Fig 1.
The block diagram of generating sample images.
Two major variables, particle size and noise level, and other relevant variables were used to create synthetic images.
Fig 2.
(a) Example of an image from the experiment conducted with a 2.0 μm silica micro-sphere immobilized to a cover slip. (b) Measured displacement of the particle with the proposed C-Sym algorithm (marked as circles) and the ground truth sinusoidal function for the first 200 frames of the experiment (solid line).
Fig 3.
Evaluation of the performance of the algorithms using a tethered micro-sphere.
(a) The algorithms are used to locate the micro-sphere position in each frame. (b) The micro-sphere is extracted from every frame using a constant sized ROI centered on the detected position. Consecutive ROIs are correlated as denoted by the operator ⊗. (c) The correlation for each frame number. An algorithm with poor precision will give a low correlation value, thus, the evolution of correlation is an indicator of the stability and robustness of the algorithm used to locate the micro-sphere.
Fig 4.
The workflow of the C-Sym algorithm.
(a) For candidate points (x, y) in a search area A, a region of interest (ROI) is defined and four templates of the particle are created, dividing the ROI horizontally and vertically and reconstructing the whole particle from each template. (b) Pairs of templates are used in Eqs 5 and 6, to create the 3-D correlation maps, CorrX and CorrY. (c) 2-D symmetry profiles, SymX and SymY, are created from correlation maps using average filtering defined by Eqs 7 and 8. (d) Symmetry profiles are interpolated using the Hermite algorithm. (e) Correlation centers are obtained from interpolated Symmetry profiles with polynomial fitting.
Fig 5.
Mean error in the center position of the particles measured using: C-Sym, CoM, CHT, XCorr QI and GFit algorithms for different particle radius and noise levels.
The bottom panel shows the scales and label of each axis. A low value of the SNR indicates noisy images. S1 and S2 Figs show examples of the images used to generate these data.
Fig 6.
Comparison of the mean error in the center position of a particle of constant radius for different SNR values.
S1 Fig 1–2 show examples of the images used to generate these data.
Fig 7.
Standard deviation of the error in the position of the center of particles measured with C-Sym, CHT, CoM, XCorr, QI and GFit, algorithms according to the particle radius and the noise level.
S1 and S2 Figs show examples of the images used to generate these data.
Fig 8.
Comparison of how the standard deviation of the error in the position of the center of particles measured with different algorithms change with noise level while using a constant particle radius of 100 (left) 50 (center) and 10 (right) pixels.
S1 and S2 Figs show examples of the images used to generate these data.
Fig 9.
Mean error in the center position of the particles measured using: C-Sym, CoM, XCorr QI and GFit algorithms for synthetic fluorescent images using different particle radius (presented in terms of the standard deviation of Gaussian distribution) and noise levels.
S3 Fig show examples of the images used to generate these data.
Fig 10.
Standard deviation of the error in the position of the center of particles with C-Sym, CoM, XCorr, QI and GFit, algorithms according to the particle radius (presented in terms of the standard deviation of Gaussian distribution) and the noise level.
S3 Fig show examples of the images used to generate these data.
Fig 11.
Comparison of how the mean error in the position of the particle centers measured with different algorithms change with noise level while using a constant particle radius of 100 (left) 50 (center) and 10 (right) pixels.
S1 Fig 3 show examples of the images used to generate these data.
Fig 12.
Comparison of how the standard deviation of the error in the center position of particles measured with different algorithms change with noise level while using a constant particle radius of 100 (left) 50 (center) and 10 (right) pixels.
S1 Fig 3 show examples of the images used to generate these data.
Fig 13.
Relative error of the amplitude of particle displacement with C-Sym, CHT, CoM, XCorr and QI, algorithms.
Table 1.
Absolute amplitude errors for the different algorithms in nm.
Fig 14.
Correlation results in the experiment with tethered particles using C-Sym, CoM, XCorr, QI and GFit algorithms.
For readability, the SD correlation for the GFit (two orders of magnitude higher than the other techniques) is not represented in the chart.
Table 2.
Correlation values for the different algorithms.