# A Multi-Agent Deep Reinforcement Learning Approach for Enhancement of COVID-19 CT Image Segmentation

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## Abstract

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## 1. Introduction

- Manual extraction and quality control take hours to process an image.
- Classical or manual labeling, at the pixel level, consumes a lot of time.
- The class discrepancy in the image datasets varies greatly, which may result in unwanted influences in the learned methods.

- Introducing an effective system to enhance semantic segmentation by modifying the traditional Deep-Q-Network to learn superior mask extraction compared to the most advanced methods.
- Proposing a multi-agent reinforcement learning (MARL) framework to extract COVID-19 masks automatically to improve the efforts of CT experts and enhance the potential of lung CT segmentation. We selected learning in the Markov decision process (MDP) to find optimal approaches in mask extraction for CT experts.
- Reducing the waiting time for experts to obtain masks manually, by introducing an alternative automatic approach.

## 2. Related Works

## 3. The Proposed Semantic Segmentation Environment

#### 3.1. RL Architecture for Mask Extraction

#### 3.2. Structural Properties of MAS_SEG

#### 3.3. The MAS Q-Learning Algorithm and the ε-Greedy Strategy

- ${S}_{c}$, ${A}_{c}$, ${R}_{c}$, and ${Q}_{c}$ represent respectively the state, action, reward, and Q-value on the Cth episode.
- $\alpha c\in \left[0,1\right]$ is the learning factor of the Cth episode.
- $\gamma \in \left[0,1\right]$ is the discount factor.
- α indicates the weight the system gives to new rewards by discounting the long-term $Q$ value.
- γ is the factor that reduces the contribution of max, which is the maximum Q-value expected in the new state.

_{ep}, S

_{ep}which respectively represent the Q-value and the state of the current episode ‘ep’.

_{C}is the number of merges (fusion) at the Cth episode, m is the reward quantization factor and is expressed as $m={N}_{f}-{N}_{rf}$. $Pa{p}_{C}^{q}$ is the agent approval with a Q-matrix containing the q-values of the state-action combinations at the Cth episode. The Q values are initially set to zero.

#### 3.4. Role of the Supervisor Agent

- Regional agents that cooperate.
- A supervisor agent, which incorporates a neural network to manage the interactions of the MAS agents and subsequently participates in the learning of the mask detector.

Algorithm 1. QL_MAS |

Initialize: The capacity Cap of the memory M, the values Q: ∀r, a|Q (r, a) = 0, The estimation weight LSTM-DQN θ = θ_0, the weight of the LSTM-DQN objectives θ′ For episode = 1 → ep do # ep represents the number of episodes Fix the initial positions of the agents according to the map from the RAG For i = 1 -> Reg do # Reg is the number of regions #N is the number of agents N = Reg Implement in each Reg i an agent A _{i}End for Do as long as t < Cap For j = 1 -> N do Calculation of the initial actions (2) Calculation of initial Q-value (1) Verification of the best adjacent neighbors satisfying the similarity criteria Negotiation to decide the optimal proposal End for Fusion Update of the map of the regions Update Reg N = Reg For j = 1 -> N do Calculation of the actions (2) Calculation of Q-value (1) Calculation of reward (4) Next state calculation (3) Save data d = {state(t), action(t), R(t), state(t + 1)} in memory M End for End Do Reset End for |

#### 3.5. Region Generation Proposal

- The first output determines whether the anchor is in the foreground or background. If it is a foreground, it suggests there is an object in the rectangle.
- If the item is not properly located in the middle of the rectangle, the second output (error) is triggered to adjust the bounding box to best fit the detected object.

#### 3.6. Markov Decision Process for Masking

- The MD is trained using a subset of the TMc mask class collection to guarantee the active learning set for several episodes and learn a good acquisition function that maximizes performance with a budget of regions $B$.
- The MD network is tested on a separate $Ev$ subset.
- To calculate the reward, we employ a different $RMc$ subset.
- The state representation is built using the $SMc$ set.

- The state lst is calculated according to the value of the function F iteration t ‘$Ft$’ and $SMc$.
- A controlled action space is constructed with $K$ group ${G}_{t}^{k}$ with $N$ regions, sampled uniformly from the processed set $D$. For every single region within each cluster, we calculate its sub-actions representation $l{a}_{t}^{k,n}$.
- The MD, RL agent, selects K sub-actions ${\left\{l{a}_{t}^{k}\right\}}_{k=1}^{K}$ using ε-greedy (greedy policy). Respectively, each single sub-action $l{a}_{t}^{k}$ is defined as the selection of a region $lrk$ (on $N$) to be processed from a set ${G}_{t}^{k}$.
- A designation of the region masks is made, then the sets are updated: $M{c}_{t+1}=M{c}_{t}\cup {\left\{r{1}_{k}\right\}}_{k=1}^{K}$ (adding the new mask images in Mc) and ${D}_{t+1}={D}_{t}/{\left\{r{1}_{k}\right\}}_{k=1}^{K}$ (removing these regions from set D).
- The MD agent is trained through one iteration on the newly added regions ${\left\{l{r}_{t}^{k}\right\}}_{k=1}^{K}$.
- RL receives the award rt+1 as the variation in performance between $lft+1$ and $lft$ on $RMc$.

#### 3.7. State Representation

#### 3.8. Action Representation

#### 3.9. Mask-Detector (MD)

## 4. Results and Discussion

#### 4.1. Dataset Collection

- COVID-19-A: the public TCIA dataset [61] containing many CT lung scans (for non-COVID-19 subjects). These data are used for the training phase. The mask detector studies these images to learn the thoracic characteristics.
- COVID-19-B: The public dataset of Ma et al. [62], which consists of annotated volumes of CT images (COVID-19), for network training. The scans were obtained via the Coronacases initiative and the Radiopaedia database.
- COVID-19-C: publicly available database with thoracic CT images [63]. (These data are used for the test phase.)
- COVID-19-D: A collection of 3D CT images of 10 confirmed COVID-19 cases, which are made available online by the Coronacases initiative [64]. (These data are used for the test phase).

