# Semi-Supervised Deep Learning for Lunar Crater Detection Using CE-2 DOM

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## Abstract

**:**

## 1. Introduction

## 2. Data Preparation

#### 2.1. Data Set Selection

#### 2.2. Data Set Labeling

- The diameter of a sample crater is no more than 1000 m.
- The shadow direction of any given crater in the same area is consistent, as a dome has opposite shadow direction in the same area at the same time.

^{2}Then, the labeled data were used to generate training and validation images. First, considering that the data should cover all kinds of craters, we sub-sampled the data of the four areas ten times and obtained eight images in total. Secondly, each image of the area was divided into a number of 512 pixel × 512 pixel image blocks, in order to speed up the model training and detection. Finally, pseudo-color images were constructed, in order to obtain the number of craters per image and to distinguish overlapping craters. In Figure 4, each crater contributes to an index value, such that the maximum value of the index is the number of craters in the image block.

#### 2.3. CE-2 DOM Comparison in Highland and Maria

## 3. Methods

#### 3.1. Mask R-CNN and No-Mask R-CNN Used for Crater Detection

#### 3.2. Crater R-CNN

#### 3.3. Two-Teachers Self-Training with Noise (TTSN)

Algorithm 1: Two-Teachers Self-training with Noise. |

Data: Incomplete labeled images divided into $\{({x}_{1},{y}_{1}),({x}_{2},{y}_{2}),\cdots ,({x}_{\frac{n}{2}},{y}_{\frac{n}{2}})\}$and $\left\{\right({x}_{\frac{n}{2}+1},{y}_{\frac{n}{2}+1)},({x}_{\frac{n}{2}+1},{y}_{\frac{n}{2}+1)},\cdots ,({x}_{n},{y}_{n})\}$. Step 1: Train the teacher models ${\mathsf{\Theta}}_{1}^{t}$ and ${\mathsf{\Theta}}_{2}^{t}$, which minimize the cross-entropy loss and smooth L${}_{1}$ loss on incomplete labeled images: $\frac{2}{n}{\sum}_{i=1}^{\frac{n}{2}}{l}_{cross}({y}_{i},f({x}_{i},noise))+\frac{2}{n}{\sum}_{i=1}^{\frac{n}{2}}{l}_{{L}_{1}}({y}_{i},f({x}_{i},noise))$, $\frac{2}{n}{\sum}_{i=\frac{n}{2}+1}^{n}{l}_{cross}({y}_{i},f({x}_{i},noise))+\frac{2}{n}{\sum}_{i=\frac{n}{2}+1}^{n}{l}_{{L}_{1}}({y}_{i},f({x}_{i},noise))$. Step 2: Use two normal (i.e., non-noisy) teacher models to generate pseudo-labels. The new pseudo-labels with confidence level higher than $\delta $ are selected and fused with manual labels. Here, $\delta $ indicates a confidence of 0.75. $\tilde{y}={({f}_{model}\left({x}_{i}\right)>\delta )}_{new}+y$ Step 3: Train a better student model, ${\mathsf{\Theta}}_{s}$, which minimizes the cross-entropy loss and smooth L${}_{1}$ loss on labeled and pseudo-labeled images. $\frac{1}{n}{\sum}_{i=1}^{n}{l}_{cross}({\tilde{y}}_{i},f({x}_{i},noise))+\frac{1}{n}{\sum}_{i=1}^{n}{l}_{{L}_{1}}({\tilde{y}}_{i},f({x}_{i},noise))$ |

#### 3.4. Model Training

## 4. Results

#### 4.1. Crater Detection Post-Processing

#### 4.2. Accuracy Evaluation

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Sample Availability

## Abbreviations

DEM | Digital Elevation Model |

DOM | Digital Orthophoto Map |

CE-2 | Chang’E-2 |

LRO | Lunar Reconnaissance Orbiter |

CDA | Crater Detection Algorithm |

## Appendix A

## References

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**Figure 2.**Labeled craters in four areas: (

**a**) Equatorial area (R1), with 8632 craters; (

**b**) high-latitude area (R2), with 8857 craters; (

**c**) Maria area (R3), with 14,501 craters; and (

**d**) Highland area (R4), with 6131 craters.

**Figure 3.**Labeled craters size-frequency distributions represented as CSFD plots, for our training areas.

**Figure 4.**Image and pseudo-color image: (

**a**) Original DOM image; and (

**b**) labeled crater samples with pseudo-color.

**Figure 9.**Illustration of the Two-Teachers Self-training with Noise model: Line 1 trains noisy data set 1 and obtains teacher model 1, which is then used to predict the noiseless data set 2. Line 2 trains noisy data set 2 and obtains teacher model 2, which is then used to predict noiseless data set 1. Finally, the output of the two is fused with the original labels and used to train the student model.

**Figure 10.**Distribution of the number of craters detected by Mask R-CNN, no-Mask R-CNN, Crater R-CNN, Crater R-CNN with TTSN, and manual labeling: (

**a**) Highland; and (

**b**) Maria.

**Figure 11.**Difference between no-Mask R-CNN and Crater R-CNN with TTSN. The detection results of Crater R-CNN with TTSN (

**a**) and no-Mask R-CNN (

**b**) are shown. It can be seen that the crater size detected by no-Mask R-CNN was larger than the actual crater size, and the number of detections was also smaller than that of Crater R-CNN with TTSN.

