Root Mean Square Minimum Distance: a Quality Metric for Localization Nanoscopy Imaging

A localization algorithm in optical localization nanoscopy plays an important role in obtaining a highquality image. By challenging 2D synthetic nanoscopy data, performances of 32 localization software packages were recently evaluated. The challenge has been advanced to focus on 3D imaging and become an open public online challenge that up to now has drawn 84 participant packages. 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 in the field. In the current challenges the root mean square error (RMSE, also termed accuracy), precision, recall, and Jaccard index (JAC), between an image of estimated fluorophore locations and the image of ground-truth locations, are used as quality metrics. As analyzed in Supplementary Discussion, these metrics depend on the full-width halfmaximum (FWHM) of the point spread function in an optical system and therefore are not universal and somewhat subjective, and in certain conditions fail to distinguish qualities of different nanoscopy images. In this paper we propose the root mean square minimum distance (RMSMD) as a quality metric for localization nanoscopy imaging, analyze its properties, and demonstrate analytically and by example its advantages over the metrics used in the current challenges. We first define the mean square minimum distance (MSMD) between two sets of n-dimensional points, X and S, as