基于交比不变性的投影仪标定

杨建柏; 赵建; 孙强

doi:10.37188/CO.2020-0111

基于交比不变性的投影仪标定

doi: 10.37188/CO.2020-0111

杨建柏^{1, 2,},
赵建^1, ,,
孙强¹

1.
中国科学院长春光学精密机械与物理研究所，吉林长春 130033
2.
中国科学院大学，北京 100049

基金项目: 国家重点研发计划（No. 2018YFC0308100，No. 2018YFC0307900）；吉林省科技发展计划项目（No. 20190302102GX，No. 20180201048GX）；中国科学院青年创新促进会会员资助项目（No. 2019226）

详细信息

作者简介:
杨建柏（1986—），男，黑龙江海伦人，博士研究生，2009年于中国石油大学获得学士学位，主要从事机器视觉及三维重建方面的研究。E-mail：yang9769@163.com

赵　建（1967—），女，吉林长春人，研究员，博士生导师，主要从事数字图像处理、目标识别与跟踪、视频编解码等方面的研究。E-mail：zhaojian6789@126.com

中图分类号: TB96；TP391
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出版历程
- 收稿日期: 2020-06-29
- 修回日期: 2020-08-12
- 网络出版日期: 2021-03-05
- 刊出日期: 2021-03-23

Projector calibration based on cross ratio invariance

YANG Jian-bai^{1, 2
,},
ZHAO Jian^{1
, ,},
SUN Qiang¹

1.
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China

Funds: Supported by National Key Research and Development Project (No. 2018YFC0308100, No. 2018YFC0307900), The Projects of Science Technology Development Plan of Jilin Province (No. 20190302102GX, No. 20180201048GX), Youth Innovation Promotion Association CAS (No. 2019226)

More Information

Corresponding author: zhaojian6789@126.com

摘要

摘要: 提出了一种新的投影仪标定方法以提高数字光栅投影三维测量中投影仪标定的准确性。该方法结合二次投影技术和交比不变性进行投影仪标定。采用二次投影技术解决投射图案与标定板图案互相干扰的问题；采用交比不变性以避免引入相机的标定误差。接着进行了对比实验，以验证所提方法的有效性。选取需要相机参数的传统投影仪标定方法以及根据全局单应性的投影仪标定方法作为对比方法。结果显示，本方法的反投影误差标准差分别从（0.2275, 0.2264）像素和（0.1397, 0.0997）像素降低到（0.0645, 0.0601）像素，反投影误差的最大值分别从1.222像素和0.5617像素降低到0.2421像素。另外，该方法还可同时标定相机，从而获得整个三维测量系统的参数。本文提出的方法可以避免相机标定参数的误差传递，提高投影仪的标定精度。
- 光栅投影 /
- 三维测量 /
- 交比不变性 /
- 投影仪标定
Abstract: In order to improve the accuracy of the projector calibration in 3D shape measurement using digital fringe projection, a new projector calibration method that combines secondary projection technology and cross-ratio invariance is proposed. The secondary projection technology is used to solve the mutual interference between the projection pattern and the calibration pattern, and the cross-ratio invariance method is used to avoid introducing camera calibration error. A comparative experiment is carried out to verify the effectiveness of the proposed method. Compared with the traditional method of projector calibration that requires camera parameters and that using global homography, the RMS values of reprojection error of this method is reduced from (0.2275, 0.2264) and (0.1397, 0.0997) pixels to (0.0645, 0.0601) pixels, and the maximum value of the reprojection error is reduced from 1.222 pixels and 0.5617 pixels to 0.2421 pixels. In addition, this method allows the camera to be simultaneously calibrated during operation, and therefore the parameters of the entire 3D measurement system can be acquired. The above results show that the method proposed in this paper can prevent error propagation of camera calibration parameters and improve the calibration accuracy of a projector.
- digital fringe projection /
- 3D shape measurement /
- cross-ratio invariance /
- projector calibration

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图 1 测量系统简化示意图

Figure 1. Schematic diagram of simplified measurement system

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图 2 基于二次投影的防图案干扰方法

Figure 2. Method for preventing pattern interference based on secondary projection

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图 3 射影变换示意图

Figure 3. Schematic diagram of projective transformation

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图 4 交比构成示意图

Figure 4. Schematic diagram of cross-ratio construction

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图 5 实验系统

Figure 5. Experimental system

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图 6 第一次投影并采集的图像：（a）姿态1，（b）姿态2，（c）姿态3

Figure 6. The acquired images for the first projection: (a) gesture 1, (b) gesture 2, (c) gesture 3

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图 7 投射位置示意图

Figure 7. Schematic diagram of the projection position

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图 8 各姿态投射位置图：（a）姿态1，（b）姿态2，（c）姿态3

Figure 8. Projection positions of each gesture: (a) gesture 1, (b) gesture 2, (c) gesture 3

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图 9 各姿态生成投射标志点图案：（a）姿态1，（b）姿态2，（c）姿态3

Figure 9. The generated projection point patterns of each gesture: (a) gesture 1, (b) gesture 2, (c) gesture 3

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图 10 二次投影后采集的标定板图案：（a）姿态1，（b）姿态2，（c）姿态3

Figure 10. Calibration plate patterns acquired after the second projection: (a) gesture 1, (b) gesture 2, (c) gesture 3

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图 11 几种方法的反投影误差结果。（a）需要相机参数法；（b）全局单应性变换法；（c）本文方法

Figure 11. Reprojection error distribution of different methods. (a) Method requiring camera parameters; (b) the global homography transformation method; (c) the method proposed in this paper

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图 12 相机标定反投影误差示意图

Figure 12. Schematic diagram of reprojection error in camera calibration

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图 13 整体系统三维示意图

Figure 13. 3D schematic diagram of the system

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表 1 标定的投影仪内部参数

Table 1. Calibrated intrinsic parameters of the projector

(pixel)
方法	参数
方法	f_u	f_v	u₀	v₀
需要相机参数标定法	3033.9020	3037.0319	976.0815	546.6816
全局单应性变换法	3040.3878	3042.7892	993.4626	553.0046
本文方法	3060.7594	3059.8479	1006.0491	540.8452

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表 2 标定的投影仪镜头畸变系数

Table 2. Calibrated lens distortion coefficients of the projector

方法	系数
方法	k₁	k₂	p₁	p₂
需要相机参数标定法	0.1102	−0.7058	0.0025	−0.0050
全局单应性变换法	0.0215	−0.4157	0.0033	−0.0014
本文方法	−0.1065	0.0058	0.0011	−0.0007

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表 3 几种方法的反投影误差

Table 3. Reprojection errors of different methods (pixel)

	x轴（MAX）	y轴（MAX）	x轴（STD）	y轴（STD）
需要相机参数标定法	1.222	1.022	0.2275	0.2264
全局单应性变换法	0.5617	0.5130	0.1397	0.0997
本文方法	0.2345	0.2421	0.0645	0.0601

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表 4 相机内部参数和畸变系数标定结果

Table 4. Calibration results of camera intrinsic parameters and distortion coefficients

f_u	f_v	u₀	v₀	k₁	k₂	p₁	p₂
2644.92	2644.11	646.56	508.34	−0.222	0.313	−0.0001	0.0001

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