# Self-Normalized Density Map (SNDM) for Counting Microbiological Objects

arXiv: https://arxiv.org/abs/2203.09474 · HTML: https://mlsanity.com/paper/2203.09474/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 50 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 21 of 21)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Cascade R-CNN: Delving into High Quality Object Detection](https://mlsanity.com/paper/1712.00726/) (2017)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Deep Speech 2: End-to-End Speech Recognition in English and Mandarin](https://mlsanity.com/paper/1512.02595/) (2015)
- [U2-Net: Going Deeper with Nested U-Structure for Salient Object Detection](https://mlsanity.com/paper/2005.09007/) (2020)
- [Exploring Uncertainty Measures in Deep Networks for Multiple Sclerosis Lesion Detection and Segmentation](https://mlsanity.com/paper/1808.01200/) (2018)
- [Counting Everyday Objects in Everyday Scenes](https://mlsanity.com/paper/1604.03505/) (2016)
- [Deeply Uncertain: Comparing Methods of Uncertainty Quantification in Deep Learning Algorithms](https://mlsanity.com/paper/2004.10710/) (2020)
- [Early Stopping is Nonparametric Variational Inference](https://mlsanity.com/paper/1504.01344/) (2015)
- [Dropout as a Bayesian Approximation: Appendix](https://mlsanity.com/paper/1506.02157/) (2015)
- [Early-detection and classification of live bacteria using time-lapse coherent imaging and deep learning](https://mlsanity.com/paper/2001.10695/) (2020)
- [Predicting Porosity, Permeability, and Tortuosity of Porous Media from Images by Deep Learning](https://mlsanity.com/paper/2007.02820/) (2020)
- [AGAR a microbial colony dataset for deep learning detection](https://mlsanity.com/paper/2108.01234/) (2021)
- [As easy as 1, 2... 4? Uncertainty in counting tasks for medical imaging](https://mlsanity.com/paper/1907.11555/) (2019)
- [Deep Learning to Detect Bacterial Colonies for the Production of Vaccines](https://mlsanity.com/paper/2009.00926/) (2020)
- [Deep neural networks approach to microbial colony detection -- a comparative analysis](https://mlsanity.com/paper/2108.10103/) (2021)
- [Generation of microbial colonies dataset with deep learning style transfer](https://mlsanity.com/paper/2111.03789/) (2021)

## Built on by (most cited first, 1 of 1)

- [Deep learning for diffusion in porous media](https://mlsanity.com/paper/2304.02104/) (2023)

## Abstract (arXiv)

The statistical properties of the density map (DM) approach to counting microbiological objects on images are studied in detail. The DM is given by U2-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 textitSelf-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.