Partition of estimated locations: an approach to accurate quality metrics for stochastic optical localization nanoscopy

Performance evaluation of localization algorithms in stochastic optical localization nanoscopy is necessary and important to applications. By simulation, a localization algorithm estimates a set of emitter locations from a simulated data movie, whose error in comparison with the set of true locations indicates the performance of the algorithm. Since the partition of estimated locations is unknown, the sample root mean square error (RMSE) cannot be computed and the universal root mean square minimum distance (RMSMD) eventually becomes saturated as localization errors become large. In this paper, we propose a partition algorithm to estimate the partition of estimated locations. It takes use of three facts: (i) the true locations are known; (ii) the number of activations for each emitter is known; (iii) an estimated location is more likely to be associated with the nearest available emitter and vice versa. The estimated partition enables to compute the sample RMSE (RMSE-P) and improve the RMSMD with modification (RMSMD-P). Two simulations are carried out to demonstrate efficacy of the partition algorithm and the metrics of RMSE-P and RMSMD-P. One investigates the effect of a large range of localization bias, and the other examines performance of the unbiased Gaussian information-achieving (UGIA) estimator. As shown by the results of both simulations, the proposed partition algorithm accurately estimates the partition in terms of F1 score; with the partition estimated by the partition algorithm the RMSE-P and RMSMD-P are approximately equal to the RMSE with the true partition in a large range of localization bias and errors. This demonstrates their broad applicability in performance evaluation of localization algorithms under the benchmark of the UGIA estimator.