Camera nonlinear distortion correction based on coplanar points

YE Feng; WANG Min; CHEN Jian-dong; HONG Zheng; LAI Yi-zong

doi:10.3788/OPE.20152310.2962

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Camera nonlinear distortion correction based on coplanar points

Information Sciences | 更新时间：2020-08-13

- Camera nonlinear distortion correction based on coplanar points
- Optics and Precision Engineering Vol. 23, Issue 10, Pages: 2962-2970(2015)
- 作者机构：
  
  华南理工大学机械与汽车工程学院,广东广州,510640
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20152310.2962
  CLC： V447.3;TP391.4
- Received：10 June 2015，
  
  Revised：02 August 2015，
  
  Published：25 October 2015
- 稿件说明：
移动端阅览
叶峰, 王敏, 陈剑东等. 共面点的摄像机非线性畸变校正[J]. 光学精密工程, 2015,23(10): 2962-2970

YE Feng, WANG Min, CHEN Jian-dong etc. Camera nonlinear distortion correction based on coplanar points[J]. Editorial Office of Optics and Precision Engineering, 2015,23(10): 2962-2970
叶峰, 王敏, 陈剑东等. 共面点的摄像机非线性畸变校正[J]. 光学精密工程, 2015,23(10): 2962-2970 DOI： 10.3788/OPE.20152310.2962.

YE Feng, WANG Min, CHEN Jian-dong etc. Camera nonlinear distortion correction based on coplanar points[J]. Editorial Office of Optics and Precision Engineering, 2015,23(10): 2962-2970 DOI： 10.3788/OPE.20152310.2962.

摘要

采用传统的Tsai两步法进行摄像机标定时

标定精度会受一阶径向畸变模型的限制。本文提出了一种同时考虑摄像机镜头径向畸变和切向畸变的摄像机模型并研究了模型求解方法来提高畸变校正精度。考虑图像中心区域畸变较小

故用中心附近点列出线性方程组计算了摄像机的部分参数;建立了综合畸变模型

将摄像机参数代入模型计算畸变参数的初始值。由于焦距和平移分量在标定板与相机平面的距离深度变化不够时难以一次性准确标定

故将其代入综合畸变模型重新计算

并运用两步迭代法逐步逼近精确解。最后

对世界坐标系进行空间几何变换、透视变换和成像变换得到的重投影图像的像素坐标并与实际测得的像素坐标值进行比较

得到校正误差。结果表明

本文的畸变校正方法平均像素误差可以达到0.114 9 pixel

优于Tsai校正方法的0.367 0 pixel

且重复性较好。

Abstract

When traditional Tsai two-stage technique is used to calibrate a camera

its calibration accuracy will be limited by first-order radial distortion model. Therefore

a camera imaging model considering both radial distortion and tangential distortion is proposed

and a new method to solve the model is presented to improve the distortion correction accuracy. As the center of an image has a smaller distortion

the image center points are used to give a linear equation group and to calculate a part of parameters of the camera. Then camera parameters are taken into comprehensive distortion model to derive the initial values of distortion coefficients. As focal length and matrix's translation value can not be calculated directly when the calibration board's depth variation is small

the values have to be retaken to model and to be calculated.Then the converged solution is approached by two-stage iterative computation. Finally

the world coordinate system is converted by space geometric transform

perspective transform and imaging transform to obtain the pixel coordinate of the reprojective image. The calibration error is obtained by calculating the mean difference between re-projection pixel coordinates and actual measured pixel coordinates of each point. Experimental result indicates that the calibration method can offer the accuracy of 0.1149 pixel

which is better than Tsai's 0.3670 pixel with well repeatability.

关键词

Keywords

references

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Related Institution

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