# NeuronAlg: An Innovative Neuronal Computational Model for Immunofluorescence Image Segmentation

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## Abstract

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## 1. Introduction

## 2. Related Works

## 3. Methods and Data

#### 3.1. Machine Learning Approaches

#### 3.1.1. U-Net

- The architecture is so simple that it can be applied to many medical imaging segmentation tasks [49].
- Even if the network is deep, it can be trained in a short time, requiring low computational resources (the U-Net used in this study [48] was trained on a GPU RTX 2070 with 8 GB of VRAM in approximately 1 h).
- This network requires few computational resources for prediction, and it has a very fast forwarding time [50].

#### 3.1.2. KG Network

#### 3.1.3. R-CNN

#### 3.2. Deterministic Approaches

#### Otsu’s Method

- The class (class 0) of pixels with a grayscale value smaller than ${T}_{Otsu}$;
- The class (class 1) of pixels with a grayscale value greater than ${T}_{Otsu}$.

#### 3.3. Watershed

- The markers are initialized with the user’s input;
- The neighboring pixels of a marked pixel are inserted into the queue with a priority proportional to the gradient modulus of the image of the inserted pixel;
- The pixel with the highest priority is extracted. If the surrounding marked pixels have the same label, the pixel is marked with this label. All the surrounding pixels that are not yet marked are inserted into the queue;
- Return to step 2, until the queue is empty.

#### Active Contour Model

#### 3.4. Datasets

#### 3.4.1. Neuroblastoma Dataset

#### 3.4.2. NucleusSeg Dataset

#### 3.4.3. ISBI 2009 Dataset

## 4. Proposed Method

#### 4.1. Why a New Approach Is Needed

#### 4.2. Wired Behaviors in Neuronal Electric Activity

#### 4.3. Segmentation

- The binary approach returns a binary image, in which every pixel is white if it belongs to an object and black otherwise. This approach considers all cells and nuclei as a single object.
- The object-by-object approach assigns a different color to each object. Consequently, cells/nuclei are distinguishable and, in general, are numbered with natural numbers.

#### 4.4. The Proposed Model

- Preprocessing phase: prepares the images for the next steps.
- Watershed analysis: splits cells/nuclei using the well-known watershed transformation [65].
- Two steps of splitting and merging phase: improves watershed separation;
- Pattern extraction phase: from the cells/nuclei masks, the contour was extracted to run the neuronal model.
- Neuronal model phase: manipulate the contour of the mask using neuronal agents;
- Postprocessing phase: Some thresholding algorithms improve the mask precision.

#### 4.5. Model Description

- Given ${V}_{up}$ (initialized at 190) and ${V}_{down}$ (initialized at 0) is calculated ${V}_{tresh}=0.5\times {V}_{u}p+0.5\times {V}_{down}$
- On the image G is performed a threshold at ${V}_{tresh}$, creating a binary mask
- The threshold binary mask is processed three times with an size $odd(5\times sf)$ and two times with an size $odd(5\times sf)$
- ${\rho}_{i}$ is calculated as the number of sufficiently large connected components of thresholding mask
- The distance is calculated ${\delta}_{i}=\left|{r}_{i}-{\rho}_{i}\right|$
- If ${\delta}_{i}$ is minimal, this configuration is saved
- In any case, if ${r}_{i}>{\rho}_{i}$, then ${V}_{up}={V}_{tresh}$ else ${V}_{down}={V}_{tresh}$
- Return to Step 1, until the desired number of iterations is reached (in this contribution, this number is 10).

#### 4.6. Evaluation Criterion and Metrics

- Intersection over Union (IoU): This is defined as $\frac{TP}{TP\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}FP\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}FN}$ and is one of the most balanced metrics.
- F1-score is defined as $\frac{2TP}{2TP\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}FP\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}FN}$ and can be proven to be almost proportional to the IoU.
- Accuracy is defined as $\frac{TP\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}TN}{TP\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}FP\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}FN\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}TN}$ and is one of the most popular metrics for machine learning. However, in object segmentation tasks, this metric can be biased in cases of sparse cells/nuclei; in these cases, the number of negative pixels can be much greater than the number of positive pixels. This means that even if the prediction is fully negative (every pixel is negative), if the ground truth ratio P/N tends to 0, then the accuracy tends to 1.
- Sensitivity is defined as $\frac{TP}{TP\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}FN}$ and can be biased if the ground truth ratio N/P tends to zero.
- Specificity is defined as $\frac{TN}{TN\phantom{\rule{3.33333pt}{0ex}}+\phantom{\rule{3.33333pt}{0ex}}FP}$ and can be biased if the ground truth ratio P/N tends to zero.

## 5. Results

#### 5.1. Adversative Noise

#### 5.2. Results for the Neuroblastoma Dataset

#### 5.3. Results on the Nucleussegdata Dataset

#### 5.4. Results on the ISBI 2009 Dataset

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1

#### Appendix A.2

**Table A1.**Intersection of Union values of the algorithms for different PSNR values of adversative noise (Neuroblastoma).

