Video-Microscopy-Based Automated Trajectory Determination for High-Velocity, Densely Clustered, Indistinguishable Objects Moving in A Directed Force Field

We present a method for tracking densely clustered, high-velocity, indistinguishable objects being spawned at a high rate and moving in a directed force field using only object centroids as inputs and no other image information. The algorithm places minimal restrictions on the velocities or accelerations of the objects being tracked and uses a methodology based on a scoring function and a back-tracking refinement process. This combination leads to successful tracking of hundreds of particles in challenging environments even when the displacement of the individual objects at successive times approaches the separation between neighboring objects in any one frame. We note that these cases can be particularly difficult to handle by existing methods. The performance of the algorithm is methodically examined by comparison to simulated trajectories which vary the temporal and spatial densities, velocities, and accelerations of the objects in motion, as well as the signal-to-noise ratio. Also, we demonstrate its capability by analyzing data from experiments with superparamagnetic microspheres moving in an inhomogeneous magnetic field in aqueous buffer at room temperature. Our method should be widely applicable since trajectory determination problems are ubiquitous in video microscopy applications in biology, materials science, physics, and engineering.