#### 4.2. Evaluation Metrics

#### 4.3. Evaluation of the DRL System

- $\mathrm{Ea}$ is the uniform random selection of areas to be labeled from all potential regions in the dataset at each phase;
- $\mathrm{Ei}\text{}$ is an uncertainty sampling approach that picks voxel-level areas with the highest cumulative Shannon entropy;
- $\mathrm{Eb}$ chooses locations with the highest cumulative BALD measure at the pixel level [65].

#### 4.4. Comparison with State-of-the-Art Methods

## 5. Conclusions and Future Works

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Overview of the proposed method: 1. A complete mask extraction is processed using the automatic COVID-19 mask extraction system. 2. The adopted segmentation network is trained using the obtained masks. 3. The segmentation network can segment CT images and provide strong predictions. Coronavirus disease, COVID-19.

**Figure 2.**Architecture for Tree-dimensional mask extraction using Reinforcement learning. Three-dimensional, (3D).

**Figure 7.**Examples of visualized segmentation results. The red, green, and blue colors respectively denote the left lung, the right lung, and the infection.

**Figure 8.**Performance evaluation of methods with an increasingly active learning budget ((

**a**) the test performance variations; (

**b**) the validation performance variations).

DataSet | %Slice with Infection |
---|---|

COVID-19-A [61] | _ |

COVID-19-B [62] | 100% |

COVID-19-C [63] | 44.9% |

COVID-19-D [64] | 52.3% |

Metrics | Formulas | Description |
---|---|---|

Accuracy (ACC) | $\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}}$ | The ratio of correctly predicted pixels to the total number of pixels in the processed image. |

Precision (P_{c}) | $\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}$ | The ratio of correctly predicted lesion pixels to the total of expected lesion pixels. |

Sensitivity (Sen) | $\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}$ | The ratio of the correctly predicted lesion pixels to the total number of real lesion pixels. |

F1 score (F1) | $2.\frac{\mathrm{Precision}.\mathrm{Recall}}{\mathrm{Precision}+\mathrm{Recall}}$ | The ratio obtained from a combination of both precision and sensitivity results. |

Specificity (S_{p}) | $\frac{\mathrm{TN}}{\mathrm{TN}+\mathrm{FP}}$ | The ratio of correctly predicted normal pixels to the total number of actual normal pixels. |

Dice coefficient (DC) | $\frac{2.\left(\mathrm{X}\cap \mathrm{Y}\right)}{\mathrm{X}+\mathrm{Y}}$ | The similarity between the method output (Y) and the ground truth (X). |

Structural metric (S_{m}) | Sm = (1 − β).Sos(Sop,Sgt) + β.Sor(Sop,Sgt) | The structural similarity between the prediction map and ground truth mask. |

Mean Absolute Error (MAE) | $\mathrm{MAE}=\frac{1}{\mathrm{w}.\mathrm{h}}$ ∑wi∑hj|Sop(i,j) − Sgt(i,j)| | Measures the pixel-wise difference. |

ACC | DC | Sen | Sp | Pc | F1 | Sm | MAE | |
---|---|---|---|---|---|---|---|---|

Our approach | 0.9712 | 0.8081 | 0.7997 | 0.9948 | 0.8621 | 0.8301 | 0.8438 | 0.0086 |

U-Net++ [43] | 0.9687 | 0.7972 | 0.7845 | 0.9952 | 0.8437 | 0.8206 | 0.8623 | 0.0085 |

COVNet [42] | 0.9698 | 0.7754 | 0.7400 | 0.9959 | 0.8470 | 0.7930 | 0.8334 | 0.0094 |

DeCoVNet [39] | 0.9697 | 0.8020 | 0.8106 | 0.9962 | 0.8347 | 0.8116 | 0.8511 | 0.0107 |

AlexNet [20] | 0.8900 | 0.6910 | 0.8110 | 0.9930 | 0.9500 | 0.8062 | 0.8475 | 0.0125 |

ResNet [18] | 0.8984 | 0.7408 | 0.7608 | 0.9937 | 0.7549 | 0.7558 | 0.8080 | 0.0157 |

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Allioui, H.; Mohammed, M.A.; Benameur, N.; Al-Khateeb, B.; Abdulkareem, K.H.; Garcia-Zapirain, B.; Damaševičius, R.; Maskeliūnas, R. A Multi-Agent Deep Reinforcement Learning Approach for Enhancement of COVID-19 CT Image Segmentation. *J. Pers. Med.* **2022**, *12*, 309.
https://doi.org/10.3390/jpm12020309

**AMA Style**

Allioui H, Mohammed MA, Benameur N, Al-Khateeb B, Abdulkareem KH, Garcia-Zapirain B, Damaševičius R, Maskeliūnas R. A Multi-Agent Deep Reinforcement Learning Approach for Enhancement of COVID-19 CT Image Segmentation. *Journal of Personalized Medicine*. 2022; 12(2):309.
https://doi.org/10.3390/jpm12020309

**Chicago/Turabian Style**

Allioui, Hanane, Mazin Abed Mohammed, Narjes Benameur, Belal Al-Khateeb, Karrar Hameed Abdulkareem, Begonya Garcia-Zapirain, Robertas Damaševičius, and Rytis Maskeliūnas. 2022. "A Multi-Agent Deep Reinforcement Learning Approach for Enhancement of COVID-19 CT Image Segmentation" *Journal of Personalized Medicine* 12, no. 2: 309.
https://doi.org/10.3390/jpm12020309