IoU | 100.0 | 40.1 | 32.7 | 26.9 | 21.1 | 15.7 |

Neuronal Alg. | 0.695 | 0.700 | 0.695 | 0.673 | 0.614 | 0.549 |

UNetRNet34 | 0.718 | 0.559 | 0.503 | 0.406 | 0.192 | 0.060 |

KG network | 0.712 | 0.704 | 0.664 | 0.593 | 0.319 | 0.025 |

Mask R-CNN | 0.682 | 0.645 | 0.576 | 0.489 | 0.348 | 0.207 |

UNet DAug. | 0.7238 | 0.6829 | 0.6492 | 0.5518 | 0.1612 | 0.0784 |

KG DAug. | 0.7281 | 0.7159 | 0.6584 | 0.5622 | 0.3323 | 0.1038 |

**Table A2.**F1-score values of the algorithms for different PSNR values of adversative noise (Neuroblastoma).

F1-score | 100.0 | 40.1 | 32.7 | 26.9 | 21.1 | 15.7 |

Neuronal Alg. | 0.805 | 0.808 | 0.802 | 0.785 | 0.739 | 0.683 |

UNetRNet34 | 0.815 | 0.678 | 0.623 | 0.523 | 0.297 | 0.111 |

KG network | 0.796 | 0.787 | 0.754 | 0.688 | 0.435 | 0.047 |

Mask R-CNN | 0.787 | 0.755 | 0.695 | 0.606 | 0.457 | 0.287 |

UNet DAug. | 0.8229 | 0.7918 | 0.7648 | 0.6812 | 0.2662 | 0.1421 |

KG DAug. | 0.8092 | 0.7976 | 0.7497 | 0.6688 | 0.4491 | 0.1751 |

**Table A3.**Accuracy values of the algorithms for different PSNR values of adversative noise (Neuroblastoma).

Accuracy | 100.0 | 40.1 | 32.7 | 26.9 | 21.1 | 15.7 |

Neuronal Alg. | 0.938 | 0.938 | 0.936 | 0.929 | 0.910 | 0.879 |

UNetRNet34 | 0.955 | 0.926 | 0.915 | 0.895 | 0.845 | 0.811 |

KG network | 0.953 | 0.952 | 0.945 | 0.932 | 0.873 | 0.804 |

Mask R-CNN | 0.943 | 0.936 | 0.923 | 0.908 | 0.881 | 0.849 |

UNet DAug. | 0.9552 | 0.9473 | 0.941 | 0.9221 | 0.8266 | 0.8117 |

KG DAug. | 0.9559 | 0.9546 | 0.9449 | 0.9249 | 0.8729 | 0.8221 |

**Table A4.**Sensitivity values of the algorithms for different PSNR values of adversative noise (Neuroblastoma).

Sensitivity | 100.0 | 40.1 | 32.7 | 26.9 | 21.1 | 15.7 |

Neuronal Alg. | 0.848 | 0.855 | 0.853 | 0.849 | 0.816 | 0.778 |

UNetRNet34 | 0.751 | 0.576 | 0.518 | 0.416 | 0.194 | 0.061 |

KG network | 0.801 | 0.779 | 0.732 | 0.637 | 0.331 | 0.026 |

Mask R-CNN | 0.751 | 0.699 | 0.626 | 0.530 | 0.377 | 0.221 |

UNet DAug. | 0.7625 | 0.7142 | 0.6769 | 0.5685 | 0.1633 | 0.0805 |

KG DAug. | 0.8161 | 0.7877 | 0.7354 | 0.6223 | 0.3512 | 0.1053 |

**Table A5.**Specificity values of the algorithms for different PSNR values of adversative noise (Neuroblastoma).

Specificity | 100.0 | 40.1 | 32.7 | 26.9 | 21.1 | 15.7 |

Neuronal Alg. | 0.953 | 0.954 | 0.952 | 0.942 | 0.926 | 0.903 |

UNetRNet34 | 0.988 | 0.993 | 0.993 | 0.995 | 0.998 | 0.999 |

KG network | 0.973 | 0.976 | 0.976 | 0.981 | 0.991 | 0.999 |

Mask R-CNN | 0.975 | 0.979 | 0.979 | 0.980 | 0.981 | 0.989 |

UNet DAug. | 0.9868 | 0.9886 | 0.9895 | 0.9925 | 0.9983 | 0.9969 |

KG DAug. | 0.9732 | 0.9762 | 0.9738 | 0.9763 | 0.9897 | 0.9977 |

**Table A6.**Intersection of Union values of the algorithms for different PSNR values of adversative noise (NucleusSegData).

IoU | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.798 | 0.799 | 0.801 | 0.794 | 0.740 | 0.510 |

UNetRNet34 | 0.778 | 0.722 | 0.680 | 0.622 | 0.516 | 0.337 |

KG network | 0.802 | 0.790 | 0.760 | 0.659 | 0.400 | 0.081 |

Mask R-CNN | 0.712 | 0.672 | 0.622 | 0.510 | 0.235 | 0.037 |

**Table A7.**F1-score values of the algorithms for different PSNR values of adversative noise (NucleusSegData).

F1-score | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.881 | 0.886 | 0.888 | 0.883 | 0.838 | 0.608 |

