基于数字图像处理的矿物颗粒形态定量分析

陈建湟 张中俭 徐文杰 李丽慧

陈建湟, 张中俭, 徐文杰, 等. 2021. 基于数字图像处理的矿物颗粒形态定量分析[J]. 工程地质学报, 29(1): 59-68. doi: 10.13544/j.cnki.jeg.2021-0003
引用本文: 陈建湟, 张中俭, 徐文杰, 等. 2021. 基于数字图像处理的矿物颗粒形态定量分析[J]. 工程地质学报, 29(1): 59-68. doi: 10.13544/j.cnki.jeg.2021-0003
Chen Jianhuang,Zhang Zhongjian, Xu Wenjie, et al. 2021. Quantitative method of shape parameters of mineral particles based on image processing[J]. Journal of Engineering Geology,29(1): 59-68. doi: 10.13544/j.cnki.jeg.2021-0003
Citation: Chen Jianhuang,Zhang Zhongjian, Xu Wenjie, et al. 2021. Quantitative method of shape parameters of mineral particles based on image processing[J]. Journal of Engineering Geology,29(1): 59-68. doi: 10.13544/j.cnki.jeg.2021-0003

基于数字图像处理的矿物颗粒形态定量分析

doi: 10.13544/j.cnki.jeg.2021-0003
基金项目: 

国家重点研发计划 2019YFC1520600

国家自然科学基金 41602329

详细信息
    作者简介:

    陈建湟(1995-),男,硕士生,主要从事工程地质方面的研究. E-mail: 2002180043@cugb. edu. cn

    通讯作者:

    张中俭(1981-),男,博士,副教授,博士生导师,主要从事工程地质方面的研究. E-mail: zhangzhongjian@cugb.edu.cn

  • 中图分类号: P642.3

QUANTITATIVE METHOD OF SHAPE PARAMETERS OF MINERAL PARTICLES BASED ON IMAGE PROCESSING

Funds: 

the National Key Research and Development Program of China 2019YFC1520600

National Natural Science Foundation of China 41602329

  • 摘要: 矿物颗粒形态的评价一般采用目估法在显微镜下观测岩石薄片,其评价结果受主观影响。本文利用岩石薄片显微照片,基于图像处理技术提出了矿物颗粒形态定量分析方法。矿物颗粒形态参数主要包括球度、凸度、长宽比、磨圆度等。该方法利用图像分割技术将显微照片中的矿物颗粒区分开,提取颗粒的像素轮廓坐标进行离散几何分析,计算矿物颗粒形态参数。特别地,由于磨圆度难以直接、准确地计算,本文总结前人经验,在傅里叶级数拟合颗粒轮廓的基础上,创新性地提出了棱角关键点识别和分组两步走的方法。本文分别计算了一组理论图形和一张岩石薄片显微照片的颗粒形态参数,验证了该方法的准确性和实用性。本文分析了图像分辨率Re、颗粒轮廓的傅里叶级数拟合优度R2、棱角关键点分组系数α对颗粒形态参数计算结果的影响,发现:(1)球度、凸度、长宽比的计算结果基本不受ReR2的影响;(2)磨圆度的计算结果受ReR2的影响,建议颗粒最小外接圆直径像素数大于200 pixel,并且存在一个最优的R2范围,在这个范围内计算的磨圆度结果接近理论值;(3)当α精确到十分位时,初步分组时选取α=0.1最为合理。
  • 图  1  颗粒形态参数计算示意图

    a. 球度;b. 凸度;c. 长宽比;d. 磨圆度

    Figure  1.  Schematic diagram of particle shape parameters

    图  2  图像分割技术及矿物颗粒轮廓提取

    a. 岩石薄片显微图片;b. 矿物颗粒着色;c. 利用阈值分割技术获取的矿物颗粒轮廓

    Figure  2.  Image segmentation technology and extraction of mineral particle contour

    图  3  磨圆度的计算流程

    Figure  3.  Calculation process of roundness

    图  4  利用傅里叶级数光滑颗粒轮廓

    a. 原始轮廓;b. 极坐标展开示意图;c. 傅里叶级数拟合曲线

    Figure  4.  Schematic diagram of smoothing particle contour based on Fourier series

    图  5  颗粒棱角关键点识别(a)及棱角圆计算(b)

    Figure  5.  Key points identification of particle edges and corners(a) and corner circle calculation(b)

    图  6  已知形态参数的理论图形(a)及棱角圆计算结果(b)

    Figure  6.  Theoretical figure with known shape parameters(a) and calculation result of corner circle(b)

