# PolSAR Image Classification Based on Statistical Distribution and MRF

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## Abstract

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## 1. Introduction

## 2. MRF-Based Classification Models

#### 2.1. Statistical Models

#### 2.2. Mixture Strategies

#### 2.2.1. Mixture Wishart for a Whole Image

#### 2.2.2. Mixture Wishart for a Class

#### 2.2.3. Comparison of the Two Mixture Strategies

- Initialize parameter ${\mathbf{\Sigma}}_{k}$ by randomly selecting one covariance matrix from each class of the image. ${\pi}_{k}$ is initialized as 1/K.
- Compute posterior probabilities using ${\mathbf{\Sigma}}_{k}$ and ${\pi}_{k}$, then update the class labels based on the maximum a posteriori decision rule.
- Update ${\mathbf{\Sigma}}_{\mathit{k}}$ and ${\pi}_{k}$ using (4) and (5).
- Check if the classification result has converged. If not, go back to Step 2. Otherwise, the iteration ends.

- Randomly select m covariance matrices from the training samples of each class as the initialization of ${\mathbf{\Sigma}}_{m}^{k}$
**.**${\pi}_{m}^{k}$ is initialized as 1/M. - Update the parameters using (4) and (5). Note that in MWC, the parameter N denotes the number of training samples of each class.
- Construct the mixture model for each class.
- Classify the image based on the ML criterion.

#### 2.3. MRF-Based Classification Model

#### 2.3.1. MRF

#### 2.3.2. Adaptive Neighborhood System

#### 2.3.3. Edge Penalty

## 3. Classification Schemes

#### 3.1. Pixel-Based Classification

#### 3.2. Region-Based Classification

- Divide the m × n image into $I=\lceil m/r\rceil \times \lceil n/r\rceil $ regions, which are not overlapping with each other. Let $X=\left\{{x}_{a},a=1,\dots ,I\right\}$ denote the region labels.
- Calculate the mean covariance matrix ${\mathbf{\Sigma}}_{a}$ for each region.
- Use (22) to update the region boundaries.
- Check the segmentation result. If the region area is smaller than a threshold p, reassign it to the adjacent region. The parameter p decides the smallest area of a region.
- Check if the segmentation result is converged. If not, go back to Step 2. Otherwise, end the iteration, and the superpixels are obtained.
- Calculate the mean covariance matrix ${\mathbf{\Sigma}}_{a}$ of each region. Apply the ML classifier to get the final classification result.

## 4. Experiments and Discussions

#### 4.1. Test Data

#### 4.2. Pixel-Based Classification

#### 4.3. Region-Based Classification

#### 4.4. Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Classification results of the two mixture algorithms. (

**a**) Pauli color-coded image. (

**b**) Mixture Wishart for a whole image (MWW). (

**c**) mixture Wishart for a class (MWC). (

**d**) Class legend.

**Figure 3.**Schematic representation for a region neighborhood. (

**a**) Segmentation result. (

**b**) The neighborhood system for Region 5.

**Figure 4.**Polarimetric datasets used for the experiments. (

**a**) Pauli color-coded image of the Flevoland data. (

**b**) Ground truth map of Flevoland. (

**c**) Class legend. (

**d**) Pauli color-coded image of the Wallerfing data. (

**e**) Ground truth map of Wallerfing. (

**f**) Class legend. (

**g**) Pauli color-coded image of the Fujian data.

**Figure 5.**Pixel-based classification results of the Flevoland data. The first row shows the classification results, and the second row shows the corresponding classification results where the ground-truth map exists. (

**a**) Wishart-MRF (WMRF). (

**b**) K-Wishart-MRF (KMRF). (

**c**) Wishart-MRF (MWMRF). (

**d**) MWMRF model without the edge penalty term (MWMRF/e).

**Figure 6.**Pixel-based classification results for the Wallerfing data. The left column shows the classification results, and the right column shows the corresponding classification results where the ground-truth map exists. (