UNetRNet34 | 0.873 | 0.834 | 0.802 | 0.758 | 0.669 | 0.491 |

KG network | 0.889 | 0.882 | 0.863 | 0.789 | 0.550 | 0.142 |

Mask R-CNN | 0.830 | 0.801 | 0.761 | 0.664 | 0.357 | 0.070 |

**Table A8.**Accuracy values of the algorithms for different PSNR values of adversative noise (NucleusSegData).

Accuracy | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.982 | 0.982 | 0.982 | 0.982 | 0.966 | 0.864 |

UNetRNet34 | 0.982 | 0.978 | 0.975 | 0.970 | 0.962 | 0.948 |

KG network | 0.983 | 0.982 | 0.980 | 0.973 | 0.953 | 0.928 |

Mask R-CNN | 0.977 | 0.973 | 0.969 | 0.959 | 0.938 | 0.917 |

**Table A9.**Sensitivity values of the algorithms for different PSNR values of adversative noise (NucleusSegData).

Sensitivity | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.853 | 0.838 | 0.841 | 0.836 | 0.824 | 0.795 |

UNetRNet34 | 0.796 | 0.735 | 0.690 | 0.630 | 0.521 | 0.340 |

KG network | 0.842 | 0.827 | 0.784 | 0.637 | 0.406 | 0.081 |

Mask R-CNN | 0.755 | 0.703 | 0.657 | 0.545 | 0.249 | 0.046 |

**Table A10.**Specificity values of the algorithms for different PSNR values of adversative noise (NucleusSegData).

Specificity | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.995 | 0.996 | 0.996 | 0.996 | 0.979 | 0.875 |

UNetRNet34 | 0.998 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

KG network | 0.996 | 0.996 | 0.997 | 0.998 | 0.999 | 1.0 |

Mask R-CNN | 0.996 | 0.996 | 0.995 | 0.995 | 0.997 | 0.990 |

**Table A11.**Intersection of Union values of the algorithms for different PSNR values of adversative noise (ISBI 2009).

IoU | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.842 | 0.845 | 0.841 | 0.823 | 0.744 | 0.610 |

UNetRNet34 | 0.773 | 0.588 | 0.431 | 0.244 | 0.080 | 0.039 |

KG network | 0.815 | 0.825 | 0.791 | 0.660 | 0.238 | 0.007 |

Mask R-CNN | 0.795 | 0.780 | 0.746 | 0.630 | 0.308 | 0.047 |

**Table A12.**F1-score values of the algorithms for different PSNR values of adversative noise (ISBI 2009).

F1-score | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.914 | 0.916 | 0.914 | 0.903 | 0.851 | 0.752 |

UNetRNet34 | 0.871 | 0.732 | 0.583 | 0.360 | 0.130 | 0.070 |

KG network | 0.898 | 0.904 | 0.883 | 0.792 | 0.356 | 0.012 |

Mask R-CNN | 0.886 | 0.876 | 0.853 | 0.766 | 0.439 | 0.080 |

**Table A13.**Accuracy values of the algorithms for different PSNR values of adversative noise (ISBI 2009).

Accuracy | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.958 | 0.959 | 0.958 | 0.953 | 0.930 | 0.885 |

UNetRNet34 | 0.940 | 0.890 | 0.849 | 0.800 | 0.759 | 0.749 |

KG network | 0.952 | 0.954 | 0.945 | 0.911 | 0.799 | 0.741 |

Mask R-CNN | 0.946 | 0.941 | 0.930 | 0.898 | 0.814 | 0.750 |

**Table A14.**Sensitivity values of the algorithms for different PSNR values of adversative noise (ISBI 2009).

Sensitivity | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.854 | 0.857 | 0.853 | 0.838 | 0.770 | 0.660 |

