Quantitative Comparison of Algorithms for Tracking Single Fluorescent Particles

Abstract

Single particle tracking has seen numerous applications in biophysics, ranging from the diffusion of proteins in cell membranes to the movement of molecular motors. A plethora of computer algorithms have been developed to monitor the sub-pixel displacement of fluorescent objects between successive video frames, and some have been claimed to have "nanometer" resolution. To date, there has been no rigorous comparison of these algorithms under realistic conditions. In this paper, we quantitatively compare specific implementations of four commonly used tracking algorithms: cross-correlation, sum-absolute difference, centroid, and direct Gaussian fit. Images of fluorescent objects ranging in size from point sources to 5 microm were computer generated with known sub-pixel displacements. Realistic noise was added and the above four algorithms were compared for accuracy and precision. We found that cross-correlation is the most accurate algorithm for large particles. However, for point sources, direct Gaussian fit to the intensity distribution is the superior algorithm in terms of both accuracy and precision, and is the most robust at low signal-to-noise. Most significantly, all four algorithms fail as the signal-to-noise ratio approaches 4. We judge direct Gaussian fit to be the best algorithm when tracking single fluorophores, where the signal-to-noise is frequently near 4.

Fluorescence Imaging with One Nanometer Accuracy: Application to Molecular Motors

“…1 Cheezum et al had compared different algorithms and quantitatively showed that a two-dimensional Gaussian function is the best fit to images of a single fluorescent dye, referred as a point spread function (PSF) ( Figure 1A,B). 2 The standard error of the mean (sem) of the PSF is a measure of localization and it can be made arbitrarily small by collecting more photons and minimizing the noise factors.…”

What do diffusion measurements tell us about membrane compartmentalisation? Emergence of the role of interprotein interactions

“…After the establishment of the trajectories [96], the mean square displacement is calculated according Eq. 6.…”

Visualizing single molecules interacting with nuclear pore complexes by narrow-field epifluorescence microscopy

“…However, there is only a weak dependence of S/N on pinhole size over the 200-500 μm diameter range. Since the limiting (minimum) S/N for reliable Gaussian fit localization (see below) is ∼4 [30] and SMF signals are inherently weak, increasing the S/N by ∼2-fold can easily make the difference between a feasible and unfeasible experiment. Further, this difference in S/N is considered an underestimate since it was obtained with dye molecules only in the focal plane, i.e., with no contributions from out-of-focus fluorescence emission.…”

“…There are four commonly used localization and tracking algorithms: the cross-correlation, sum-absolute difference, centroid, and Gaussian fit methods. For a sub-wavelength diameter particle, the Gaussian fit is the superior algorithm in terms of both accuracy and precision [30]. The localization precision of a moving particle is inherently worse than that of an immobilized particle due to errors that arise from movement during image acquisition.…”

“…Furthermore, for low signal levels, such as those typically observed in SMF experiments, this expression reduces to , which is a conservative (over)estimate of the true noise. A second approach is to estimate the noise with that arising from the higher noise level measurement, σ o [30]. The problem with this approach is that σ o may be poorly defined because the measurement is fleeting, e.g., nuclear transport events can occur within a few frames.…”