Geometric camery calibration: the virtual camera approach

Accurate dimensional measurements made with TV cameras require a careful geometric calibration of the imaging device. This work presents a new calibration approach that makes use of the virtual camera paradigm, in which a calibrated surface (target) plays the role of the image plane of a distortionless, fictitious camera. The method yields a simple closed form solution for the calibration parameters. We use an error analysis to estimate the influence of the calibration set-up on the angular measures. We use simulation to verify the analysis. The results of experimental tests are also reported, indicating good accuracy of the proposed procedure compared to some of the best-known calibration methods.     

Image-based lens geometric distortion correction using minimization of average bicoherence index

In this paper, a lens geometric distortion correction method for low-cost digital cameras is described. The lens distortion coefficient is estimated by the value minimizing average bicoherence index which denotes image-dependent higher-order correlations in the frequency domain. In order to formulate the minimization of the average bicoherence index in terms of the lens distortion coefficient alone, the feasibility of a square-pixel assumption and the effect of the image center bias on the image quality are shown experimentally. At the same time, a computationally efficient method for calculating the bicoherence index is proposed, which comprises an approximation of coordinate resampling and development of a relationship between the lens distortion coefficients of the original and its reduced image. Depending on the spatial distribution of image features, the performance of the proposed method can be made comparable to that of precision camera calibration.     

Algorithms for coplanar camera calibration

Abstract. Coplanar camera calibration is the process of determining the extrinsic and intrinsic camera parameters from a given set of image and world points, when the world points lie on a two-dimensional plane. Noncoplanar calibration, on the other hand, involves world points that do not lie on a plane. While optimal solutions for both the camera-calibration procedures can be obtained by solving a set of constrained nonlinear optimization problems, there are significant structural differences between the two formulations. We investigate the computational and algorithmic implications of such underlying differences, and provide a set of efficient algorithms that are specifically tailored for the coplanar case. More specifically, we offer the following: (1) four algorithms for coplanar calibration that use linear or iterative linear methods to solve the underlying nonlinear optimization problem, and produce sub-optimal solutions. These algorithms are motivated by their computational efficiency and are useful for real-time low-cost systems. (2) Two optimal solutions for coplanar calibration, including one novel nonlinear algorithm. A constraint for the optimal estimation of extrinsic parameters is also given. (3) A Lyapunov type convergence analysis for the new nonlinear algorithm. We test the validity and performance of the calibration procedures with both synthetic and real images. The results consistently show significant improvements over less complete camera models. Received: 30 September 1998 / Accepted: 12 January 2000     

摄像机镜头畸变的研究

分析了摄像机成像模型和镜头非线性畸变模型,通过实验的方法求得了镜头的径向畸变系数,并首次根据图像复原原理将镜头的畸变系数引入边缘的亚像素定位算法中,最后通过对图像测量系统进行了标定,用实验的方法定量地比较了镜头径向畸变对测量精度的影响。同时,在标定的过程中通过“二次标定”的方法消除了“单次标定”所引入的系统误差,提高了测量精度。实验证明,通过对镜头的畸变进行校正来提高亚像素边缘定位精度的方法是有效的、显著的。     

鱼眼镜头的标定和畸变校正研究

为在使用鱼眼镜头得到大视野图像的同时得到正常的视觉效果,研究鱼眼镜头的成像模型及内外参数的标定过程.相比常用的标定算法,采用基于镜头模型的标定方法;针对Davide Scaramuzza提出的全方位相机标定工具箱,指出其不足之处,对角点坐标的精度、标定系数矩阵稳定性和角点范围随意性三方面进行优化和提高;根据标定结果对鱼眼畸变图像进行畸变校正,得到正常视觉的平面图.实验结果表明,优化后的方法实现简单、鲁棒性强、结果准确.     

一种基于非量测畸变校正的摄像机标定方法

设计一种基于非量测畸变校正的摄像机标定方法.该方法利用单参数除式模型校正镜头畸变,根据直线透视投影保留同素性,通过拉凡格氏法（LM）优化标定出畸变模型系数和摄像机主点坐标,然后校正成像点,使其满足针孔模型映射关系.根据内参数的两个基本方程,线性求解剩余参数.实验表明,该方法在非量测标定过程具有较好的鲁棒性,且对比张正友标定方法,可在单幅标靶图像下进行标定,避免了模型内外参数耦合在一起,提高了标定效率.     