UNetRNet34 | 0.777 | 0.591 | 0.433 | 0.245 | 0.081 | 0.040 |

KG network | 0.821 | 0.833 | 0.798 | 0.665 | 0.239 | 0.007 |

Mask R-CNN | 0.807 | 0.797 | 0.782 | 0.666 | 0.320 | 0.048 |

**Table A15.**Specificity values of the algorithms for different PSNR values of adversative noise (ISBI 2009).

Specificity | 100.0 | 43.0 | 34.5 | 28.7 | 22.6 | 16.6 |

Neuronal Alg. | 0.995 | 0.995 | 0.995 | 0.994 | 0.987 | 0.965 |

UNetRNet34 | 0.998 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

KG network | 0.998 | 0.996 | 0.997 | 0.998 | 0.999 | 1.0 |

Mask R-CNN | 0.995 | 0.992 | 0.984 | 0.982 | 0.993 | 0.997 |

## References

- Gurcan, M.N.; Boucheron, L.E.; Can, A.; Madabhushi, A.; Rajpoot, N.M.; Yener, B. Histopathological Image Analysis: A Review. IEEE Rev. Biomed. Eng.
**2009**, 2, 147–171. [Google Scholar] [CrossRef] [PubMed] - Hill, A.A.; LaPan, P.; Li, Y.; Haney, S.A. Impact of image segmentation on high-content screening data quality for SK-BR-3 cells. BMC Bioinform.
**2007**, 8, 340. [Google Scholar] [CrossRef] [PubMed] - Ristevski, B.; Chen, M. Big Data Analytics in Medicine and Healthcare. J. Integr. Bioinform.
**2018**, 15. [Google Scholar] [CrossRef] [PubMed] - Verghese, A.C.; Shah, N.H.; Harrington, R.A. What This Computer Needs Is a Physician: Humanism and Artificial Intelligence. JAMA
**2018**, 319, 19–20. [Google Scholar] [CrossRef] [PubMed] - James, A.P.; Dasarathy, B.V. Medical image fusion: A survey of the state of the art. Inf. Fusion
**2014**, 19, 4–19. [Google Scholar] [CrossRef] - Mikołajczyk, A.; Grochowski, M. Data augmentation for improving deep learning in image classification problem. In Proceedings of the 2018 International Interdisciplinary PhD Workshop, IIPhDW 2018, Swinoujscie, Poland, 9–12 May 2018; pp. 117–122. [Google Scholar]
- Sotiras, A.; Davatzikos, C.; Paragios, N. Deformable medical image registration: A survey. IEEE Trans. Med. Imaging
**2013**, 32, 1153–1190. [Google Scholar] [CrossRef] - Heimann, T.; Meinzer, H. Statistical shape models for 3D medical image segmentation: A review. Med. Image Anal.
**2009**, 13, 543–563. [Google Scholar] [CrossRef] - Litjens, G.; Kooi, T.; Bejnordi, B.; Setio, A.; Ciompi, F.; Ghafoorian, M.; Laak, J.; Ginneken, B.; Sánchez, C. A survey on deep learning in medical image analysis. Med. Image Anal.
**2017**, 42, 60–88. [Google Scholar] [CrossRef] - Isensee, F.; Jaeger, P.; Kohl, S.; Petersen, J.; Maier-Hein, K. nnU-Net: A self-configuring method for deep learning-based biomedical image segmentation. Nat. Methods
**2021**, 18, 203–211. [Google Scholar] [CrossRef] - Albahri, A.; Duhaim, A.M.; Fadhel, M.A.; Alnoor, A.; Baqer, N.S.; Alzubaidi, L.; Albahri, O.; Alamoodi, A.; Bai, J.; Salhi, A.; et al. A systematic review of trustworthy and explainable artificial intelligence in healthcare: Assessment of quality, bias risk, and data fusion. Inf. Fusion
**2023**, 96, 156–191. [Google Scholar] [CrossRef] - Palermo, R.D.; Cascio, D.; Raso, G.; Tegolo, D. A Wavelet approach to extract main features from indirect immunofluorescence images. In Proceedings of the 20th International Conference on Computer Systems and Technologies, Ruse, Bulgaria, 16–17 June 2019. [Google Scholar]
- Pajares, G.; de la Cruz, J.M. A wavelet-based image fusion tutorial. Pattern Recognit.
**2004**, 37, 1855–1872. [Google Scholar] [CrossRef] - Santis, I.D.; Zanoni, M.; Arienti, C.; Bevilacqua, A.; Tesei, A. Density Distribution Maps: A Novel Tool for Subcellular Distribution Analysis and Quantitative Biomedical Imaging. Sensors
**2021**, 21, 1009. [Google Scholar] [CrossRef] [PubMed] - Wählby, C.; Lindblad, J.; Vondrus, M.; Bengtsson, E.; Björkesten, L. Algorithms for Cytoplasm Segmentation of Fluorescence Labelled Cells. Anal. Cell. Pathol. J. Eur. Soc. Anal. Cell. Pathol.
**2002**, 24, 101–111. [Google Scholar] [CrossRef] [PubMed] - Rizk, A.; Paul, G.; Incardona, P.; Bugarski, M.; Mansouri, M.; Niemann, A.; Ziegler, U.; Berger, P.; Sbalzarini, I.F. Segmentation and quantification of subcellular structures in fluorescence microscopy images using Squassh. Nat. Protoc.
**2014**, 9, 586–596. [Google Scholar] [CrossRef] [PubMed] - Vununu, C.; Lee, S.H.; Kwon, K.R. A Classification Method for the Cellular Images Based on Active Learning and Cross-Modal Transfer Learning. Sensors
**2021**, 21, 1469. [Google Scholar] [CrossRef] - Lupascu, C.A.; Tegolo, D. Automatic Unsupervised Segmentation of Retinal Vessels Using Self-Organizing Maps and K-Means Clustering. In Proceedings of the 7th International Meeting on Computational Intelligence Methods for Bioinformatics and Biostatistics, Palermo, Italy, 16–18 September 2010; pp. 263–274. [Google Scholar]
- Basar, S.; Ali, M.; Ochoa-Ruiz, G.; Zareei, M.; Waheed, A.; Adnan, A. Unsupervised color image segmentation: A case of RGB histogram based K-means clustering initialization. PLoS ONE
