Fast and high-accuracy localization for three-dimensional single-particle tracking

Abstract

We report a non-iterative localization algorithm that utilizes the scaling of a three-dimensional (3D) image in the axial direction and focuses on evaluating the radial symmetry center of the scaled image to achieve the desired single-particle localization. Using this approach, we analyzed simulated 3D particle images by wide-field microscopy and confocal microscopy respectively, and the 3D trajectory of quantum dots (QDs)-labeled influenza virus in live cells. Both applications indicate that the method can achieve 3D single-particle localization with a sub-pixel precision and sub-millisecond computation time. The precision is almost the same as that of the iterative nonlinear least-squares 3D Gaussian fitting method, but with two orders of magnitude higher computation speed. This approach can reduce considerably the time and costs for processing the large volume data of 3D images for 3D single-particle tracking, which is especially suited for 3D high-precision single-particle tracking, 3D single-molecule imaging and even new microscopy techniques.

Figure 1. The schematic of the 3D radial symmetry algorithm.

(a) The image generated by sampling the point spread function (PSF) of wide-field microscopy on a 3D grid with a lattice size of 20 nm. (b) The 3D CCD image simulated from the PSF image (a) with a signal-to-noise (S/N) ratio of 20. The blue crosses indicate the true center of the 3D particle. (c) The implementation procedure: scaling the 3D image in axial direction, and calculating the center position (the blue point) of the 3D single particle with the minimal distance to all gradient lines (the purple arrow lines).

Figure 2. Estimation of the localization accuracy using simulated 3D particle images.

(a) Localization errors of 1000 simulated images with the S/N ratio of 20 with centroid, Gaussian fitting, and radial symmetry algorithm, respectively. The errors indicate the difference between the fitting position and the true position in each dimension. (b) The 3D scatter plots of the errors illustrating the error ranges of three methods in three dimensions. (c, d) The total errors and computation times calculated from a series of simulated images with the S/N ratios of 3 ~ 100.

Figure 3. Three-dimensional tracking individual quantum dots-labeled influenza viruses in live cells.

(a) 3D images of single virus labeled with QDs for tracking. The length between major tickmark is 1 μm. (b, c) Trajectories of the single virus given by radial symmetry (b) and Gaussian fitting methods (c), respectively. The color of the trajectories indicates a time axis from blue to red. (d) MSD-Time plots of the trajectories analyzed by radial symmetry and Gaussian fitting methods. The difference between the two plots is shown in (e).