A localization algorithm in optical localization nanoscopy plays an important role in obtaining a high-quality image. A universal and objective metric , which is crucial and necessary to evaluate qualities of nanoscopy images and performances of localization algorithms , has not yet been established. The metrics of root mean square error (RMSE or accuracy) , precision, recall, and Jaccard index (JAC) are currently used in the literature but in certain conditions fail in distinguishing qualities of different nanoscopy images . In this paper, the root mean square minimum distance (RMSMD) is proposed as a quality metric for localization nanoscopy images . Its properties are analyzed and demonstrated by examples which also show the advantages over RMSE, precision, recall and JAC . As a universal and objective metric, the RMSMD can be broadly applied to applications that need to measure average, local, and mutual fitness of two sets of points.
A localization algorithm in 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. An experiment that an unbiased estimator achieving the Fisher information and Cramer-Rao lower bound (CRLB) localizes emitters frame by frame independently is simulated and the result demonstrates the superior sensitivity of RMSMD over the other four metrics. The RMSMD of an information-achieving nanoscopy image benchmarks localization nanoscopy images and localization algorithms . As a universal and objective metric, RMSMD can be broadly employed in various applications to measure the mutual fitness of two sets of points.
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