# An Application of Pixel Interval Down-Sampling (PID) for Dense Tiny Microorganism Counting on Environmental Microorganism Images

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## Abstract

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## 1. Introduction

- We propose PID-Net for dense tiny object counting. MaxPooling and pixel interval down-sampling are concatenated as down-sampling to extract spatial local and global features.
- The operation of max-pooling may lose some local features of tiny objects while segmentation, and the edge lines may not be connected after max-pooling. However, the PID-Net can cover a more detailed region.
- The proposed PID-Net achieves better counting performance than other models on the EM (yeast) counting task.

## 2. Related Work

#### 2.1. Classical Counting Methods

#### 2.2. Machine-Learning-Based Counting Methods

## 3. PID-Net-Based Yeast Counting Method

#### 3.1. Basic Knowledge of SegNet

#### 3.2. Basic Knowledge of U-Net

#### 3.3. The Structure of PID-Net

#### 3.4. Counting Approach

## 4. Experiments

#### 4.1. Experimental Setting

#### 4.1.1. Image Dataset

#### 4.1.2. Training, Validation and Test Data Setting

#### 4.1.3. Experimental Environment

#### 4.1.4. Hyper Parameters

#### 4.2. Evaluation Metrics

#### 4.3. Evaluation of Segmentation and Counting Performance

#### 4.3.1. Comparison of Different Down-Sampling Methods

#### 4.3.2. Comparison with Other Methods

#### 4.4. Repeatability Tests

#### 4.5. Computational Time

#### 4.6. Discussion

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PID-Net | pixel interval down-sampling network |

CNN | convolutional neural network |

EMs | environmental microorganisms |

SVM | support vector machine |

PCA | principal-component analysis |

BPNN | back propagation neural network |

ANN | artificial neural network |

ReLU | rectified linear unit |

Adam | adaptive moment estimation |

SGD | stochastic gradient descent |

NGD | natural gradient descent |

GT | ground truth |

FC | fully connected |

IoU | intersection over union |

TP | true positive |

TN | true negative |

FP | false positive |

FN | false negative |

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**Figure 4.**The images in yeast cell dataset. (

**a**) The original yeast image and (

**b**) the corresponding ground truth images.

Category | Subcategory | Related Work |
---|---|---|

Thresholding-Based Methods | [35,36,37] | |

Classical Methods | Edge Detection-based Methods | [38,39,40] |

Watershed-Based Methods | [41,42,43,44] | |

Hough Transformation | [45,46,47] | |

Machine-Learning-Methods | Classical Machine-Learning-Based Methods | [48,49,50,51] |

Deep-Learning-Based Methods | [52,53,54,55] |

**Table 2.**The definitions of evaluation metrics. CA and HD are abbreviations of the Counting Accuracy and Hausdorff Distance, respectively.

Metric | Definition | Metric | Definition |
---|---|---|---|

Accuracy | $\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}}$ | Dice | $\frac{2\times |{V}_{pred}\bigcap {V}_{GT}|}{|{V}_{pred}|+|{V}_{GT}|}$ |

Jaccard | $\frac{|{V}_{pred}\bigcap {V}_{GT}|}{|{V}_{pred}\bigcup {V}_{GT}|}$ | Precision | $\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}$ |

CA | $1-\frac{|{N}_{pred}-{N}_{GT}|}{{N}_{GT}}$ | HD | ${d}_{H}(X,Y)=max(su{p}_{x\in X}in{f}_{y\in Y}d(x,y),su{p}_{y\in Y}in{f}_{x\in X}d(x,y))$ |

**Table 3.**The average segmentation evaluation indices of predicted images. A, D, J, P, C and H are abbreviations of the Accuracy, Dice, Jaccard, Precision, Counting Accuracy (in %) and Hausdorff Distance (in pixels/per image), respectively.

Methods | A | D | J | P | C | H |
---|---|---|---|---|---|---|

PID-Net | 97.51 | 95.86 | 92.10 | 96.02 | 96.97 | 4.6272 |

PID-Net-M1 | 96.90 | 94.71 | 90.05 | 94.71 | 67.84 | 5.0110 |

PID-Net-M2 | 97.42 | 95.75 | 91.89 | 95.68 | 96.88 | 4.7204 |

**Table 4.**The average segmentation evaluation indices of predicted images. A, D, J, P, C and H are abbreviations of the Accuracy, Dice, Jaccard, Precision, Counting Accuracy (in %) and Hausdorff Distance (in pixels/per image), respectively.

