Spaepen², and Michael P. Brenner^1,2

¹Physics Department, Harvard University, USA
²School of Engineering and Applied Sciences, Harvard University, USA

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Issue

Vol. 105, Iss. 4 — April 2022

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Images

Figure 1
Comparison of the correlation tracking results to those of the Crocker-Grier algorithm in simulated data using a Morse pair potential [Eq. (3)]. The $x$ axis shows the mean particle displacement divided by the mean interparticle separation in units of $r_{0}$ . This metric serves as a proxy for the time and enables ready comparison between simulation and experiment. The $y$ axis shows the tracking accuracy, or the fraction of correctly identified particle labels. The uncertainties are standard errors based on 25 independent simulations.
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Figure 2
Comparison of the correlation tracking algorithm to the Crocker-Grier algorithm as a function of interaction range. The results are computed on simulated data using a Morse potential [Eq. (3)]. The $x$ axis shows the parameter $α$ in the Morse potential which varies inversely with interaction range. The $y$ axis shows the fraction of correctly identified particle labels. Error bars are based on 25 independent simulations.
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Figure 3
(a) Sample of a trajectory in which the correlation tracking algorithm makes accurate predictions but the Crocker-Grier algorithm makes an error on the third frame. The particle we are tracking is shown in blue, and the incorrectly identified particle is shown in red. The final frame is overlaid on the previous frame (partially transparent). (b) Histogram showing the length of a given trajectory before the first error is made. The blue data points are results for correlation tracking whereas the pink results are for the Crocker-Grier algorithm. The means of each distribution are given by the dashed vertical lines. (c) Sample error made by the correlation tracking algorithm. Distributions of simulated particle positions are shown in blue and red, respectively, while the true particle positions are given in brighter shades of blue and red (overlaid). The correlation tracking algorithm mistakes the blue particle for the red particle.
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Figure 4
3D rendered image of the colloidal particles in the first frame of the tracking experiment. The front half of the sample has been removed to reveal the red particles at the center, which are used for the tracking analysis. The particle diameter is $1.75 μ m$ .
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Figure 5
Comparison of correlation tracking to Crocker-Grier in a three-dimensional experimental hard-sphere system. The primary $x$ axis (bottom) shows the time between frames measured in seconds. The secondary $x$ axis (top) shows the mean particle displacement in units of the particle diameter. The secondary axis is included for easier comparison to simulation. The $y$ axis shows the fraction of correctly labeled particles. The error bars show the standard error, computed for 10 independent tracking events that use different central particles and different starting frames.
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Figure 6
Comparison of the correlation tracking algorithm to the Crocker-Grier algorithm in simulated data on particles with multiple colors, interacting via a Morse potential (left) and a soft sphere potential (right). The particles were allowed to evolve such that their distance, measured in units of $r_{0}$ per average interparticle separation, was 0.11 for the Morse potential, and 0.069 for the soft-sphere potential. The $y$ axis shows the fraction of correctly labeled particles in that frame. Error bars are based on 25 independent simulations.
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