  A data movie of stochastic optical localization nanoscopy contains spatial
and temporal correlations, both providing information of emitter locations. The
majority of localization algorithms in the literature estimate emitter
locations by frame-by-frame localization (FFL), which exploit only the spatial
correlation and leave the temporal correlation into the FFL nanoscopy images.
The temporal correlation contained in the FFL images, if exploited, can improve
the localization accuracy and the image quality. In this paper, we analyze the
properties of the FFL images in terms of root mean square minimum distance
(RMSMD) and root mean square error (RMSE). It is shown that RMSMD and RMSE can
be potentially reduced by a maximum fold equal to the square root of the
average number of activations per emitter. Analyzed and revealed are also
several statistical properties of RMSMD and RMSE and their relationship with
respect to a large number of data frames, bias and variance of localization
errors, small localization errors, sample drift, and the worst FFL image.
Numerical examples are taken and the results confirm the prediction of
analysis. The ideas about how to develop an algorithm to exploit the temporal
correlation of FFL images are also briefly discussed. The results suggest
development of two kinds of localization algorithms: the algorithms that can
exploit the temporal correlation of FFL images and the unbiased localization
algorithms.

Image and Video Processing