**a**) WMRF. (

**b**) KMRF. (

**c**) MWMRF. (

**d**) MWMRF/e.

**Figure 7.**Pixel-based classification results for the Fujian data. (

**a**) WMRF. (

**b**) KMRF. (

**c**) MWMRF. (

**d**) MWMRF/e.

**Figure 8.**Region-based segmentation and classification results of the Flevoland area. (

**a**,

**b**) Segmentation results of the whole image. (

**a**) WMRF. (

**b**) KMRF. (

**c**) Classification result with WMRF. (

**d**) Classification result with KMRF.

**Figure 9.**Region-based segmentation and classification results of the Wallerfing area. (

**a**,

**b**) Segmentation results of the whole image. (

**a**) WMRF. (

**b**) KMRF (

**c**) Classification result with WMRF. (d) Classification result with KMRF.

**Figure 10.**Region-based segmentation and classification results of the Fujian dataset. (

**a**,

**b**) Segmentation results of the whole image. (

**a**) WMRF. (

**b**) KMRF (

**c**) Classification result with WMRF. (

**d**) Classification result with KMRF.

Method | Class 1 Bare Soil | Class 2 Barely | Class 3 Lucerne | Class 4 Pea | Class 5 Potatoes | Class 6 Rape Seed | Class 7 Beet | Class 8 Wheat | OA | Kappa |
---|---|---|---|---|---|---|---|---|---|---|

WMRF | 97.56% | 95.49% | 93.83% | 94.37% | 92.51%% | 87.88% | 86.75% | 90.30% | 91.56% | 0.9005 |

KMRF | 97.58% | 95.41% | 94.10% | 94.51% | 92.39% | 89.29% | 88.35% | 90.94% | 92.12% | 0.9071 |

MWMRF | 97.59% | 97.74% | 95.64% | 95.71% | 95.49% | 98.03% | 93.25% | 96.74% | 96.44% | 0.9580 |

MWMRF/e | 97.37% | 97.62% | 95.00% | 95.47% | 94.97% | 97.33% | 92.65% | 96.35% | 96.02% | 0.9530 |

Method | Class1 Barley | Class 2 Corn | Class 3 Potatoes | Class 4 Sugar Beet | Class 5 Wheat | OA | Kappa |
---|---|---|---|---|---|---|---|

WMRF | 88.31% | 73.44% | 58.81% | 79.95% | 92.38% | 82.25% | 0.7563 |

KMRF | 88.24% | 74.27% | 61.59% | 79.76% | 92.19% | 82.47% | 0.7609 |

MWMRF | 90.47% | 79.15% | 63.30% | 83.79% | 92.72% | 84.40% | 0.7854 |

MWMRF/e | 86.13% | 79.12% | 48.98% | 84.24% | 95.13% | 84.04% | 0.7783 |

Method | Class 1 Bare Soil | Class 2 Barely | Class 3 Lucerne | Class 4 Pea | Class 5 Potatoes | Class 6 Rape Seed | Class 7 Beet | Class 8 Wheat | OA | Kappa |
---|---|---|---|---|---|---|---|---|---|---|

WMRF | 99.64% | 95.35% | 91.87% | 90.77% | 99.95% | 93.00% | 93.00% | 88.59% | 93.46% | 0.9231 |

KMRF | 97.01% | 87.37% | 84.69% | 89.58% | 89.41% | 98.24% | 87.63% | 87.93% | 90.45% | 0.8879 |

Method | Class1 Barley | Class 2 Corn | Class 3 Potatoes | Class 4 Sugar Beet | Class 5 Wheat | OA | Kappa |
---|---|---|---|---|---|---|---|

WMRF | 86.41% | 75.40% | 70.91% | 84.20% | 89.29% | 83.62% | 0.7763 |

KMRF | 86.03% | 75.07% | 70.10% | 82.10% | 89.57% | 83.20% | 0.7706 |

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**MDPI and ACS Style**

Yin, J.; Liu, X.; Yang, J.; Chu, C.-Y.; Chang, Y.-L.
PolSAR Image Classification Based on Statistical Distribution and MRF. *Remote Sens.* **2020**, *12*, 1027.
https://doi.org/10.3390/rs12061027

**AMA Style**

Yin J, Liu X, Yang J, Chu C-Y, Chang Y-L.
PolSAR Image Classification Based on Statistical Distribution and MRF. *Remote Sensing*. 2020; 12(6):1027.
https://doi.org/10.3390/rs12061027

**Chicago/Turabian Style**

Yin, Junjun, Xiyun Liu, Jian Yang, Chih-Yuan Chu, and Yang-Lang Chang.
2020. "PolSAR Image Classification Based on Statistical Distribution and MRF" *Remote Sensing* 12, no. 6: 1027.
https://doi.org/10.3390/rs12061027