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摘要: 研究陶瓷晶粒尺寸分布对估计陶瓷样品的物理属性具有重要意义, 当前主要依赖人工方法测量晶粒尺寸, 由于晶粒形状不规则且大小不一, 因此人工方法测量效率低、误差大. 针对该问题, 提出一种数据与模型联合驱动的陶瓷材料晶粒分割算法. 该算法首先通过图像预处理解决材料表面反光导致的灰度不均匀问题; 其次利用本文提出的鲁棒分水岭变换实现图像中晶粒的预分割, 解决传统分水岭算法存在的过分割以及分割区域个数与轮廓精度难以平衡的问题; 最后根据本文提出的轻量级富卷积特征网络输出晶粒轮廓并利用该轮廓对预分割结果进行优化. 与主流图像分割算法相比, 提出的算法一方面利用鲁棒分水岭变换实现了更为准确的晶粒区域定位, 另一方面利用图像的低层与高层特征融合获取了更为精准的晶粒轮廓. 实验结果表明, 提出的算法不仅能够实现陶瓷材料晶粒尺寸的精准计算, 而且具有较高的计算效率, 为分析陶瓷材料物理属性提供了客观准确的数据.Abstract: The research of the distribution of ceramic grain sizes is significant for estimating physical properties of ceramic materials. At present, researchers mainly use manual methods to measure ceramic grains, which leads to low efficiency and high error due to the irregular shape and different sizes of grains in ceramic images. To solve this issue, a new algorithm used for grain segmentation of ceramic materials is proposed in this paper. This algorithm first performs image pre-processing to solve the problem of intensity inhomogeneity caused by surface reflection of materials in the imaging process. Secondly, a robust watershed transform (RWT) is presented and used for pre-segmentation of grains in scanning electron microscope (SEM) images, which solves two problems existing in traditional watershed transform, one is over-segmentation and the other is the difficulty of balancing the number of segmentation regions and the accuracy of boundaries. Finally, we present a lightweight and richer convolutional features network (LRCF) used for grain contour prediction, and use the results generated by LRCF to optimize the pre-segmentation result. Compared with popular image segmentation algorithms, the proposed algorithm shows two advantages. On one hand, it achieves more accurate grain region segmentation due to the employment of RWT; on the other hand, it provides more accurate grain boundaries due to the optimization of LRCF. Experimental results show that the proposed algorithm not only provides accurate grain sizes of ceramic materials, but also shows high calculation efficiency, which is significant for property analysis of ceramic materials.
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图 1 总体流程图, 其中, SE为结构边缘算法(Structured Edge, SE)[32]
Fig. 1 Overall flow chart, where SE denotes edge detection algorithm based on structured forests
图 2 原图与预处理结果对比, 预处理算法能有效解决陶瓷SEM图像的灰度不均匀问题(a)-(d)为原图 (e)-(h)为经过预处理的图像
Fig. 2 Comparison of original and pre-processed images, the pre-processing algorithm can effectively solve the issue of uneven grayscale of ceramic SEM image (a)-(d) original images (e)-(h) pre-processed images.
图 3 不同参数的MGR-WT对图像的分割结果对比,
$ r $ 是用于梯度重建的圆形结构元半径Fig. 3 Segmentation result comparison using MRG-WT with different parameters,
$ r $ is the radius of structural element for gradient reconstruction
图 4 RWT与MGR-WT对陶瓷材料晶粒的分割结果对比 (a) 未去除小区域的形态学分水岭算法分割结果(b) MGR-WT分割结果 (c) RWT分割结果 (d) RWT和MGR-WT的分割结果与Ground Truth对比(b线表示RWT结果, g线表示MGR-WT结果, p线表示Ground Truth结果)
Fig. 4 Comparison of the segmentation results of ceramic grains between RWT and MGR-WT (a) segmentation result using watershed transform without removing small areas (b) segmentation result using MGR-WT (c) robust watershed segmentation (RWT) result (d) comparison of the segmentation results of RWT and MGR-WT with Ground Truth (line b for RWT, line g for MGR-WT and line p for Ground Truth)
图 5 基于RWT的图像分割结果, 分割后结果存在双线轮廓问题
Fig. 5 Segmentation results obtained by RWT suffer from the problem of double line contour
图 6 去除双线 (a) RWT分割结果(b) 对(a)去除双线的结果 (c) 去除双线前后的结果对比
Fig. 6 Removing double lines (a) segmentation result using RWT (b) removing double line from (a) (c) comparison of (a) and (b)
图 9 基于LRCF与分水岭变换的图像分割 (a) 基于LRCF的轮廓预测 (b) 基于LRCF的MGR-WT结果 (c)基于LRCF的分割结果与Ground Truth对比(y线表示Ground Truth)