Methods | A | D | J | P | C | H |
---|---|---|---|---|---|---|

PID-Net | 97.51 | 95.86 | 92.10 | 96.02 | 96.97 | 4.6272 |

SegNet | 94.69 | 90.34 | 84.02 | 88.50 | 68.82 | 6.3604 |

YeaZ (in [77]) | - | 94.00 | - | - | - | - |

U-Net | 97.47 | 95.71 | 91.84 | 95.62 | 91.33 | 4.6666 |

Attention U-Net | 96.62 | 93.36 | 88.96 | 92.67 | 83.44 | 5.1184 |

Trans U-Net | 96.84 | 93.60 | 88.99 | 93.25 | 91.32 | 5.0715 |

Swin U-Net | 96.47 | 92.99 | 88.32 | 92.43 | 91.95 | 5.3140 |

Hough | 82.12 | 61.12 | 44.74 | 88.26 | 73.66 | 9.2486 |

Otsu | 84.23 | 65.71 | 49.90 | 87.66 | 74.34 | 8.9165 |

Watershed | 78.67 | 50.15 | 34.88 | 78.61 | 63.34 | 9.6873 |

**Table 5.**The evaluation indices of Repeatability Tests. A, D, J, P, C and H are abbreviations of the Accuracy, Dice, Jaccard, Precision, Counting Accuracy (in %) and Hausdorff Distance (in pixels/per image), respectively.

Methods | A | D | J | P | C | H |
---|---|---|---|---|---|---|

PID-Net | 97.51 | 95.86 | 92.10 | 96.02 | 96.97 | 4.6272 |

PID-Net (Re 1) | 97.51 | 95.79 | 91.97 | 95.91 | 95.26 | 4.5865 |

PID-Net (Re 2) | 97.33 | 95.59 | 91.62 | 95.70 | 96.25 | 4.7290 |

PID-Net (Re 3) | 97.54 | 95.91 | 92.18 | 96.21 | 96.82 | 4.6023 |

PID-Net (Re 4) | 97.37 | 95.64 | 91.70 | 95.70 | 95.51 | 4.7471 |

PID-Net (Re 5) | 97.43 | 95.66 | 91.73 | 92.24 | 96.26 | 4.6395 |

Model | Training Time | Mean Training Time | Test Time | Mean Test Time |
---|---|---|---|---|

PID-Net | 10,438.86 | 7.10 | 454.68 | 0.93 |

U-Net | 6198.00 | 4.21 | 257.64 | 0.53 |

Swin-UNet | 7884.36 | 5.36 | 319.50 | 0.65 |

Att-UNet | 6983.58 | 4.75 | 296.64 | 0.61 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Zhao, X.; Jiang, T.; Rahaman, M.M.; Yao, Y.; Lin, Y.-H.; Zhang, J.; Pan, A.; Grzegorzek, M.; Li, C.
An Application of Pixel Interval Down-Sampling (PID) for Dense Tiny Microorganism Counting on Environmental Microorganism Images. *Appl. Sci.* **2022**, *12*, 7314.
https://doi.org/10.3390/app12147314

**AMA Style**

Zhang J, Zhao X, Jiang T, Rahaman MM, Yao Y, Lin Y-H, Zhang J, Pan A, Grzegorzek M, Li C.
An Application of Pixel Interval Down-Sampling (PID) for Dense Tiny Microorganism Counting on Environmental Microorganism Images. *Applied Sciences*. 2022; 12(14):7314.
https://doi.org/10.3390/app12147314

**Chicago/Turabian Style**

Zhang, Jiawei, Xin Zhao, Tao Jiang, Md Mamunur Rahaman, Yudong Yao, Yu-Hao Lin, Jinghua Zhang, Ao Pan, Marcin Grzegorzek, and Chen Li.
2022. "An Application of Pixel Interval Down-Sampling (PID) for Dense Tiny Microorganism Counting on Environmental Microorganism Images" *Applied Sciences* 12, no. 14: 7314.
https://doi.org/10.3390/app12147314