Fig. 1: The 3D SMLM particle fusion pipeline and results of the simulation study.
From: 3D particle averaging and detection of macromolecular symmetry in localization microscopy
a Pair registration of all segmented particles results in relative transformations Mij (translations tij and rotations Rij). The redundant information in the all-to-all registration matrix is utilized for improving the registration errors by means of Lie-algebraic averaging, which results in Mi absolute transformations. The relative transformations are recomputed as MjMi−1. From them, a consistency check (based on only rotations Rij) is applied via a threshold ε on the rotation error to remove outlier registrations Mij from the all-to-all matrix. After two iterations, this results in a data-driven template. Additionally, the rotation error residuals that are encoded in the histogram of Sij can be used to infer symmetry group(s) of the particle structure and to subsequently impose symmetry on the data. Finally, five rounds of bootstrapping are applied to improve the final reconstruction by registering every particle to the derived template. b Ground-truth fusion of 100 simulated NPCs indicating the height, radius, the angular shift between the cytoplasmic and nuclear rings in the same NPC. c Registration error for simulated PAINT and STORM data for different degree of labeling (DOL), mean localization uncertainties (σ = 4, 8, and 13 nm) and number of localizations per particle. Successful super-particle reconstruction is possible below a registration error of 25 nm. d Registration error of simulated PAINT data with 50% DOL and tilt angle of 60 degrees at different number of particles per dataset. e Registration error of simulated PAINT data with 75% DOL and arbitrary pose at different number of particles per dataset. Solid lines indicate the mean and shaded area show the standard error of the mean (n = 15).
