# Shadow Enhancement Using 2D Dynamic Stochastic Resonance for Hyperspectral Image Classification

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dynamic Stochastic Resonance

#### 2.2. Convolutional Neural Network

#### 2.3. Two-Dimensional DSR Shadow Enhancement for Hyperspectral Image Classification by CNN Embedded with Multiple Attention Mechanisms

#### 2.3.1. Two-Dimensional Dynamic Stochastic Resonance

#### 2.3.2. Three-Dimensional Convolutional Neural Network with Multiple Attention Mechanisms

#### 2.3.3. The Procedure of the Proposed MAM-3DCNN

## 3. Experiment

#### 3.1. Dataset

#### 3.2. Parameter Setting

#### 3.2.1. Setup of 2D DSR Parameters

#### 3.2.2. Parameter Setting of MAM-3DCNN

#### 3.3. Experimental Results

#### 3.3.1. Shadow Enhancement by 2D DSR

#### 3.3.2. Classification Results

## 4. Discussion

#### 4.1. Analysis of 2D DSR Effect on Shadow Enhancement

#### 4.2. The Classification Performance Discussion of Considered Measures

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The main structure of the CNN. Conv1 and Conv2 represent Convolutional Layers 1 and 2. Pooling1 and Pooling2 stand for Pooling Layers 1 and 2.

**Figure 4.**The iterative process of 2D DSR on the k-th band of the HSI. A $2\times 2$ window is used to slide the sampling. The dashed lines of different types represent relevant pixels involved in updating the enhancement value of a pixel through Equation (11). The ①,…, ④ correspond to the relationship between the pixels in the first to fourth sub-formulas in Equation (12). $I\times J$ represents the size of the data in each band of the HSI.

**Figure 5.**The main structure of the proposed MAM-3DCNN. The size of the convolutional kernel is $3\times 3\times 3$, and the 8 3DConv means 3D convolution with 8 convolutional kernels. GAP is the global average pooling. ⊗ denotes the positionwise dot product. The 256 FC1 is the 1st fully connected layer with 256 neurons.

**Figure 6.**The specific structure of ECA. The input feature maps’ height and width are represented by H and W, and C is the number of channels. p represents the required adjacent channels to obtain the cross-channel interaction information of each channel and can be adaptively determined via a mapping of C. Sigmoid is the activation function.

**Figure 7.**The basic structure of the CBAM. The channel attention module assesses the importance of each channel and gives the input channels the corresponding weights, and the spatial attention offers different attention to pixels in each channel according to the significance.

**Figure 8.**The detailed structure of the CA and SA in the CBAM. The $H\times W\times C$ represents the data with the H height, W width, and C channels. r is the compression ratio. ⊕ denotes elementwise summation. Mean and Max represent the average pooling and maximum pooling. Concat means feature fusion.

**Figure 11.**Comparison of classification accuracy under different rs. The best result of the OA, AA, and Kappa can be obtained when r = 1.

**Figure 12.**The ${1}^{ST}$ band of HYDICE enhanced by 1D and 2D DSR. (

**a**) Original HYDICE; (

**b**) 1D DSR; (

**c**) 2D DSR.

**Figure 13.**Classification results: (

**a**) 2DCNN; (

**b**) GAB-2DCNN; (

**c**) MAM-2DCNN; (

**d**) 3DCNN; (

**e**) GAB-3DCNN; (

**f**) CBAM-3DCNN; (

**g**) SE-3DCNN; (

**h**) DA-3DCNN; (

**i**) ECA-3DCNN; (

**j**) DECA-3DCNN; (

**k**) ECA-CBAM-3DCNN; (

**l**) MAM-3DCNN.

**Figure 14.**Comparison of spectral curves. Solid, dashed, and dotted lines represent the spectral curves of road and grass not in the shadow area, in the shadow areas, and after enhancement, respectively. (

**a**) Spectral curves of road. (

**b**) Spectral curves of grass.

**Table 1.**Information of the ground truth. The labels, sample number, and represented colors for each category in the ground truth are displayed.

Number | Color | Sample | Label |
---|---|---|---|

1 | 33,184 | Grass | |

2 | 10,850 | Tree | |

3 | 3376 | Road | |

4 | 1686 | Road in shadow | |

5 | 323 | Grass in shadow | |

6 | 537 | Target 1 | |

7 | 514 | Target 2 | |

8 | 4135 | Target 3 |

Layer | Kernel | Kernel Size | Activation | Dropout | ||
---|---|---|---|---|---|---|

3DConv | 8 | 3 × 3 × 3 | Relu | - | ||

MAM | ECA1 | 1DConv | 1 | p = 3 | Sigmoid | - |

ECA2 | 1DConv | 1 | p = 3 | Sigmoid | - | |

CBAM | FC3/FC5 (3DConv) | 8 | 1 × 1 × 1 | Relu | - | |

FC4/FC6 (3DConv) | 8 | 1 × 1 × 1 | - | - | ||

3DConv | 1 | 3 × 3 × 3 | Sigmoid | - | ||

FC1 | 256 | - | Relu | 0.6 | ||

FC2 | 128 | - | Relu | 0.5 |

Name | Setting |
---|---|

Window size | 11 |

Test ratio | 0.8 |

Learning rate | 0.001 |

Optimizer | Adam |

Epoch | 100 |

Loss function | Categorical cross-entropy |

Data | Original | Enhanced by 1D DSR | Enhanced by 2D DSR |
---|---|---|---|

OA | 96.5388 | 97.0277 | 97.3508 |

AA | 89.8357 | 89.8990 | 91.0473 |

Kappa | 94.0936 | 94.7531 | 95.4368 |

**Table 5.**Classification accuracy of the considered methods. The 2DCNN and 3DCNN with different attention modules are included.

