  The statistical properties of the density map (DM) approach to counting
microbiological objects on images are studied in detail. The DM is given by
U$^2$-Net. Two statistical methods for deep neural networks are utilized: the
bootstrap and the Monte Carlo (MC) dropout. The detailed analysis of the
uncertainties for the DM predictions leads to a deeper understanding of the DM
model's deficiencies. Based on our investigation, we propose a
self-normalization module in the network. The improved network model, called
\textit{Self-Normalized Density Map} (SNDM), can correct its output density map
by itself to accurately predict the total number of objects in the image. The
SNDM architecture outperforms the original model. Moreover, both statistical
frameworks -- bootstrap and MC dropout -- have consistent statistical results
for SNDM, which were not observed in the original model. The SNDM efficiency is
comparable with the detector-base models, such as Faster and Cascade R-CNN
detectors.
