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

U2-Net and ResNet50-Based Automatic Pipeline for Bacterial Colony Counting

In this paper, an automatic colony counting system based on an improved image preprocessing algorithm and convolutional neural network (CNN)-assisted automatic counting method was developed. Firstly, we assembled an LED backlighting illumination platform as an image capturing system to obtain photographs of laboratory cultures. Consequently, a dataset was introduced consisting of 390 photos of agar plate cultures, which included 8 microorganisms. Secondly, we implemented a new algorithm for image preprocessing based on light intensity correction, which facilitated clearer differentiation between colony and media areas. Thirdly, a U2-Net was used to predict the probability distribution of the edge of the Petri dish in images to locate region of interest (ROI), and then threshold segmentation was applied to separate it. This U2-Net achieved an F1 score of 99.5% and a mean absolute error (MAE) of 0.0033 on the validation set. Then, another U2-Net was used to separate the colony region within the ROI. This U2-Net achieved an F1 score of 96.5% and an MAE of 0.005 on the validation set. After that, the colony area was segmented into multiple components containing single or adhesive colonies. Finally, the colony components (CC) were innovatively rotated and the image crops were resized as the input (with 14,921 image crops in the training set and 4281 image crops in the validation set) for the ResNet50 network to automatically count the number of colonies. Our method achieved an overall recovery of 97.82% for colony counting and exhibited excellent performance in adhesion classification. To the best of our knowledge, the proposed "light intensity correction-based image preprocessing→U2-Net segmentation for Petri dish edge→U2-Net segmentation for colony region→ResNet50-based counting" scheme represents a new attempt and demonstrates a high degree of automation and accuracy in recognizing and counting single-colony and multi-colony targets.

Hybrid Approach to Colony-Forming Unit Counting Problem Using Multi-Loss U-Net Reformulation

Colony-Forming Unit (CFU) counting is a complex problem without a universal solution in biomedical and food safety domains. A multitude of sophisticated heuristics and segmentation-driven approaches have been proposed by researchers. However, U-Net remains the most frequently cited and used deep learning method in these domains. The latter approach provides a segmentation output map and requires an additional counting procedure to calculate unique segmented regions and detect microbial colonies. However, due to pixel-based targets, it tends to generate irrelevant artifacts or errant pixels, leading to inaccurate and mixed post-processing results. In response to these challenges, this paper proposes a novel hybrid counting approach, incorporating a multi-loss U-Net reformulation and a post-processing Petri dish localization algorithm. Firstly, a unique innovation lies in the multi-loss U-Net reformulation. An additional loss term is introduced in the bottleneck U-Net layer, focusing on the delivery of an auxiliary signal that indicates where to look for distinct CFUs. Secondly, the novel localization algorithm automatically incorporates an agar plate and its bezel into the CFU counting techniques. Finally, the proposition is further enhanced by the integration of a fully automated solution, which comprises a specially designed uniform Petri dish illumination system and a counting web application. The latter application directly receives images from the camera, processes them, and sends the segmentation results to the user. This feature provides an opportunity to correct the CFU counts, offering a feedback loop that contributes to the continued development of the deep learning model. Through extensive experimentation, the authors of this paper have found that all probed multi-loss U-Net architectures incorporated into the proposed hybrid approach consistently outperformed their single-loss counterparts, as well as other comparable models such as self-normalized density maps and YOLOv6, by at least 1% to 3% in mean absolute and symmetric mean absolute percentage errors. Further significant improvements were also reported through the means of the novel localization algorithm. This reaffirms the effectiveness of the proposed hybrid solution in addressing contemporary challenges of precise in vitro CFU counting.

Multi-Loss U-Net Reformulation as an Efficient Solution to the Colony-Forming Unit Counting Problem

U-Net is undoubtedly the most cited and popularized deep learning architecture in the biomedical domain. Starting with image, volume, or video segmentation in numerous practical applications, such as digital pathology, and continuing to Colony-Forming Unit (CFU) segmentation, new emerging areas require an additional U-Net reformulation to solve some inherent inefficiencies of a simple segmentation-tailored loss function, such as the Dice Similarity Coefficient, being applied at the training step. One of such areas is segmentation-driven CFU counting, where after receiving a segmentation output map one should count all distinct segmented regions belonging to different detected microbial colonies. This problem can be a challenging endeavor, as a pure segmentation objective tends to produce many irrelevant artifacts or flipped pixels. Our novel multi-loss U-Net reformulation proposes an efficient solution to the aforementioned problem. It introduces an additional loss term at the bottom-most U-Net level, which focuses on providing an auxiliary signal of where to look for distinct CFUs. In general, our experiments show that all probed multi-loss U-Net architectures consistently outperform their single-loss counterparts, which embark on the Dice Similarity Coefficient and Cross-Entropy training losses alone.

Deep learning for diffusion in porous media

We adopt convolutional neural networks (CNN) to predict the basic properties of the porous media. Two different media types are considered: one mimics the sand packings, and the other mimics the systems derived from the extracellular space of biological tissues. The Lattice Boltzmann Method is used to obtain the labeled data necessary for performing supervised learning. We distinguish two tasks. In the first, networks based on the analysis of the system's geometry predict porosity and effective diffusion coefficient. In the second, networks reconstruct the concentration map. In the first task, we propose two types of CNN models: the C-Net and the encoder part of the U-Net. Both networks are modified by adding a self-normalization module [Graczyk et al. in Sci Rep 12, 10583 (2022)]. The models predict with reasonable accuracy but only within the data type, they are trained on. For instance, the model trained on sand packings-like samples overshoots or undershoots for biological-like samples. In the second task, we propose the usage of the U-Net architecture. It accurately reconstructs the concentration fields. In contrast to the first task, the network trained on one data type works well for the other. For instance, the model trained on sand packings-like samples works perfectly on biological-like samples. Eventually, for both types of the data, we fit exponents in the Archie's law to find tortuosity that is used to describe the dependence of the effective diffusion on porosity.