Method | 2D CNN | GAB- 2DCNN | MAM- 2DCNN | 3D CNN | GAB- 3DCNN | CBAM- 3DCNN | SE- 3DCNN | DA- 3DCNN | ECA- 3DCNN | DECA- 3DCNN | ECA- CBAM- 3DCNN | MAM- 3DCNN |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Grass | 0.9900 | 0.9900 | 0.9900 | 0.9900 | 0.9900 | 0.9900 | 0.9900 | 0.9900 | 0.9900 | 0.9900 | 0.9900 | 0.9900 |

Tree | 0.9725 | 0.9700 | 0.9750 | 0.9820 | 0.9840 | 0.9860 | 0.9820 | 0.9800 | 0.9860 | 0.9860 | 0.9855 | 0.9869 |

Road | 0.9550 | 0.9600 | 0.9645 | 0.9700 | 0.9740 | 0.9720 | 0.9740 | 0.9680 | 0.9680 | 0.9690 | 0.9695 | 0.9700 |

Road in shadow | 0.7925 | 0.8260 | 0.8320 | 0.8820 | 0.8420 | 0.8620 | 0.8560 | 0.8560 | 0.8520 | 0.8520 | 0.8430 | 0.8538 |

Grass in shadow | 0.8975 | 0.8960 | 0.9020 | 0.9440 | 0.9220 | 0.9180 | 0.9240 | 0.9160 | 0.9280 | 0.9120 | 0.9120 | 0.9138 |

Target 1 | 0.8425 | 0.8760 | 0.8946 | 0.8920 | 0.8760 | 0.8940 | 0.8840 | 0.8720 | 0.8840 | 0.8856 | 0.8860 | 0.9008 |

Target 2 | 0.6625 | 0.6920 | 0.7220 | 0.7180 | 0.6260 | 0.7060 | 0.6340 | 0.6020 | 0.6420 | 0.6650 | 0.7130 | 0.7623 |

Target 3 | 0.8775 | 0.8520 | 0.8600 | 0.9060 | 0.9320 | 0.9320 | 0.9200 | 0.9180 | 0.9260 | 0.9200 | 0.9230 | 0.9346 |

OA (%) | 96.4257 | 96.4329 | 96.7200 | 97.3508 | 97.4475 | 97.5317 | 97.3340 | 97.2464 | 97.4746 | 97.5021 | 97.5334 | 97.6698 |

AA (%) | 87.2958 | 88.3053 | 88.5750 | 91.0473 | 89.3490 | 90.7666 | 89.6266 | 88.7892 | 89.8707 | 89.8806 | 90.1023 | 90.9980 |

Kappa (%) | 93.8280 | 93.8515 | 94.4820 | 95.4368 | 95.5951 | 95.7482 | 95.4046 | 95.2485 | 95.5757 | 95.5780 | 95.7650 | 95.9789 |

**Table 6.**Classification of the original and 2D-DSR-enhanced HYDICE by methods based on the GNN and GAN.

Evaluation | 3D-GAN | MARP-GNN | MAM-3DCNN | |||
---|---|---|---|---|---|---|

HYDICE | 2D DSR | HYDICE | 2D DSR | HYDICE | 2D DSR | |

OA (%) | 96.22 | 97.02 | 96.44 | 97.38 | 96.83 | 97.67 |

AA (%) | 87.33 | 90.13 | 88.50 | 90.35 | 89.61 | 91.00 |

Kappa (%) | 93.49 | 94.36 | 94.55 | 95.13 | 94.52 | 95.98 |

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## Share and Cite

**MDPI and ACS Style**

Liu, Q.; Fu, M.; Liu, X.
Shadow Enhancement Using 2D Dynamic Stochastic Resonance for Hyperspectral Image Classification. *Remote Sens.* **2023**, *15*, 1820.
https://doi.org/10.3390/rs15071820

**AMA Style**

Liu Q, Fu M, Liu X.
Shadow Enhancement Using 2D Dynamic Stochastic Resonance for Hyperspectral Image Classification. *Remote Sensing*. 2023; 15(7):1820.
https://doi.org/10.3390/rs15071820

**Chicago/Turabian Style**

Liu, Qiuyue, Min Fu, and Xuefeng Liu.
2023. "Shadow Enhancement Using 2D Dynamic Stochastic Resonance for Hyperspectral Image Classification" *Remote Sensing* 15, no. 7: 1820.
https://doi.org/10.3390/rs15071820