**2020**, 15, e0240015. [Google Scholar] [CrossRef] - Kolmogorov, V.; Zabih, R. What energy functions can be minimized via graph cuts? IEEE Trans. Pattern Anal. Mach. Intell.
**2002**, 26, 147–159. [Google Scholar] [CrossRef] - Boykov, Y.; Veksler, O.; Zabih, R. Fast Approximate Energy Minimization via Graph Cuts. In Proceedings of the Seventh IEEE International Conference on Computer Vision, Corfu, Greece, 20–27 September 1999; Volume 1, pp. 377–384. [Google Scholar]
- Liu, Z.; Song, Y.; Sheng, V.S.; Wang, L.; Jiang, R.; Zhang, X.; Yuan, D. Liver CT sequence segmentation based with improved U-Net and graph cut. Expert Syst. Appl.
**2019**, 126, 54–63. [Google Scholar] [CrossRef] - Cootes, T.; Taylor, C.J.; Cooper, D.H.; Graham, J. Active Shape Models-Their Training and Application. Comput. Vis. Image Underst.
**1995**, 61, 38–59. [Google Scholar] [CrossRef] - Soomro, S.; Munir, A.; Choi, K.N. Fuzzy c-means clustering based active contour model driven by edge scaled region information. Expert Syst. Appl.
**2019**, 120, 387–396. [Google Scholar] [CrossRef] - Roerdink, J.B.T.M.; Meijster, A. The Watershed Transform: Definitions, Algorithms and Parallelization Strategies. Fundam. Inform.
**2000**, 41, 187–228. [Google Scholar] [CrossRef] - Bieniek, A.; Moga, A.N. An efficient watershed algorithm based on connected components. Pattern Recognit.
**2000**, 33, 907–916. [Google Scholar] [CrossRef] - Minaee, S.; Boykov, Y.; Porikli, F.M.; Plaza, A.J.; Kehtarnavaz, N.; Terzopoulos, D. Image Segmentation Using Deep Learning: A Survey. IEEE Trans. Pattern Anal. Mach. Intell.
**2020**, 44, 3523–3542. [Google Scholar] [CrossRef] [PubMed] - Pan, W.; Liu, Z.; Song, W.; Zhen, X.; Yuan, K.; Xu, F.; Lin, G.N. An Integrative Segmentation Framework for Cell Nucleus of Fluorescence Microscopy. Genes
**2022**, 13, 431. [Google Scholar] [CrossRef] [PubMed] - Valen, D.A.V.; Kudo, T.; Lane, K.M.; Macklin, D.N.; Quach, N.T.; DeFelice, M.M.; Maayan, I.; Tanouchi, Y.; Ashley, E.A.; Covert, M.W. Deep Learning Automates the Quantitative Analysis of Individual Cells in Live-Cell Imaging Experiments. PLoS Comput. Biol.
**2016**, 12, e1005177. [Google Scholar] [CrossRef] - Graham, S.; Vu, Q.D.; e Ahmed Raza, S.; Azam, A.; Tsang, Y.W.; Kwak, J.T.; Rajpoot, N.M. Hover-Net: Simultaneous segmentation and classification of nuclei in multi-tissue histology images. Med. Image Anal.
**2019**, 58, 101563. [Google Scholar] [CrossRef] - Zeng, Z.; Xie, W.; Zhang, Y.; Lu, Y. RIC-Unet: An Improved Neural Network Based on Unet for Nuclei Segmentation in Histology Images. IEEE Access
**2019**, 7, 21420–21428. [Google Scholar] [CrossRef] - Mishra, A.; Majhi, S.K. A comprehensive survey of recent developments in neuronal communication and computational neuroscience. J. Ind. Inf. Integr.
**2019**, 13, 40–54. [Google Scholar] [CrossRef] - Kellermann, C.; Neumann, E.; Ostermann, J. A New Preprocessing Approach to Reduce Computational Complexity for Time Series Forecasting with Neuronal Networks: Temporal Resolution Warping. In Proceedings of the 2021 International Symposium on Computer Science and Intelligent Controls, ISCSIC, Rome, Italy, 12–14 November 2021; pp. 324–328. [Google Scholar]
- Middendorf, J.M.; Ita, M.E.; Winkelstein, B.A.; Barocas, V.H. Local tissue heterogeneity may modulate neuronal responses via altered axon strain fields: Insights about innervated joint capsules from a computational model. Biomech. Model. Mechanobiol.
**2021**, 20, 2269–2285. [Google Scholar] [CrossRef] - Harris, M.R.; Wytock, T.P.; Kovács, I.A. Computational Inference of Synaptic Polarities in Neuronal Networks. Adv. Sci.
**2022**, 9, 2104906. [Google Scholar] [CrossRef] - Srivastava, V.; Parker, D.J. Editorial: Mathematical, Computational, and Empirical Approaches to Exploring Neuronal Mechanisms Underlying Cognitive Functions. Front. Hum. Neurosci.
**2022**, 16, 896213. [Google Scholar] [CrossRef] [PubMed] - Brennan, C.; Aggarwal, A.; Pei, R.; Sussillo, D.; Proekt, A. One dimensional approximations of neuronal dynamics reveal computational strategy. PLoS Comput. Biol.
**2023**, 19, e1010784. [Google Scholar] [CrossRef] - Deng, L.; Yu, D. Deep Learning: Methods and Applications. Found. Trends Signal Process.
**2014**, 7, 197–387. [Google Scholar] [CrossRef] - Khan, A.; Sohail, A.; Zahoora, U.; Qureshi, A.S. A survey of the recent architectures of deep convolutional neural networks. Artif. Intell. Rev.
**2019**, 53, 5455–5516. [Google Scholar] [CrossRef] - Tajbakhsh, N.; Shin, J.Y.; Gurudu, S.R.; Hurst, R.T.; Kendall, C.B.; Gotway, M.B.; Liang, J. Convolutional Neural Networks for Medical Image Analysis: Full Training or Fine Tuning? IEEE Trans. Med. Imaging
**2016**, 35, 1299–1312. [Google Scholar] [CrossRef] [PubMed] - Alzubaidi, L.; Zhang, J.; Humaidi, A.J.; Al-dujaili, A.; Duan, Y.; Al-Shamma, O.; Santamaría, J.; Fadhel, M.A.; Al-Amidie, M.; Farhan, L. Review of deep learning: Concepts, CNN architectures, challenges, applications, future directions. J. Big Data
**2021**, 8, 53. [Google Scholar] [CrossRef] [PubMed] - Lavitt, F.; Rijlaarsdam, D.J.; van der Linden, D.; Węglarz-Tomczak, E.; Tomczak, J.M. Deep Learning and Transfer Learning for Automatic Cell Counting in Microscope Images of Human Cancer Cell Lines. Appl. Sci.
