Monocrystalline Silicon Diameter Detection Image Threshold Segmentation Method Using Multi-objective Artificial Fish Swarm Algorithm
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摘要: 为提高对硅单晶直径检测图像高亮光环的分割精度, 提出了一种基于多目标人工鱼群算法的二维直方图区域斜分多阈值分割方法.首先设计了一种多目标人工鱼群算法, 并且改进了快速构造Pareto非劣解集的方法, 然后以最大类间方差和最大熵同时作为测度函数, 搜索最优的二维直方图区域斜分分割阈值.仿真结果表明, 所设计的多目标人工鱼群优化算法具有较高的搜索精度, 硅单晶直径检测图像分割实验结果表明, 提出的改进二维直方图区域斜分多阈值分割方法对高亮光环具有较高的分割精度.
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关键词:
- 硅单晶直径检测 /
- 阈值分割 /
- 二维直方图区域斜分法 /
- 多目标优化 /
- 人工鱼群算法
Abstract: Combined with the multi-objective artificial fish swarm algorithm (MAFSA), a 2D histogram multi-threshold oblique segmentation method is proposed to improve the segmentation accuracy of the highlight halo for monocrystalline silicon diameter detection. Firstly, a multi-objective artificial fish swarm algorithm is designed and the approach to find the non-dominating set in a population efficiently is improved. Then, the maximum between-class variance and maximum entropy are simultaneously employed as measure functions to search the best thresholds of 2D histogram oblique segmentation. Simulated experiments show that the designed MAFSA has a relatively high search accuracy. Meanwhile, image segmentation experiments conducted on practical monocrystalline silicon diameter detection demonstrate that the proposed 2D histogram multi-threshold oblique segmentation method achieves fine precision on segmenting the highlight halo. -
图 6 TDR-150单晶炉直径检测装置实物图
Fig. 6 Photos of TDR-150 single crystal silicon furnace diameter detecting device
图 8 等径10 mm时四种方法的多阈值分割结果
Fig. 8 Results of different methods for multi-threshold image segmentation at 10 mm length in body growth
图 9 等径10 mm时四种方法的二值化图像
Fig. 9 Binarization image of different methods at 10 mm length in body growth
图 10 等径400 mm时四种方法的多阈值分割结果
Fig. 10 Results of different methods for multi-threshold image segmentation at 400 mm length in body growth
图 11 等径400 mm时四种方法的二值化图像
Fig. 11 Binarization image of different methods at 400 mm length in body growth
表 1 ZDT标准测试函数集
Table 1 ZDT standard test function set
函数标号 目标函数 变量数 变量范围 采样点数 ZDT1 ${\left\{ \begin{array}{l} \min {f_1}(\mathit{\boldsymbol{x}}) = {x_1}\\ \min {f_2}(\mathit{\boldsymbol{x}}) = g(\mathit{\boldsymbol{x}})(1 - \sqrt {{x_1}/g(\mathit{\boldsymbol{x}})} )\\ {\rm{s}}.{\rm{t}}.\quad g(\mathit{\boldsymbol{x}}) = 1 + 9(\sum\nolimits_{i = 2}^n {{x_i}} )/(n - 1) \end{array} \right.}$ 30 xi ∈ [0, 1] 1 000 ZDT2 ${\left\{ \begin{array}{l} \min {f_1}(\mathit{\boldsymbol{x}}) = {x_1}\\ \min {f_2}(\mathit{\boldsymbol{x}}) = g(\mathit{\boldsymbol{x}})(1 - {({x_1}/g(\mathit{\boldsymbol{x}}))^2})\\ {\rm{s}}.{\rm{t}}.