﻿ 微分算子和直线拟合在十字丝中心定位中的应用 Application of Differential Operator and Linear Fitting in Crosshair Center Pinpoint

Software Engineering and Applications
Vol.04 No.03(2015), Article ID:15527,7 pages
10.12677/SEA.2015.43007

Application of Differential Operator and Linear Fitting in Crosshair Center Pinpoint

Bochao Liu, Jian Zhao

Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun Jilin

Email: liubochao@ciomp.ac.cn

Received: Jun. 19th, 2015; accepted: Jun. 22nd, 2015; published: Jun. 26th, 2015

ABSTRACT

In order to satisfy the requirement of crosshair center pinpoint for lens decentration measurement, a crosshair center pinpoint method based on differential operator and linear fitting is proposed. First, the edges of crosshair in both X and Y directions can be obtained by using differential operator to compute the difference in both X and Y directions. Then, two linear equations in both X and Y directions are fitted with orthogonal least square method using the edges obtained. Finally, the intersection point of the two linear equations is used as the crosshair center. Experimental results indicate that the precision of the crosshair center pinpoint is less than one pixel in the images grabbed by the CCD whose resoluntion is 1292 × 964 pixel and pixel size is 3.75 μm × 3.75 μm and the precision of pinpoint is less than 2 μm in lens decentration measurement. It can satisfy the system requirements of non-contact, online, real time, higher precision and rapid speed, as well as strong anti-jamming and stabilization.

Keywords:Crosshair Center, Differential Operator, Linear Fitting, Sub-Pixel

Email: liubochao@ciomp.ac.cn

1. 引言

2. 微分算子提取垂直边缘和水平边缘

3. 最小二乘直线拟合

3.1. 经典的最小二乘直线拟合

Figure 1. Vertical operator and horizontal operator 图1. 垂直算子和水平算子

Figure 2. Real-time image of crosshair 图2. 实时的十字丝图像

Figure 3. Schematic diagram of horizontal and vertical edge 图3. 垂直和水平边缘示意图

Figure 4. Classical least square linear fitting 图4. 经典最小二乘直线拟合

1) 假设拟合后的直线方程为y = kx + b，其中k为斜率，b为截距，是最终要求的两个量；

2) 假定任意一点的x坐标xi是准确的，求使得取得最小值时的k和b；

3) 根据2中的要求，应有成立；

4) 解3中的方程可得：

3.2. 正交的最小二乘直线拟合

Figure 5. Orthogonal least square linear fitting 图5. 正交最小二乘直线拟合

2) 计算任意一点(xi, yi)到直线y = kx + b的距离

3) 求使得取得最小值时的k和b；

4) 根据3中的要求同样应有成立，即

5) 解4中的方程可得：

4. 测量实验与结果

(a) 10 ms (b) 15 ms (c) 20 ms (d) 25 ms(e) 30 ms (f) 35 ms (g) 40 ms (h) 45 ms

Figure 6. Images of different exposure time 图6. 不同曝光时间图像

5. 结论

Application of Differential Operator and Linear Fitting in Crosshair Center Pinpoint. 软件工程与应用,03,51-58. doi: 10.12677/SEA.2015.43007

1. 1. 陶李, 王珏, 邹永宁 (2012) 改进的Zernike矩工业CT图像边缘检测.中国光学, 1, 48-56.

2. 2. 杜飞明, 廖兆曙, 张桂林 (2007) 一种十字丝中心坐标检测方法. 计算技术与自动化, 3, 81-85.

3. 3. 郭帮辉 (2014) 基于镜面间隔和中心偏差测量的光学镜头辅助装调设备的研究. 博士论文, 中国科学院大学, 北京.

4. 4. 赵阳, 巩岩 (2012) 投影物镜小比率模型的计算机辅助装调. 中国光学, 4, 94-400.

5. 5. 丁畅 (2014) 图像处理的偏微分方程方法研究. 硕士论文, 大连海事大学, 大连.

6. 6. 姚宜斌, 黄书华, 孔建 (2014) 空间直线拟合的整体最小二乘算法. 武汉大学学报(信息科学版), 5, 571-574.

7. 7. 刘国栋, 刘炳国, 陈凤栋 (2009) 亚像素定位算法精度评价方法的研究. 光学学报, 12, 3446-3451.

8. 8. 王林波, 王延杰, 邸男 (2014) 基于几何特征的圆形标志点亚像素中心定位. 液晶与显示, 6, 1003-1009.

9. 9. Rafael, C.G., Richard, E.W., 著, 阮秋琦, 阮智宇, 译 (2005) Digital image processing. 2nd Edition, 电子工业出版社, 北京.

10. 10. 赵慧, 刘建华, 梁俊杰 (2014) 5种常见边缘检测方法的比较分析. 现代电子技术, 6, 89-92.

11. 11. 刘道华, 张礼涛, 曾召霞 (2013) 基于正交最小二乘法的径向基神经网络模型. 信阳师范学院学报(自然科学版), 3, 428-431.

12. 12. 陈阔, 冯华君, 徐之海 (2013) 亚像素精度的行星中心定位算法. 光学精密工程, 7, 1881-1890.