Chinese Optics, Volume. 18, Issue 1, 42(2025)
Structured light surface shape measurement method for highly reflective surfaces
Fig. 3. Fringe images captured under different exposures. (a) Low exposure image; (b) high exposure image
Fig. 4. Luminance distribution on an aluminum alloy metal plate. (a) Camera captured image; (b) HDR composite image
Fig. 7. Exposure time prediction algorithm based on irradiance segmentation
Fig. 9. Response curve of the camera and the irradiance distribution image. (a) Camera response curve; (b) irradiance image; (c) distribution curve of gray scale and irradiance in a specific line; (d) gray-scale variation curves of different points
Fig. 11. Phase and point cloud processing results of different methods. (a) Phase pictures obtained by different methods; (b) point cloud data of PMP method; (c) phase error of the 900th line obtained by different methods; (d) point cloud data of the proposed method
Fig. 12. Deviation results of point cloud reconstruction by different methods
Fig. 13. Processing results of brake disc (a)−(c) and sheet metal workpiece (d)−(f)
Table 1. The steps of the FCM algorithm in this paper
View tableView in ArticleTable 1. The steps of the FCM algorithm in this paper
算法 1 高斯度量下的模糊C均值聚类算法输入: 数据集 ${\mathbf{X}} = \{ {x_1},{x_2},\cdots,{x_L}\} $ , 聚类数量$K$ , 最大迭代次数$T = 50$ ,收敛阈值$\varepsilon = {10^{ - 6}}$ , 正则化系数$\gamma = 0.2$ .输出: 隶属度矩阵 $ {\boldsymbol{U}} = \{ {u_{ij}}\} $ #数据点${x_i}$ 对聚类中心${c_j}$ 的隶属度聚类中心矩阵$ {\boldsymbol{C}} = \{ {c_1},{c_2},...,{c_K}\} $ .1：使用欧式距离度量下的模糊C均值聚类方法初始化隶属度矩阵 ${\boldsymbol{U}^{(o)}}$ ，聚类中心矩阵${\boldsymbol{C}^{(o)}}$ , 和协方差矩阵$ {\boldsymbol{\Sigma }^{(o)}} $ 2：对于每一轮迭代，执行以下步骤直到收敛或达到最大迭代次数: a. 根据式(9)计算每个数据点到所有聚类中心的距离 b. 根据距离更新隶属度矩阵 ${\boldsymbol{U}}$ ：${{\boldsymbol{u}}_{ij}} = - \Phi ({{\boldsymbol{x}}_j}|{{\boldsymbol{c}}_i},{{\boldsymbol{\Sigma}} _i})/2\gamma $ c. 更新聚类中心矩阵${\mathbf{C}}$ ：$ {{\boldsymbol{c}}_i} = \displaystyle\sum\limits_{j = 1}^L {{{\boldsymbol{u}}_{ij}}{{\boldsymbol{x}}_j}} /\displaystyle\sum\limits_{j = 1}^L {{{\boldsymbol{u}}_{ij}}} $ d. 更新协方差矩阵$ {\boldsymbol{\Sigma }} $ ：$ {{\boldsymbol{\Sigma}} _i} = \left[ {\displaystyle\sum\limits_{j = 1}^L {{{\boldsymbol{u}}_{ij}}{{({{\boldsymbol{x}}_j} - {{\boldsymbol{c}}_i})}^{\mathrm{T}}}} ({{\boldsymbol{x}}_j} - {{\boldsymbol{c}}_i})} \right]/\displaystyle\sum\limits_{j = 1}^L {{{\boldsymbol{u}}_{ij}}} $ e. 检测终止条件 计算聚类中心的变化量是否小于收敛阈值$\varepsilon $ 如果变化量小于$\varepsilon $ 或得到最大迭代次数$T$ ，则停止迭代3：输出最终的聚类中心矩阵 ${\boldsymbol{C}}$ 和隶属度矩阵${\boldsymbol{U}}$
Table 2. Main parameters of monocular structured light system
View tableView in ArticleTable 2. Main parameters of monocular structured light system
性能参数 参数值 相机分辨率 2448 （H）×2048（V）投影仪分辨率 1028 （H）×720（V）测量幅面大小/mm 400×300 标准测距/mm 630 曝光时间调节范围/ms 0~640 投射光源 蓝光LED
Table 3. Exposure time series of different methods
(unit: ms) View tableView in ArticleTable 3. Exposure time series of different methods
(unit: ms) 曝光次数 PMP 文献[ 14 ]算法文献[ 15 ]算法本文算法 1 100 2.69 1.58 0.75 2 - 15.50 10.13 22.92 3 - 109.73 102.69 59.19 4 - 162.21 269.32 113.22 5 - 203.36 469.32 231.11
Table 4. Results obtained by different clustering numbers
View tableView in ArticleTable 4. Results obtained by different clustering numbers
聚类 数量 点云 数量 最大偏差/ mm 标准偏差/ mm RMS/ mm 计算时间/ s 3 532158 2.2817 0.0728 0.0839 53.08 4 574999 1.4990 0.0321 0.0532 85.47 5 604978 0.4789 0.0188 0.0332 130.81 6 656688 0.3612 0.0182 0.0303 201.33 7 680096 0.3010 0.0174 0.0293 294.54
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Yun WANG, Jian-ying GUO, Jun-zhe LIANG, Feng ZHU, Guang-xi CHEN, Mao-dong REN, Jin LIANG. Structured light surface shape measurement method for highly reflective surfaces[J]. Chinese Optics, 2025, 18(1): 42
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Received: May. 10, 2024
Accepted: Sep. 3, 2024
Published Online: Mar. 14, 2025
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