**2021**, 11, 4912. [Google Scholar] [CrossRef] - Liang, B.; Li, H.; Su, M.; Li, X.; Shi, W.; Wang, X. Detecting Adversarial Image Examples in Deep Neural Networks with Adaptive Noise Reduction. IEEE Trans. Dependable Secur. Comput.
**2017**, 18, 72–85. [Google Scholar] [CrossRef] - Pan, X.; Yang, D.; Li, L.; Liu, Z.; Yang, H.; Cao, Z.; He, Y.; Ma, Z.; Chen, Y. Cell detection in pathology and microscopy images with multi-scale fully convolutional neural networks. World Wide Web
**2018**, 21, 1721–1743. [Google Scholar] [CrossRef] - Krotov, D.; Hopfield, J.J. Unsupervised learning by competing hidden units. Proc. Natl. Acad. Sci. USA
**2019**, 116, 7723–7731. [Google Scholar] [CrossRef] - Springenberg, J.T.; Dosovitskiy, A.; Brox, T.; Riedmiller, M.A. Striving for Simplicity: The All Convolutional Net. arXiv
**2014**, arXiv:11412.6806. [Google Scholar] - Sabour, S.; Frosst, N.; Hinton, G.E. Dynamic Routing Between Capsules. arXiv
**2017**, arXiv:11710.09829. [Google Scholar] - Ronneberger, O.; Fischer, P.; Brox, T. U-Net: Convolutional Networks for Biomedical Image Segmentation. arXiv
**2015**, arXiv:11505.04597. [Google Scholar] - Siddique, N.A.; Paheding, S.; Elkin, C.P.; Devabhaktuni, V.K. U-Net and Its Variants for Medical Image Segmentation: A Review of Theory and Applications. IEEE Access
**2020**, 9, 82031–82057. [Google Scholar] [CrossRef] - Wu, G.; Guo, Y.; Song, X.; Guo, Z.; Zhang, H.; Shi, X.; Shibasaki, R.; Shao, X. A Stacked Fully Convolutional Networks with Feature Alignment Framework for Multi-Label Land-cover Segmentation. Remote Sens.
**2019**, 11, 1051. [Google Scholar] [CrossRef] - Yi, J.; Wu, P.; Huang, Q.; Qu, H.; Liu, B.; Hoeppner, D.J.; Metaxas, D.N. Multi-scale Cell Instance Segmentation with Keypoint Graph based Bounding Boxes. In Medical Image Computing and Computer Assisted Intervention—MICCAI 2019; Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Springer: Cham, Switzerland, 2019; pp. 369–377. [Google Scholar]
- He, K.; Gkioxari, G.; Dollár, P.; Girshick, R.B. Mask R-CNN. IEEE Trans. Pattern Anal. Mach. Intell.
**2017**, 42, 386–397. [Google Scholar] [CrossRef] - Otsu, N. A threshold selection method from gray level histograms. IEEE Trans. Syst. Man Cybern.
**1979**, 9, 62–66. [Google Scholar] [CrossRef] - Stockman, G.C.; Shapiro, L.G. Computer Vision; Prentice-Hall: Hoboken, NJ, USA, 2001. [Google Scholar]
- Kittler, J.; Illingworth, J. On threshold selection using clustering criteria. IEEE Trans. Syst. Man Cybern.
**1985**, SMC-15, 652–655. [Google Scholar] [CrossRef] - Lee, S.U.; Chung, S.Y.; Park, R.H. A comparative performance study of several global thresholding techniques for segmentation. Comput. Vis. Graph. Image Process.
**1990**, 52, 171–190. [Google Scholar] [CrossRef] - Beucher, S. The Watershed Transformation Applied To Image Segmentation. Scanning Microsc. Suppl.
**1992**, 6, 299–314. [Google Scholar] - Kornilov, A.S.; Safonov, I.V. An Overview of Watershed Algorithm Implementations in Open Source Libraries. J. Imaging
**2018**, 4, 123. [Google Scholar] [CrossRef] - Meyer, F. Color image segmentation. In Proceedings of the International Conference on Image Processing and its Applications, Maastricht, The Netherlands, 7–9 April 1992; pp. 303–306. [Google Scholar]
- OpenCV. Open-Source Computer Vision Library. 2015. Available online: https://opencv.org/about/ (accessed on 10 January 2022).
- Kass, M.; Witkin, A.P.; Terzopoulos, D. Snakes: Active contour models. Int. J. Comput. Vis.
**2004**, 1, 321–331. [Google Scholar] [CrossRef] - Ciecholewski, M. An edge-based active contour model using an inflation/deflation force with a damping coefficient. Expert Syst. Appl.
**2016**, 44, 22–36. [Google Scholar] [CrossRef] - Akbari, P.; Ziaei, A.; Azarnoush, H. Deep Active Contours Using Locally Controlled Distance Vector Flow. Signal Image Video Process.
**2021**, 16, 1773–1781. [Google Scholar] - Im, K.; Mareninov, S.; Diaz, M.F.P.; Yong, W.H. An Introduction to Performing Immunofluorescence Staining. Methods Mol. Biol.
**2018**, 1897, 299–311. [Google Scholar] - Kromp, F.; Bozsaky, E.; Rifatbegovic, F.; Fischer, L.; Ambros, M.I.; Berneder, M.; Weiss, T.; Lazic, D.; Doerr, W.; Hanbury, A.; et al. An annotated fluorescence image dataset for training nuclear segmentation methods. Sci. Data
**2020**, 7, 262–270. [Google Scholar] [CrossRef] [PubMed] - Nigam, I.; Agrawal, S.; Singh, R.; Vatsa, M. Revisiting HEp-2 Cell Image Classification. IEEE Access
**2015**, 3, 3102–3113. [Google Scholar] [CrossRef] - Gunesli, G.N.; Sokmensuer, C.; Gunduz-Demir, C. AttentionBoost: Learning What to Attend for Gland Segmentation in Histopathological Images by Boosting Fully Convolutional Networks. IEEE Trans. Med. Imaging
**2020**, 39, 4262–4273. [Google