Self-normalized density map (SNDM) for counting microbiological objects

Abstract

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$$^2$$ 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 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.

Deep learning for diffusion in porous media

“…Eventually, for task I, we consider two more network architectures obtained from the C-Net and the U-Net-Half, by replacing the last hidden layer with the self-normalized (SN) module. It is the structure proposed by Graczyk et al 29 to correct the network’s output. The SN mechanism is motivated by the observation that getting the deep neural network with good qualitative predictions is usually simple.…”

“…For task II, we propose considering the U-Net architecture, designed to face the biomedical image segmentation problem 29 , 30 . This type of network architecture was utilized, i.e., to predict the membrane’s flow properties, taking its morphology as input 25 and simulating a fluid flow in the porous materials 27 .…”

“…To estimate how uncertain the network predictions are, we exploit the Monte Carlo (MC) dropout technique 31 , 34 . Graczyk et al 29 adopt this method to estimate uncertainties for network predictions in the analysis of microbiological data. In short, to get uncertainty for the network response, we run network times, keeping the dropout layers active.…”

“…One of them is adapted from our previous work 21 on predicting porosity, permeability, and tortuosity in porous media. Additionally, both architectures are modified by adding a self-normalized (SN) module, proposed by Graczyk et al 29 . The modified architectures work with higher precision than vanilla ones.…”

“…All our architectures contain batch normalization layers, which was essential for getting successful fits 21 . Eventually, we modify the vanilla models by adding the self-normalization module 29 . Additionally, in this paper, we study the adaptation of the U-Net architecture for reconstructing the concentration field.…”