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Three-dimensional particle tracking is an essential tool in studying dynamicsunder the microscope, namely, fluid dynamics in microfluidic devices, bacteriataxis, cellular trafficking. The 3d position can be determined using 2d imagingalone by measuring the diffraction rings generated by an out-of-focusfluorescent particle, imaged on a single camera. Here I present a ringdetection algorithm exhibiting a high detection rate, which is robust to thechallenges arising from ring occlusion, inclusions and overlaps, and allowsresolving particles even when near to each other. It is capable of real timeanalysis thanks to its high performance and low memory footprint. The proposedalgorithm, an offspring of the circle Hough transform, addresses the need toefficiently trace the trajectories of many particles concurrently, when theirnumber in not necessarily fixed, by solving a classification problem, andovercomes the challenges of finding local maxima in the complex parameter spacewhich results from ring clusters and noise. Several algorithmic conceptsintroduced here can be advantageous in other cases, particularly when dealingwith noisy and sparse data. The implementation is based on open-source andcross-platform software packages only, making it easy to distribute and modify.It is implemented in a microfluidic experiment allowing real-timemulti-particle tracking at 70 Hz, achieving a detection rate which exceeds 94%and only 1% false-detection.

Robust and highly performant ring detection algorithm for 3d particle tracking using 2d microscope imaging