Scholar] [CrossRef] [PubMed] - Kromp, F.; Fischer, L.; Bozsaky, E.; Ambros, I.M.; Dorr, W.; Beiske, K.; Ambros, P.F.; Hanbury, A.; Taschner-Mandl, S. Evaluation of Deep Learning Architectures for Complex Immunofluorescence Nuclear Image Segmentation. IEEE Trans. Med. Imaging
**2021**, 40, 1934–1949. [Google Scholar] [CrossRef] - Koyuncu, C.F.; Cetin-Atalay, R.; Gunduz-Demir, C. Object-Oriented Segmentation of Cell Nuclei in Fluorescence Microscopy Images. Cytom. Part A
**2018**, 93, 1019–1028. [Google Scholar] [CrossRef] - Coelho, L.P.; Shariff, A.; Murphy, R.F. Nuclear segmentation in microscope cell images: A hand-segmented dataset and comparison of algorithms. In Proceedings of the 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Boston, MA, USA, 28 June–1 July 2009; pp. 518–521. [Google Scholar]
- Goodfellow, I.J.; Shlens, J.; Szegedy, C. Explaining and Harnessing Adversarial Examples. arXiv
**2014**, arXiv:1412.6572. [Google Scholar] - Bar, A.; Lohdefink, J.; Kapoor, N.; Varghese, S.; Huger, F.; Schlicht, P.; Fingscheidt, T. The Vulnerability of Semantic Segmentation Networks to Adversarial Attacks in Autonomous Driving: Enhancing Extensive Environment Sensing. IEEE Signal Process. Mag.
**2021**, 38, 42–52. [Google Scholar] [CrossRef] - Zhao, H.; Qi, X.; Shen, X.; Shi, J.; Jia, J. ICNet for Real-Time Semantic Segmentation on High-Resolution Images. arXiv
**2017**, arXiv:1704.08545. [Google Scholar] - Chaddad, A.; Peng, J.; Xu, J.; Bouridane, A. Survey of Explainable AI Techniques in Healthcare. Sensors
**2023**, 23, 634. [Google Scholar] [CrossRef] [PubMed] - Lobov, S.A.; Chernyshov, A.V.; Krilova, N.P.; Shamshin, M.O.; Kazantsev, V.B. Competitive learning in a spiking neural network: Towards an intelligent pattern classifier. Sensors
**2020**, 20, 500. [Google Scholar] [CrossRef] - Migliore, M.; Novara, G.; Tegolo, D. Single neuron binding properties and the magical number 7. Hippocampus
**2008**, 18, 1122–1130. [Google Scholar] [CrossRef] - Hodgkin, A.L.; Huxley, A.F.; Eccles, J.C. Propagation of electrical signals along giant nerve fibres. Proc. R. Soc. Lond. Ser. Biol. Sci.
**1952**, 140, 177–183. [Google Scholar] [CrossRef] - Dutta, S.; Kumar, V.; Shukla, A.; Mohapatra, N.; Ganguly, U. Leaky Integrate and Fire Neuron by Charge-Discharge Dynamics in Floating-Body MOSFET. Sci. Rep.
**2017**, 7, 8257–8265. [Google Scholar] [CrossRef] - Squadrani, L.; Curti, N.; Giampieri, E.; Remondini, D.; Blais, B.; Castellani, G. Effectiveness of Biologically Inspired Neural Network Models in Learning and Patterns Memorization. Entropy
**2022**, 24, 682. [Google Scholar] [CrossRef] - Brunel, N. Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comput. Neurosci.
**2000**, 8, 183–208. [Google Scholar] [CrossRef] - Giacopelli, G.; Migliore, M.; Tegolo, D. Graph-theoretical derivation of brain structural connectivity. Appl. Math. Comput.
**2020**, 377, 125150. [Google Scholar] [CrossRef] - Gewaltig, M.; Diesmann, M. NEST (NEural Simulation Tool). Scholarpedia
**2007**, 2, 1430. [Google Scholar] [CrossRef] - Ye, Q. Signed Euclidean distance transform and its applications. In Proceedings of the International Conference On Pattern Recognition, Rome, Italy, 14–17 November 1988; pp. 495–499. [Google Scholar]
- Jung, A.B.; Wada, K.; Crall, J.; Tanaka, S.; Graving, J.; Reinders, C.; Yadav, S.; Banerjee, J.; Vecsei, G.; Kraft, A.; et al. Imgaug. 2020. Available online: https://github.com/aleju/imgaug (accessed on 10 January 2022).
- AMIA Supports ONC Efforts to Develop Trusted Exchange Framework. American Medical Informatics Association. Available online: https://amia.org/public-policy/public-comments/amia-supports-onc-efforts-develop-trusted-exchange-framework (accessed on 10 January 2022).
- Lawrence, J.; Malmsten, J.; Rybka, A.; Sabol, D.; Triplin, K. Comparing TensorFlow Deep Learning Performance Using CPUs, GPUs, Local PCs and Cloud. In Proceedings of the Student-Faculty Research Day, Pace University, 5 May 2017; pp. C1-1–C1-7. [Google Scholar]
- Rowley, A.; Brenninkmeijer, C.; Davidson, S.; Fellows, D.; Gait, A.; Lester, D.; Plana, L.; Rhodes, O.; Stokes, A.; Furber, S. SpiNNTools: The Execution Engine for the SpiNNaker Platform. Front. Neurosci.
**2019**, 13, 231. [Google Scholar] [CrossRef] [PubMed] - Orchard, G.; Frady, E.; Rubin, D.; Sanborn, S.; Shrestha, S.; Sommer, F.; Davies, M. Efficient Neuromorphic Signal Processing with Loihi 2. In Proceedings of the IEEE Workshop On Signal Processing Systems, SiPS: Design And Implementation, Coimbra, Portugal, 19–20 October 2021; pp. 254–259. [Google Scholar] [CrossRef]
- Lundberg, S.M.; Lee, S.I. A Unified Approach to Interpreting Model Predictions. arXiv
**2017**, arXiv:11705.07874. [Google Scholar] - Ribeiro, M.; Singh, S.; Guestrin, C. “Why Should I Trust You?” explaining the predictions of any classifier. In Proceedings of the 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Proceedings of the Demonstrations Session, NAACL-HLT 2016, San Diego, CA, USA, 12–17 June 2016; pp. 97–101. [Google Scholar]

