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基于交比不变性的投影仪标定

杨建柏 赵建 孙强

杨建柏, 赵建, 孙强. 基于交比不变性的投影仪标定[J]. 中国光学, 2021, 14(2): 320-328. doi: 10.37188/CO.2020-0111
引用本文: 杨建柏, 赵建, 孙强. 基于交比不变性的投影仪标定[J]. 中国光学, 2021, 14(2): 320-328. doi: 10.37188/CO.2020-0111
YANG Jian-bai, ZHAO Jian, SUN Qiang. Projector calibration based on cross ratio invariance[J]. Chinese Optics, 2021, 14(2): 320-328. doi: 10.37188/CO.2020-0111
Citation: YANG Jian-bai, ZHAO Jian, SUN Qiang. Projector calibration based on cross ratio invariance[J]. Chinese Optics, 2021, 14(2): 320-328. 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
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: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

Projector calibration based on cross ratio invariance

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
  • 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。
  • 图  1  测量系统简化示意图

    Figure  1.  Schematic diagram of simplified measurement system

    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

    图  3  射影变换示意图

    Figure  3.  Schematic diagram of projective transformation

    图  4  交比构成示意图

    Figure  4.  Schematic diagram of cross-ratio construction

    图  5  实验系统

    Figure  5.  Experimental system

    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

    图  7  投射位置示意图

    Figure  7.  Schematic diagram of the projection position

    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

    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

    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

    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

    图  12  相机标定反投影误差示意图

    Figure  12.  Schematic diagram of reprojection error in camera calibration

    图  13  整体系统三维示意图

    Figure  13.  3D schematic diagram of the system

    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
    fufvu0v0
    需要相机参数标定法3033.90203037.0319976.0815546.6816
    全局单应性变换法3040.38783042.7892993.4626553.0046
    本文方法3060.75943059.84791006.0491540.8452
    下载: 导出CSV

    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
    k1k2p1p2
    需要相机参数标定法0.1102−0.70580.0025−0.0050
    全局单应性变换法0.0215−0.41570.0033−0.0014
    本文方法−0.10650.00580.0011−0.0007
    下载: 导出CSV

    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1.2221.0220.22750.2264
    全局单应性变换法0.56170.51300.13970.0997
    本文方法0.23450.24210.06450.0601
    下载: 导出CSV

    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

    fufvu0v0k1k2p1p2
    2644.922644.11646.56508.34−0.2220.313−0.00010.0001
    下载: 导出CSV
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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:  2021-04-01

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