稳定精确的摄像机标定方法

在Tsai两步法的基础上提出了一种更加稳定精确的摄像机标定方法。由于Tsai两步法中只考虑了摄像机镜头的径向畸变因素,所以为了提高摄像机的标定精度,在其基础上考虑了镜头的切向畸变情况。在求解摄像机参数的过程中,第一步同Tsai两步法采用最小二乘法求解线性方程得到外部参数,再利用最小二乘法求解关于畸变参数K1,K2,K3,K4的线性方程组,最终求得摄像机的内外所有参数。通过实验对该方法进行了验证。     

Robust refinement methods for camera calibration and 3D reconstruction from multiple images

This paper proposes robust refinement methods to improve the popular patch multi-view 3D reconstruction algorithm by Furukawa and Ponce (2008). Specifically, a new method is proposed to improve the robustness by removing outliers based on a filtering approach. In addition, this work also proposes a method to divide the 3D points in to several buckets for applying the sparse bundle adjustment algorithm (SBA) individually, removing the outliers and finally merging them. The residuals are used to filter potential outliers to reduce the re-projection error used as the performance evaluation of refinement. In our experiments, the original mean re-projection error is about 47.6. After applying the proposed methods, the mean error is reduced to 2.13.     

双线阵CCD相机的畸变校正和标定方法

在双线阵CCD的三维重建中,对线阵CCD相机的标定和镜头畸变校正是基础环节。提出了一种用于三维重建中的双线阵CCD标定及镜头畸变校正方法。根据左右相机间的单应性关系,以及线阵CCD的成像原理,将双目相机间的空间关系分解成姿态角与错切角的关系。通过靶图数据的拟合,对姿态角和镜头畸变进行校正,根据求出的错切角完成相机间的标定,实现对具有镜头畸变的双线阵CCD的标定。实验结果表明,标定和校正精度满足后续三维重建中图像匹配的需求。     

一种改进的相机标定方法

摄像机标定与图像畸变修正是摄影测量、视觉检测、计算机视觉等领域的重点研究课题之一,在测绘、工业控制、导航、军事等领域得到了极大的应用。研究了摄像机模型,摄像机标定等内容。对DLT的标定方法进行了改进,在摄像机模型中全面考虑了镜头的畸变,利用图像中心附近点畸变量较小的性质,提出一种摄像机内外部参数和像差修正参数分离的标定方法。并举例说明了基于同一物体的两幅图画三维重构的具体实验步骤和方法,分析了影响精度的因素。     

一种使用校正模板的非线性摄像机标定方法

基于图像点满足的特定直线方程以及相邻图像点之间距离相等的性质,对标定模板图像进行校正,并通过改进的张正友标定法,提出了一种新的使用校正模板的非线性摄像机标定方法。与现存的方法进行比较发现,该方法能够实现较高精度的摄像机标定,鲁棒性比较强,且能够大大地降低算法的复杂度。     

Segment Based Camera Calibration

The basic idea of calibrating a camera system in previous approaches is to determine camera parmeters by using a set of known 3D points as calibration reference.In this paper,we present a method of camera calibration in whih camera parameters are determined by a set of 3D lines.A set of constraints is derived on camea parameters in terms of perspective line mapping.Form these constraints,the same perspective transformation matrix as that for point mapping can be computed linearly.The minimum number of calibration lines is 6.This result generalizes that of Liu,Huang and Faugeras^[12] for camera location determination in which at least 8 line correspondences are required for linear computation of camera location.Since line segments in an image can be located easily and more accurately than points,the use of lines as calibration reference tends to ease the computation in inage preprocessing and to improve calibration accuracy.Experimental results on the calibration along with stereo reconstruction are reported.     

Simple and efficient method of calibrating a motorized zoom lens

In this work, three servo motors are used to independently control the aperture, zoom, and focus of our zoom lens. Our goal is to calibrate, efficiently, the camera parameters for all the possible configurations of lens settings. We use a calibration object suitable for zoom lens calibration to deal with the defocusing problem. Instead of calibrating the zoom lens with respect to the three lens settings simultaneously, we perform the monofocal camera calibration, adaptively, over the ranges of the zoom and focus settings while fixing the aperture setting at a preset value. Bilinear interpolation is used to provide the values of the camera parameters for those lens settings where no observations are taken. The adaptive strategy requires the monofocal camera calibration only for the lens settings where the interpolated camera parameters are not accurate enough, and is hence referred to as the calibration-on-demand method. Our experiments show that the proposed calibration-on-demand method can provide accurate camera parameters for all the lens settings of a motorized zoom lens, even though the camera calibration is performed only for a few sampled lens settings.     

