  A localization algorithm in stochastic optical localization nanoscopy plays
an important role in obtaining a high-quality image. A universal and objective
metric is crucial and necessary to evaluate qualities of nanoscopy images and
performances of localization algorithms. In this paper, we propose root mean
square minimum distance (RMSMD) as a quality metric for localization nanoscopy
images. RMSMD measures an average, local, and mutual fitness between two sets
of points. Its properties common to a distance metric as well as unique to
itself are presented. The ambiguity, discontinuity, and inappropriateness of
the metrics of accuracy, precision, recall, and Jaccard index, which are
currently used in the literature, are analyzed. A numerical example
demonstrates the advantages of RMSMD over the four existing metrics that fail
to distinguish qualities of different nanoscopy images in certain conditions.
The unbiased Gaussian estimator that achieves the Fisher information and
Cramer-Rao lower bound (CRLB) of a single data frame is proposed to benchmark
the quality of localization nanoscopy images and the performance of
localization algorithms. The information-achieving estimator is simulated in an
example and the result demonstrates the superior sensitivity of RMSMD over the
other four metrics. As a universal and objective metric, RMSMD can be broadly
employed in various applications to measure the mutual fitness of two sets of
points.