\quad g(\mathit{\boldsymbol{x}}) = 1 + 9(\sum\nolimits_{i = 2}^n {{x_i}} )/(n - 1) \end{array} \right.}$ 30 xi ∈ [0, 1] 1 000 ZDT3 ${\left\{ \begin{array}{l} \min {f_1}(\mathit{\boldsymbol{x}}) = {x_1}\\ \min {f_2}(\mathit{\boldsymbol{x}}) = g(\mathit{\boldsymbol{x}})(1 - \sqrt {({x_1}/g(\mathit{\boldsymbol{x}}))} - {x_1}\sin (10\pi {x_1})/g(\mathit{\boldsymbol{x}}))\\ {\rm{s}}.{\rm{t}}.\quad g(\mathit{\boldsymbol{x}}) = 1 + 9(\sum\nolimits_{i = 2}^n {{x_i}} )/(n - 1) \end{array} \right.}$ 30 xi ∈ [0, 1] 1 000 ZDT4 $\left\{ {\begin{array}{*{20}{l}} {\min {f_1}(\mathit{\boldsymbol{x}}) = {x_1}}\\ {\min {f_2}(\mathit{\boldsymbol{x}}) = g(\mathit{\boldsymbol{x}})(1 - \sqrt {{x_1}/g(\mathit{\boldsymbol{x}})} )}\\ {{\rm{s}}.{\rm{t}}.\quad g(\mathit{\boldsymbol{x}}) = 1 + 10(n - 1) + \sum\nolimits_{i = 2}^n {\left( {x_i^2 - 10\cos \left( {4\pi {x_i}} \right)} \right)} } \end{array}} \right.$ 10 xi ∈ [0, 1]
xi ∈ [-5, 5]
i=2, …, n1 000 ZDT6 $\left\{ {\begin{array}{*{20}{l}} {\min {f_1}(\mathit{\boldsymbol{x}}) = 1 - \exp ( - 4{x_1}){{\sin }^6}(6\pi {x_1})}\\ {\min {f_2}(\mathit{\boldsymbol{x}}) = g(\mathit{\boldsymbol{x}})(1 - {{({x_1}/g(\mathit{\boldsymbol{x}}))}^2})}\\ {{\rm{s}}.{\rm{t}}.\quad g(\mathit{\boldsymbol{x}}) = 1 + 10(n - 1) + \sum\nolimits_{i = 2}^n {\left( {x_i^2 - 10\cos \left( {4\pi {x_i}} \right)} \right)} } \end{array}} \right.$ 10 xi ∈ [0, 1] 1 000 
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表 2 多种算法对比实验结果
Table 2 Experimental results of different algorithms
对比方法 NSGA-Ⅱ p-OCEA peMOPSO MPSOCell 本文方法 测试函数 IGD 时间(s) IGD 时间(s) IGD 时间(s) IGD 时间(s) IGD 时间(s) ZDT1 0.0123 7 131.89 0.0826 6 288.28 0.0100 5 689.27 0.0172 2 599.12 0.0088 986.87 ZDT2 0.0207 6 367.91 0.0977 6 350.72 0.4995 3 190.81 0.0088 2 598.90 0.0211 829.74 ZDT3 0.0060 6 167.51 0.0532 6 531.65 0.0087 2 008.90 0.0116 1 285.60 0.0197 987.56 ZDT4 0.0354 6 443.92 0.0191 6 325.01 0.0138 1 107.43 7.5031 1 740.71 0.0597 551.46 ZDT6 96.8043 6 391.91 95.9782 6 656.29 71.1176 1 405.68 86.0420 917.85 0.4865 651.83
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表 3 等径10 mm时各种方法分割结果的性能指标
Table 3 Results of efficiency among different methods for image segmentation at 10 mm length in body growth
方法 PSNR (dB) 分类误差率（％) 运行时间（s) 方法1 12.8480 0.8008 11.0274 方法2 30.0228 0.1849 4.6387 方法3 31.0546 0.1772 1.8061 本文方法 35.1589 0.0626 7.6084
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表 4 等径400 mm时各种方法分割结果的性能指标
Table 4 Results of efficiency among different methods for image segmentation at 400 mm length in body growth
方法 PSNR (dB) 分类误差率（％) 运行时间（s) 方法1 13.9686 0.6600 12.1390 方法2 32.1443 0.1042 4.6601 方法3 32.0341 0.0944 2.5306 本文方法 34.8116 0.0826 7.5028
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