Fig. 9 Image segmentation using the combination of LRCF and watershed transform (a) contour prediction using LRCF (b) segmentation result using the combination of LRCF and MGR-WT (c)comparison segmentation results of LRCF-MGR-WT and Ground Truth (line y for Ground Truth)
图 10 轮廓优化 (a) 优化前结果 (b) 优化后结果 (c) 优化前后与Ground Truth对比(图中p线为优化结果, g线为优化前结果, y线为Ground Truth)
Fig. 10 Contour optimization (a) the result before optimization (b) optimized results (c) comparison among (a), (b) and Ground Truth(line p for optimization result, line g for optimization result, line y for Ground Truth)
表 1 不同方法对陶瓷晶粒分割的性能指标对比(第一组实验, 未镀金的图像)
Table 1 Performance comparison of different approaches for ceramic grain segmentation (the first group of experiments for unplated image)
Methods CV↑ VI↓ GCE↓ BDE↓ Liu’s-MGR [38] 0.2889 3.4270 0.4742 7.3230 Random Walker [39] 0.3556 2.9003 0.1407 13.2147 SLIC [14] 0.3547 3.0524 0.4396 10.1678 LSC [15] 0.3455 2.8820 0.3563 7.5911 Banerjee’s [30] 0.5959 2.1992 0.2031 3.9182 SE-MGR-WT [32] 0.4680 2.3887 0.1364 5.0346 SE-AMR-WT [40] 0.8287 1.1280 0.1122 1.6261 RCF-MGR-WT [23] 0.6636 1.4952 0.0955 3.5651 LRCF-RWT 0.8697 0.8710 0.0763 1.6262 
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表 2 不同方法对陶瓷晶粒分割的性能指标对比(第二组实验, 镀金的图像)
Table 2 Performance comparison of different approaches for ceramic grain segmentation (the second group of experiments for gilded image)
Methods CV↑ VI↓ GCE↓ BDE↓ Liu’s-MGR [38] 0.2622 3.8053 0.3565 6.9440 Random Walker [39] 0.3823 2.9517 0.2202 16.4378 SLIC [14] 0.3279 3.0962 0.4070 11.3350 LSC [15] 0.3347 2.8418 0.3265 8.0651 Banerjee’s [30] 0.7035 1.7175 0.1052 2.7484 SE-MGR-WT [32] 0.7979 1.2031 0.1033 2.0565 SE-AMR-WT [40] 0.8757 0.9909 0.1110 1.2623 RCF-MGR-WT [23] 0.5771 1.7691 0.0895 4.8813 LRCF-RWT 0.9217 0.6699 0.0628 1.0201
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表 3 人工测量晶粒尺寸结果(单位: 像素)
Table 3 Grain sizes using manual method (Units: pixels)
测量者1 测量者2 测量者3 测量者4 测量者5 1 94.55 89.17 93.39 94.22 88.51 2 90.92 100.33 105.38 91.48 99.91 3 107.50 100.91 102.09 96.49 89.91 4 101.61 89.91 92.08 94.42 93.38 5 108.31 103.88 95.16 102.45 93.52 6 112.51 108.21 112.34 109.70 107.84 7 101.85 104.13 102.80 94.40 89.73
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表 4 不同方法对陶瓷晶粒尺寸的计算结果对比(单位: 像素)
Table 4 Comparison of ceramic grain sizes using different approaches (Units: pixels)
人工测量 Ground Truth Liu’s-MGR [38] RW [39] SLIC [14] LSC [15] Banerjee’s [30] SE-MGR-WT [32] SE-AMR-WT [40] RCF-MGR-WT [23] LRCF-RWT 1 92.26 97.80 88.00 195.16 74.33 63.95 92.58 48.88 83.73 63.07 98.56 2 97.24 98.00 85.60 161.54 74.48 63.66 86.59 55.09 94.34 75.08 99.15 3 99.83 92.33 82.81 175.15 76.66 62.39 105.29 50.92 90.52 63.08 92.47 4 93.29 93.34 65.97 206.96 75.72 62.73 86.45 53.17 87.70 65.21 92.48 5 100.50 96.09 74.38 192.80 75.99 68.04 102.02 67.25 93.87 59.95 96.76 6 110.08 98.93 69.83 177.56 76.48 70.01 104.08 76.38 96.00 59.31 100.65 7 99.68 96.61 78.18 183.03 75.50 71.71 114.28 85.29 93.98 53.59 97.67
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表 5 不同方法计算陶瓷晶粒尺寸结果的误差(单位: 像素)
Table 5 Error comparison of different approaches on ceramic grain size computation (Units: pixels)
Liu’s-MGR [38] RW [39] SLIC [14] LSC [15] Banerjee’s [30] SE-MGR-WT [32] SE-AMR-WT [40] RCF-MGR-WT [23] LRCF-RWT 1 -9.80 +97.36 -23.47 -33.85 -5.22 -48.92 -14.07 -34.73 -0.76 2 -12.40 +63.54 -23.52 -34.34 -11.41 -42.91 -3.66 -22.92 +1.15 3 -9.52 +82.82 -15.67 -29.94 -12.96 -41.41 -1.81 -29.25 -0.14 4 -27.37 +113.62 -17.62 -30.61 -6.89 -40.17 -5.64 -28.13 -0.86 5 -21.71 +96.71 -20.1 -28.05 +6.07 -28.84 -2.22 -36.14 -0.67 6 -29.10 +18.63 -22.45 -28.92 +5.15 -19.55 -2.93 -39.62 +1.72 7 -18.43 +86.42 -21.11 -24.90 +17.67 -11.32 -2.63 -43.02 -1.06
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