**Figure 12.**Detection accuracy under different radii: (

**a**–

**c**) show the precision, recall, and F${}_{1}$ of the four methods in whole test set, respectively.

**Figure 13.**Distribution of craters detected by Crater R-CNN with TTSN in Highland (

**a**) and Maria (

**b**) regions: Green, true positives; red, false positives; blue, true negatives.

**Figure 14.**Difference between Mask R-CNN and Crater R-CNN with TTSN: (

**a**,

**b**), Mask R-CNN in Highland and Maria; (

**c**,

**d**), Crater R-CNN with TTSN in Highland and Maria.

Year | Author | Count | Minimum Diameter (km) | Methods |
---|---|---|---|---|

1935 | Mary Blagg [7] | 677 | 50 | manual |

1965 | D. W. G. Arthur [8,9,10,11] | 17,000 | 3.5 | manual |

1978 | Wood [12] | 11,500 | 7 | manual |

1985 | Rodionova [13] | 14,923 | 10 | manual |

2010 | Head [14] | 5185 | 20 | manual |

2013 | Goran Salamunićcar [15] | 78,287 | 8 | CDA |

2015 | Öhman [16] | 8716 | 1 | manual |

2015 | Wang Jiao [17] | 106,030 | 0.5 | manual |

2018 | Povilaitis [18] | 22,746 | 5 | manual |

2018 | Robbins [19] | 1,296,879 | 1 | manual |

Region | Longitude Range (${}^{\circ}$) | Latitude Range (${}^{\circ}$) |
---|---|---|

R1 | −172.51∼−164.99 | −7.01∼0.01 |

R2 | −178.00∼−164.97 | 62.99∼70.01 |

R3 | −63.01∼−53.99 | 34.99∼39.40 |

R4 | 159.98∼170.02 | 43.44∼49.01 |

R5 | −59.44∼−58.60 | 39.41∼41.16 |

R6 | 165.34∼ 68.91 | 41.99∼43.43 |

Area | Mean | Variance | Comentropy | EOG |
---|---|---|---|---|

Maria | 113.84 | 2924.19 | 5.17 | 624.81 |

Highland | 80.96 | 2756.20 | 6.91 | 126.14 |

Type | Model | R | P | F${}_{1}$ | IoU | $\mathit{Pre}\_\mathit{R}/\mathit{R}$ |
---|---|---|---|---|---|---|

Whole | Mask R-CNN | 0.369 | 0.666 | 0.475 | 0.682 | 0.602 |

no Mask R-CNN | 0.435 | 0.743 | 0.549 | 0.76 | 1.19 | |

Crater R-CNN | 0.495 | 0.839 | 0.622 | 0.892 | 0.962 | |

Crater R-CNN with TTSN | 0.635 | 0.905 | 0.747 | 0.886 | 0.964 | |

Highland | Mask R-CNN | 0.405 | 0.617 | 0.489 | 0.695 | 0.624 |

no Mask R-CNN | 0.439 | 0.71 | 0.542 | 0.776 | 1.25 | |

Crater R-CNN | 0.525 | 0.827 | 0.642 | 0.896 | 1.01 | |

Crater R-CNN with TTSN | 0.661 | 0.914 | 0.767 | 0.895 | 1.01 | |

Maria | Mask R-CNN | 0.29 | 0.871 | 0.435 | 0.642 | 0.538 |

no Mask R-CNN | 0.428 | 0.827 | 0.564 | 0.726 | 0.105 | |

Crater R-CNN | 0.43 | 0.872 | 0.576 | 0.88 | 0.846 | |

Crater R-CNN with TTSN | 0.581 | 0.885 | 0.702 | 0.865 | 0.833 |

Type | Size | R | P | F${}_{1}$ |
---|---|---|---|---|

Whole | Radius < 100 m | 0.549 | 0.915 | 0.687 |

100 m ≤ Radius < 200 m | 0.754 | 0.944 | 0.838 | |

200 m ≤ Radius | 0.816 | 0.794 | 0.805 | |

Highland | Radius < 100 m | 0.581 | 0.938 | 0.718 |

100 m ≤ Radius < 200 m | 0.779 | 0.96 | 0.86 | |

200 m ≤ Radius | 0.832 | 0.774 | 0.802 | |

Maria | Radius < 100 m | 0.476 | 0.871 | 0.615 |

100 m ≤ Radius < 200 m | 0.714 | 0.907 | 0.799 | |

200 m ≤ Radius | 0.768 | 0.922 | 0.838 |

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**MDPI and ACS Style**

Zang, S.; Mu, L.; Xian, L.; Zhang, W.
Semi-Supervised Deep Learning for Lunar Crater Detection Using CE-2 DOM. *Remote Sens.* **2021**, *13*, 2819.
https://doi.org/10.3390/rs13142819

**AMA Style**

Zang S, Mu L, Xian L, Zhang W.
Semi-Supervised Deep Learning for Lunar Crater Detection Using CE-2 DOM. *Remote Sensing*. 2021; 13(14):2819.
https://doi.org/10.3390/rs13142819

**Chicago/Turabian Style**

Zang, Sudong, Lingli Mu, Lina Xian, and Wei Zhang.
2021. "Semi-Supervised Deep Learning for Lunar Crater Detection Using CE-2 DOM" *Remote Sensing* 13, no. 14: 2819.
https://doi.org/10.3390/rs13142819