Single-pixel interior filling function approach for detecting and correcting errors in particle tracking

Abstract

We present a general method for detecting and correcting biases in the outputs of particle-tracking experiments. Our approach is based on the histogram of estimated positions within pixels, which we term the single-pixel interior filling function (SPIFF). We use the deviation of the SPIFF from a uniform distribution to test the veracity of tracking analyses from different algorithms. Unbiased SPIFFs correspond to uniform pixel filling, whereas biased ones exhibit pixel locking, in which the estimated particle positions concentrate toward the centers of pixels. Although pixel locking is a well-known phenomenon, we go beyond existing methods to show how the SPIFF can be used to correct errors. The key is that the SPIFF aggregates statistical information from many single-particle images and localizations that are gathered over time or across an ensemble, and this information augments the single-particle data. We explicitly consider two cases that give rise to significant errors in estimated particle locations: undersampling the point spread function due to small emitter size and intensity overlap of proximal objects. In these situations, we show how errors in positions can be corrected essentially completely with little added computational cost. Additional situations and applications to experimental data are explored in SI Appendix. In the presence of experimental-like shot noise, the precision of the SPIFF-based correction achieves (and can even exceed) the unbiased Cramér-Rao lower bound. We expect the SPIFF approach to be useful in a wide range of localization applications, including single-molecule imaging and particle tracking, in fields ranging from biology to materials science to astronomy.imaging | particle tracking | error correction | pixel locking | Cramér-Rao lower bound

Reactive optical matter: light-induced motility in electrodynamically asymmetric nanoscale scatterers

“…This introduced pixel locking error, in which the particle positions were localized toward the center of the pixels. The pixel locking error was corrected (removed) by applying the single pixel interior fill factor (SPIFF) algorithm 12,13 .…”

Direct Visualization of Barrier Crossing Dynamics in a Driven Optical Matter System

“…However, this method of particle localization uses the center-of-mass method which can lead to significant errors especially when particles come in close proximity, and the SPIFF algorithm was used to alleviate these errors. 36,37 A refinement algorithm was used that improves the accuracy of the positions of the particles by performing a non-linear least-squares (NLLS) fit of a Gaussian function to each distribution of pixel intensities for each nanoparticle. This allows extracting the particle positions with much greater accuracy especially in the case of overlapping features.…”

Biases in particle localization algorithms

“…This problematic bias is known as pixel bias or pixel locking and is discussed extensively in the literature [3,5,6,9,10,14,15,17,28]. The finite sampling from the pixelation breaks the translational invariance of the image and prevents simple heuristics from getting the exact answer.…”