A comparative review of camera calibrating methods with accuracy evaluation

Camera calibrating is a crucial problem for further metric scene measurement. Many techniques and some studies concerning calibration have been presented in the last few years. However, it is still difficult to go into details of a determined calibrating technique and compare its accuracy with respect to other methods. Principally, this problem emerges from the lack of a standardized notation and the existence of various methods of accuracy evaluation to choose from. This article presents a detailed review of some of the most used calibrating techniques in which the principal idea has been to present them all with the same notation. Furthermore, the techniques surveyed have been tested and their accuracy evaluated. Comparative results are shown and discussed in the article. Moreover, code and results are available in internet.     

A robust method to recognize critical configuration for camera calibration

When space points and camera optical center lie on a twisted cubic, no matter how many pairs there are used from the space points to their image points, camera parameters cannot be determined uniquely. This configuration is critical for camera calibration. We set up invariant relationship between six space points and their image points for the critical configuration. Then based on the relationship, an algorithm to recognize the critical configuration of at least six pairs of space and image points is proposed by using a constructed criterion function, where no any explicit computation on camera projective matrix or optical center is needed. Experiments show the efficiency of the proposed method.     

A new calibration model of camera lens distortion

Lens distortion is one of the main factors affecting camera calibration. In this paper, a new model of camera lens distortion is presented, according to which lens distortion is governed by the coefficients of radial distortion and a transform from ideal image plane to real sensor array plane. The transform is determined by two angular parameters describing the pose of the real sensor array plane with respect to the ideal image plane and two linear parameters locating the real sensor array with respect to the optical axis. Experiments show that the new model has about the same correcting effect upon lens distortion as the conventional model including all the radial distortion, decentering distortion and prism distortion. Compared with the conventional model, the new model has fewer parameters to be calibrated and more explicit physical meaning.     

摄像机镜头畸变的鲁棒校正方法

针对计算机视觉中的镜头畸变问题,设计一种鲁棒的校正方法.该方法基于空间直线的成像特性来定义畸变测度,通过非线性优化完成畸变校正.采用微粒群全局优化算法,将传统优化方法、标准微粒群算法和基于不同策略的微粒群算法的性能进行对比.实验结果表明,带变异算子基于对位学习的微粒群算法具有较强的鲁棒性,在低噪声下,微粒群算法的校正性能优于传统算法.最后通过不同畸变程度的校正实例验证了所提出方法的有效性.     

非线性优化模型的数码相机定标

通过构造非线性模型,对经典标定方法进行了补充,同时也解决了在样本数据较少情况下的数码相机精确定位问题。利用线性转换模型得到投影矩阵,设定m₃=1为约束条件,通过分解参数矩阵求出数码相机内外部参数,并将其作为非线性优化模型的初始值;然后构造非线性优化模型,建立目标函数J=∑pi-p(A,k1,k2,R,ti,Pi)²,求解在约束条件h^T(A^-1)^TA^-₁h₂=0和h^T1(A^-1)TA-1h₁=h^T2(A^-1)^TA^-1h₂下的最优解,从而实现数码相机的精确标定。对给出的单样本情况进行了求解,结果表明此算法可以达到较高的精度。     

基于畸变模型优化的网络摄像机标定*

针对低分辨率网络数码摄像机用于定量量测的标定问题, 提出一种非线性畸变的构建与优化方法。该方法结合多项式模型与传统的畸变模型;利用回归分析原理对模型进行自动精化,以优选显著的畸变参数,从而建立了一种自适应的摄像机畸变模型。运用构建的畸变模型,利用自检校光束法平差方法对同种型号的三个低成本网络摄像机实施标定和畸变纠正。结果表明,该模型有效补偿了通用畸变模型残存的畸变系统差,同时有效的避免了过度参数化的问题,有助于提高摄像机的标定精度和稳健性,使得摄像机的标定精度达到子像素。