The workflow of the <i>C-Sym</i> algorithm.

<p>(a) For candidate points (<i>x</i>, <i>y</i>) 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 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.e006" target="_blank">5</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.e007" target="_blank">6</a>, to create the 3-D correlation maps, <i>Corr</i>_<i>X</i> and <i>Corr</i>_<i>Y</i>. (c) 2-D symmetry profiles, <i>Sym</i>_<i>X</i> and <i>Sym</i>_<i>Y</i>, are created from correlation maps using average filtering defined by Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.e008" target="_blank">7</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.e009" target="_blank">8</a>. (d) Symmetry profiles are interpolated using the Hermite algorithm. (e) Correlation centers are obtained from interpolated Symmetry profiles with polynomial fitting.</p

Mean error in the center position of the particles measured using: <i>C-Sym</i>, <i>CoM</i>, <i>CHT</i>, <i>XCorr QI</i> and <i>GFit</i> algorithms for different particle radius and noise levels.

<p>The bottom panel shows the scales and label of each axis. A low value of the SNR indicates noisy images. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.s001" target="_blank">S1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.s002" target="_blank">S2</a> Figs show examples of the images used to generate these data.</p

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.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.s001" target="_blank">S1 Fig</a> 3 show examples of the images used to generate these data.</p

Relative error of the amplitude of particle displacement with <i>C-Sym</i>, <i>CHT</i>, <i>CoM</i>, <i>XCorr</i> and <i>QI</i>, algorithms.

<p>Relative error of the amplitude of particle displacement with <i>C-Sym</i>, <i>CHT</i>, <i>CoM</i>, <i>XCorr</i> and <i>QI</i>, algorithms.</p

Mean error in the center position of the particles measured using: <i>C-Sym</i>, <i>CoM</i>, <i>XCorr QI</i> and <i>GFit</i> algorithms for synthetic fluorescent images using different particle radius (presented in terms of the standard deviation of Gaussian distribution) and noise levels.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.s003" target="_blank">S3 Fig</a> show examples of the images used to generate these data.</p

Evaluation of the performance of the algorithms using a tethered micro-sphere.

<p>(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.</p

Absolute amplitude errors for the different algorithms in nm.

<p>Absolute amplitude errors for the different algorithms in nm.</p

Standard deviation of the error in the position of the center of particles measured with <i>C-Sym</i>, <i>CHT</i>, <i>CoM</i>, <i>XCorr</i>, <i>QI</i> and <i>GFit</i>, algorithms according to the particle radius and the noise level.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.s001" target="_blank">S1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0175015#pone.0175015.s002" target="_blank">S2</a> Figs show examples of the images used to generate these data.</p

Correlation values for the different algorithms.

<p>Correlation values for the different algorithms.</p

The block diagram of generating sample images.

<p>Two major variables, particle size and noise level, and other relevant variables were used to create synthetic images.</p