# Shape from Shading-Based Study of Silica Fusion Characterization Problems

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Model

#### 3.1. Image Pre-Processing

#### 3.2. Indicators of the Trajectory and Edge Profile Characteristics of the Silicon Dioxide Plasmas

#### 3.3. Theoretical Knowledge of the SFS Model

#### 3.4. SFS Model Building

## 4. Model Analysis

^{3}/s. The slower melting rate is around 0.0015 mm

^{3}/s.

## 5. Model Test

^{3}, and the mass of silica at each moment is obtained and tested. The variation of mass with time is shown in Figure 14.

^{2}. The actual area of the silicon dioxide at each moment is examined in this way; see Figure 18.

## 6. Conclusions

^{3}/s and the slower melting rate is about 0.0015 mm

^{3}/s. This provides data to support the blast furnace slag direct fiber formation process. The introduction of the algorithmic model into the actual production process has certain advantages. Therefore, the SFS model established in this paper has some practical value and is worth promoting in related enterprises.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Convolution operation corresponding to the pixel value matrix of the silicon dioxide image.

**Figure 13.**Volume change of silicon dioxide at each moment during the melting process in the high-temperature cell.

**Figure 14.**Graph of the mass change of silicon dioxide at each moment during the melting process in the high-temperature cell.

**Figure 15.**Volume rate variation of silicon dioxide at each moment during high-temperature cell melting.

**Figure 16.**Graph of the change in mass rate of silicon dioxide at each moment during the melting process in the temperature cell.

**Figure 17.**Variation of the perimeter of silicon dioxide at each moment during the melting process in the high-temperature cell.

**Table 1.**Position of the center of mass at each moment during the melting of silicon dioxide in a hot cell.

Moment | Coordinate Points | Moment | Coordinate Points |
---|---|---|---|

1 | (225, 202) | 25 | (209, 223) |

2 | (224, 205) | 26 | (208, 212) |

3 | (217, 226) | 27 | (191, 232) |

4 | (220, 225) | 28 | (176, 246) |

5 | (213, 244) | 29 | (171, 241) |

6 | (236, 235) | 30 | (166, 242) |

7 | (221, 239) | 31 | (164, 245) |

8 | (218, 235) | 32 | (161, 243) |

9 | (215, 235) | 33 | (165, 244) |

10 | (214, 234) | 34 | (168, 240) |

11 | (214, 237) | 35 | (176, 244) |

12 | (209, 239) | 36 | (169, 239) |

13 | (208, 236) | 37 | (198, 233) |

14 | (204, 233) | 38 | (193, 234) |

15 | (197, 237) | 39 | (195, 228) |

16 | (281, 225) | 40 | (190, 236) |

17 | (203, 239) | 41 | (171, 245) |

18 | (200, 237) | 42 | (164, 240) |

19 | (199, 237) | 43 | (156, 245) |

20 | (195, 234) | 44 | (142, 250) |

21 | (198, 233) | 45 | (139, 253) |

22 | (190, 237) | 46 | (140, 249) |

23 | (191, 234) | 47 | (136, 253) |

24 | (202, 231) | 48 | (126, 265) |

Moment | Volume (mm ^{3}) | Rate (mm ^{3}/s) | Moment | Volume (mm ^{3}) | Rate (mm ^{3}/s) |
---|---|---|---|---|---|

1 | 4.24 | 0.95 | 25 | 0.97 | 0.44 |

2 | 3.30 | 1.32 | 26 | 1.40 | 0.31 |

3 | 4.61 | 0.76 | 27 | 1.71 | 0.49 |

4 | 3.85 | 0.75 | 28 | 1.22 | 0.23 |

5 | 3.10 | 0.65 | 29 | 1.45 | 0.31 |

6 | 2.46 | 0.17 | 30 | 1.14 | 0.23 |

7 | 2.29 | 0.60 | 31 | 1.37 | 0.20 |

8 | 1.69 | 0.24 | 32 | 1.17 | 0.08 |

9 | 1.93 | 0.32 | 33 | 1.25 | 0.06 |

10 | 1.61 | 0.20 | 34 | 1.19 | 0.10 |

11 | 1.81 | 0.48 | 35 | 1.09 | 0.15 |

12 | 2.29 | 0.39 | 36 | 1.24 | 0.18 |

13 | 1.90 | 0.02 | 37 | 1.06 | 0.03 |

14 | 1.92 | 0.21 | 38 | 1.03 | 0.13 |

15 | 2.13 | 0.08 | 39 | 0.91 | 0.02 |

16 | 2.21 | 0.58 | 40 | 0.89 | 0.05 |

17 | 1.63 | 0.47 | 41 | 0.94 | 0.04 |

18 | 2.10 | 0.41 | 42 | 0.89 | 0.16 |

19 | 1.69 | 0.11 | 43 | 0.73 | 0.04 |

20 | 1.58 | 0.10 | 44 | 0.69 | 0.20 |

21 | 1.68 | 0.06 | 45 | 0.49 | 0.06 |

22 | 1.74 | 0.02 | 46 | 0.43 | 0.09 |

23 | 1.76 | 0.07 | 47 | 0.52 | 0.04 |

24 | 1.83 | 0.87 | 48 | 0.47 | 0.05 |

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**MDPI and ACS Style**

Yang, A.; Wang, L.-J.; Ma, W.-N.; Tang, M.; Chen, J.
Shape from Shading-Based Study of Silica Fusion Characterization Problems. *Minerals* **2022**, *12*, 1286.
https://doi.org/10.3390/min12101286

**AMA Style**

Yang A, Wang L-J, Ma W-N, Tang M, Chen J.
Shape from Shading-Based Study of Silica Fusion Characterization Problems. *Minerals*. 2022; 12(10):1286.
https://doi.org/10.3390/min12101286

**Chicago/Turabian Style**

Yang, Aimin, Li-Jing Wang, Wei-Ning Ma, Mei Tang, and Jing Chen.
2022. "Shape from Shading-Based Study of Silica Fusion Characterization Problems" *Minerals* 12, no. 10: 1286.
https://doi.org/10.3390/min12101286