# Digital Image Processing Method for Characterization of Fractures, Fragments, and Particles of Soil/Rock-Like Materials

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Image Processing Method Based on Color Gradient

_{F}.

#### 2.2. Description of the Proposed Image Processing Method

## 3. Application of the Proposed Image Processing Method

#### 3.1. Fractal Dimension of Fracture Network

#### 3.2. Block Size Distribution of Rock Fragments

#### 3.3. Fractal Dimension and Particle Size Distribution of Microparticles in Rock

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flowchart of the image-processing method for analyzing the properties of rock fracturing and block/particle size distribution.

**Figure 2.**Description of the image-processing method for determining the fractal dimension of the world coastline and the size distribution of land, including (

**a**) a world coastline map, (

**b**) a simplified world coastline map, (

**c**) color gradient distribution, (

**d**) color gradient-based recognition of the coastline, (

**e**) calculation process of the fractal dimension, (

**f**) result of the fractal dimension of the coastline, (

**g**) connected domain of land, (

**h**) calculation process of equivalent diameter, and (

**i**) the result of equivalent diameter distribution of land.

**Figure 3.**Fractal dimension of the crack network of the mud layer, including (

**a**) cracks of the mud layer, (

**b**) color gradient distribution, (

**c**) recognized cracks, and (

**d**) fractal dimension of the crack network.

**Figure 4.**Fractal dimension of the crack network in a ceramic panel, including (

**a**) cracks in the ceramic panel, (

**b**) color gradient distribution, (

**c**) recognized cracks, and (

**d**) fractal dimension of the crack network.

**Figure 5.**Fractal dimension of the fracture network in a rock mass, including (

**a**) fractures in the rock mass, (

**b**) color gradient distribution, (

**c**) recognized fractures, and (

**d**) fractal dimension of the fracture network.

**Figure 6.**Calculation results of the fractal dimension of a fracture network by different methods, including (

**a**) the color gradient-based method proposed in this study, (

**b**) a gray gradient-based method, (

**c**) a binary gradient-based method, (

**d**) a color image-based method, (

**e**) a gray image-based method, (

**f**) a binary image-based method, and (

**g**) a manual outlining and color-based method.

**Figure 7.**Block size distribution of rock fragments produced in rock mechanics tests, which include (

**a**) red sandstone, (

**b**) granite, and (

**c**) marble.

**Figure 8.**Fractal dimension and particle size distribution of microparticles in rock, including (

**a**) contacts and particles in rock, (

**b**) color gradient distribution, (

**c**) recognized fractures between microparticles in rock, (

**d**) fractal dimension of fractures, (

**e**) connected domains of particles, and (

**f**) the frequency histogram and cumulative distribution curve of particle sizes.

Method | Calculation Time for Fracture Identification and Fractal Dimension/ms | Fractal Dimension | Difference Rate of Fractal Dimension Relative to the Result by Manual Outlining/% |
---|---|---|---|

Color gradient-based method proposed in this study | 1490.733 | 1.5991 | 0.33 |

Gray gradient-based method [11] | 1003.207 | 1.5669 | 1.69 |

Binary gradient-based method [11] | 1187.949 | 1.5299 | 4.01 |

Color image-based method (designed in this study for comparison) | 196.739 | 1.4181 | 11.02 |

Gray image-based method | 143.722 | 1.4911 | 6.44 |

Binary image-based method [14] | 155.167 | 1.4775 | 7.3 |

Manual outlining and color-based method (designed in this study for comparison) | 157.846 (Before it, the outlining time has 4 h) | 1.5938 | -- |

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**MDPI and ACS Style**

Pi, Z.; Zhou, Z.; Li, X.; Wang, S.
Digital Image Processing Method for Characterization of Fractures, Fragments, and Particles of Soil/Rock-Like Materials. *Mathematics* **2021**, *9*, 815.
https://doi.org/10.3390/math9080815

**AMA Style**

Pi Z, Zhou Z, Li X, Wang S.
Digital Image Processing Method for Characterization of Fractures, Fragments, and Particles of Soil/Rock-Like Materials. *Mathematics*. 2021; 9(8):815.
https://doi.org/10.3390/math9080815

**Chicago/Turabian Style**

Pi, Zizi, Zilong Zhou, Xibing Li, and Shaofeng Wang.
2021. "Digital Image Processing Method for Characterization of Fractures, Fragments, and Particles of Soil/Rock-Like Materials" *Mathematics* 9, no. 8: 815.
https://doi.org/10.3390/math9080815