    图  7  图 2所示白云石矿物棱角圆的计算结果

    Figure  7.  Results of corners circles of the dolomite minerals(see Fig. 2)in micrograph

    图  8  不同图像分辨率棱角圆计算结果

    Figure  8.  Results of corners circle with different image resolution

    图  9  最小外接圆直径像素数目与磨圆度计算值的关系

    Figure  9.  The relation between the pixel numbers and the roundness values

    图  10  不同傅里叶级数拟合状态下的颗粒棱角圆计算结果

    a. 颗粒原始轮廓;b. 欠拟合;c. 优拟合;d. 过拟合

    Figure  10.  Results of particle corner circles under different Fourier series fitting states

    图  11  nR2Π计算值之间的关系

    Figure  11.  The relationship between the values of n,R2 and Π

    图  12  根据R2Π划分不同傅里叶级数拟合状态

    Figure  12.  Different Fourier series fitting states according to R2 and Π

    图  13  所统计的20个颗粒图像的P值分布图(a)及其不同区间占比统计(b)

    Figure  13.  Value distribution map of P based on 20 particle images(a) and its proportion of different intervals(b)

    表  1  理论图形的绘制参数和形态参数计算结果

    Table  1.   Results of drawing parameters and shape parameters of theoretical graphs

    图形编号 理论图形绘制参数 轮廓像素个数 球度S 凸度C 长宽比A 磨圆度Π
    ds R r np SL SJ 误差/% CL CJ 误差/% AL AJ 误差/% ΠL ΠJ 误差/%
    1 1000 875.93 350.37 1348 0.991 0.930 -6.20 1.000 0.997 -0.30 0.995 0.969 -2.60 0.400 0.395 -1.10
    2 1000 954.92 763.93 1383 0.966 0.980 1.40 1.000 0.997 -0.30 0.984 0.990 0.50 0.800 0.801 0.10
    3 1000 938.13 375.25 1378 0.981 0.963 -1.80 1.000 0.997 -0.30 0.989 0.984 -0.50 0.400 0.387 -3.20
    4 1000 978.49 782.79 1397 0.932 0.989 6.20 1.000 0.997 -0.30 0.969 0.994 2.50 0.800 0.800 0
    ds为最小外接圆半径;R为最大内切圆半径;r为倒角半径;下标L代表参数的理论值;下标J代表参数的计算值
    下载: 导出CSV

    表  2  图 2所示白云石矿物颗粒的轮廓像素信息与形态参数计算结果

    Table  2.   Pixel information of dolomite mineral particle profile(see Fig. 2) and results of the shape parameters

    图形编号 1 2 3 4 5 6 7 8 9 平均值
    轮廓像素个数 954 990 774 1095 214 745 1049 1001 690 834.67
    最小外接圆直径像素/pixel 352.49 365.85 270.19 338.95 72.15 275.50 362.79 387.59 268.36 299.32
    球度S 0.76 0.75 0.72 0.75 0.70 0.84 0.77 0.66 0.66 0.74
    凸度C 0.92 0.93 0.91 0.83 0.75 0.96 0.94 0.90 0.90 0.89
    长宽比A 0.64 0.75 0.60 0.87 0.69 0.90 0.75 0.56 0.62 0.71
    磨圆度Π 0.36 0.35 0.36 0.26 0.22 0.39 0.41 0.36 0.22 0.33
    磨圆度等级 次圆 次圆 次圆 次圆 次棱角 次圆 次圆 次棱角 次圆
    下载: 导出CSV

    表  3  同一颗粒不同分辨率的图像信息及其形态参数计算结果

    Table  3.   Results of shape parameters of the same particle with different resolution

    最小外接圆直径像素/pixel 图像像素尺寸 轮廓像素个数 拟合优度R2 球度S 凸度C 长宽比A 磨圆度Π
    102.6 100×116 259 0.990 0.809 0.937 0.867 0.228
    153.8 150×173 392 0.998 0.810 0.937 0.872 0.133
    206.0 200×231 526 0.999 0.809 0.937 0.873 0.117
    412.7 400×461 1051 0.999 0.809 0.940 0.867 0.124
    619.7 600×692 1582 0.999 0.809 0.941 0.868 0.121
    826.0 800×922 2109 0.999 0.810 0.941 0.868 0.122
    1032.7 1000×1153 2637 0.999 0.810 0.941 0.867 0.120
    1239.4 1200×1383 3163 0.999 0.810 0.942 0.868 0.118
    前两组颗粒轮廓像素个数少于500个,计算时利用傅里叶级数关系式插值至500个
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-01-07
  • 修回日期:  2021-02-08
  • 刊出日期:  2021-02-01

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