**Figure 1.**Example of a complex image in which some nuclei cannot be clearly distinguished from the cytoplasm.

**Figure 2.**Sketch of our deterministic method (NeuronalAlg): (

**a**) preprocessing module extracts a rough segmentation of the input image; (

**b**) split and merge module as a first step for improving the previous segmentation; (

**c**) last step of the rough segmentation; (

**d**) main core of the task: neuronal method. This module improves the segmentation with a neuronal agent; (

**e**) postprocessing phase, to extract the binary mask.

**Figure 7.**Performance in terms of IoU (

**a**), F1-score (

**b**), accuracy (

**c**), sensitivity (

**d**) and specificity (

**e**) for each algorithm on the Neuroblastoma dataset.

**Figure 8.**Performances in terms of IoU (

**a**), F1-score (

**b**), Accuracy (

**c**), Sensitivity (

**d**) and Specificity (

**e**) for each algorithm on NucleusSegData dataset.

**Figure 9.**Performances in terms of IoU (

**a**), F1-score (

**b**), accuracy (

**c**), sensitivity (

**d**), and specificity (

**e**) for each algorithm on the ISBI 2009 dataset [70].

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**MDPI and ACS Style**

Giacopelli, G.; Migliore, M.; Tegolo, D.
NeuronAlg: An Innovative Neuronal Computational Model for Immunofluorescence Image Segmentation. *Sensors* **2023**, *23*, 4598.
https://doi.org/10.3390/s23104598

**AMA Style**

Giacopelli G, Migliore M, Tegolo D.
NeuronAlg: An Innovative Neuronal Computational Model for Immunofluorescence Image Segmentation. *Sensors*. 2023; 23(10):4598.
https://doi.org/10.3390/s23104598

**Chicago/Turabian Style**

Giacopelli, Giuseppe, Michele Migliore, and Domenico Tegolo.
2023. "NeuronAlg: An Innovative Neuronal Computational Model for Immunofluorescence Image Segmentation" *Sensors* 23, no. 10: 4598.
https://doi.org/10.3390/s23104598