基于平面镜的摄像机内参数线性标定方法

提出了一种全新的基于平面镜的摄像机标定方法。该方法无需任何标定物,利用平面镜的反射性质和灭点、灭线等理论,通过移动摄像机或平面镜作至少2次平移运动(各次平移间应存在旋转运动)即可线性地标定摄像机的内参数。模拟图像实验和真实图像实验表明所提出的方法能快速、方便地对摄像机进行标定,具有较好的稳定性和精度。     

Estimation of mirror shape and extrinsic parameters in axial non-central catadioptric systems

We propose a method to estimate the mirror shape and position, and the extrinsic parameters in axial non-central catadioptric systems (i.e. systems with an axial symmetrical mirror and a pinhole camera with its optical center located at the mirror axis). Our method requires one or more images of a planar calibration pattern consisting of points and lines with known position (e.g. a checkerboard), and that the camera be internally calibrated. We also present an alternative algorithm for the particular case of catadioptric systems with spherical mirror, were the estimation is achieved by fitting quartic curves to the images of lines of the calibration pattern. An analytical solution is presented for every method. Each analytical solution is then refined by a non-linear optimization procedure. We present experimental results, on simulated and real images, that demonstrate the validity of our work.     

Estimating parameters of noncentral catadioptric systems using bundle adjustment

This paper describes a new method to calibrate the intrinsic and extrinsic parameters of a generalized catadioptric camera (central or noncentral). The algorithm has two steps. The first one is the estimation of correspondences between incident lines in space and pixels (black box model calibration) in an arbitrary world reference frame. The second step is the calibration of the intrinsic parameters of the pinhole camera, the coefficients of the mirror expressed by a quadric (quadric mirror shape and the pose of the camera in relation to it), the position of the optical center of the camera in the world reference frame and its relative orientation (pose of the camera in world reference frame). A projection model relaxing Snell’s Law is derived. The deviations from Snell’s Law and the image reprojection errors are minimized by means of bundle adjustment. Information about the apparent contour of the mirror can be used to reduce the uncertainty in the estimation by introducing a new term in the cost function of the second step minimization process. Simulations and real experiments show good accuracy and robustness for this framework. However, the convergence is dependent on the initial guess as expected. A well-behaved algorithm to automatically generate the initial estimate to be used in the bundle adjustment is also presented.     

Catadioptric Stereo Using Planar Mirrors

By using mirror reflections of a scene, stereo images can be captured with a single camera (catadioptric stereo). In addition to simplifying data acquisition single camera stereo provides both geometric and radiometric advantages over traditional two camera stereo. In this paper, we discuss the geometry and calibration of catadioptric stereo with two planar mirrors. In particular, we will show that the relative orientation of a catadioptric stereo rig is restricted to the class of planar motions thus reducing the number of external calibration parameters from 6 to 5. Next we derive the epipolar geometry for catadioptric stereo and show that it has 6 degrees of freedom rather than 7 for traditional stereo. Furthermore, we show how focal length can be recovered from a single catadioptric image solely from a set of stereo correspondences. To test the accuracy of the calibration we present a comparison to Tsai camera calibration and we measure the quality of Euclidean reconstruction. In addition, we will describe a real-time system which demonstrates the viability of stereo with mirrors as an alternative to traditional two camera stereo.     

一种抛物面摄像机系统的标定方法

由抛物面镜和电荷耦合器件(CCD)摄像机构成的视觉系统视场较大、成像过程复杂。为此,提出一种抛物面摄像机系统的标定方法。引入扩展的基本矩阵概念,利用该矩阵实现系统参数的标定,封装系统的非线性成像过程,从而避免复杂的数值计算。实验结果表明,利用该方法可得到较好的标定结果。     

A calibration method for paracatadioptric camera from sphere images

For paracatadioptric camera, the estimation of intrinsic parameters from sphere images is still an open and challenging problem. In this paper, we propose a calibration method for paracatadioptric camera based on sphere images, which only requires that the projected contour of parabolic mirror is visible on the image plane in one view. We have found that, under central catadioptric camera, a sphere is projected to two conics on the image plane, which are defined as a pair of antipodal sphere images. The conic that is visible on the image plane is called the sphere image, while the other invisible conic is called the antipodal sphere image. In the other aspect, according to the image formation of central catadioptric camera, these two conics can also be considered as the projections of two parallel circles on the viewing sphere by a virtue camera. That is to say, if three pairs of antipodal sphere images are known, central catadioptric camera can be directly calibrated by the calibration method based on two parallel circles. Therefore, the problem of calibrating central catadioptric camera is transferred to the estimations of sphere images and their antipodal sphere images. Based on this idea, we first initialize the intrinsic parameters of the camera by the projected contour of parabolic mirror, and use them to initialize the antipodal sphere images. Next, we study properties of several pairs of antipodal sphere images under paracatadioptric camera. Then, these properties are used to optimize sphere images and their antipodal sphere images, so as to calibrate the paracatadioptric camera. Experimental results on both simulated and real image data have demonstrated the effectiveness of our method.     

基于半镜面靶标的无重叠视域相机全局标定

针对智能无人车、监控等多相机全局标定问题,往往存在无重叠视域或无法单向观测的情况,因此本文提出了一种基于半镜面平面靶标的多相机全局标定方法。该方法首先完成了单相机的内参数标定,然后固定点激光器并投射光线到第一个相机c1视场内并进行散斑点的观测,接着利用半镜面平面靶将光路反射到第二个相机c2视场内并观测散斑点像,由于单相机自身的内外参数已经标定,因此可计算得到反射光路的直线方程,最后根据直线的方向向量可计算全局坐标系的转换矩阵 和平移向量 。仿真和实验的结果表明,所提方法在500mm-1200mm距离,相机视域 范围内,其标定误差为0.36毫米。相对于现有方法,本文所提方法具有更广泛的适应性,可针对多相机复杂视场结构完成标定,同时具有设备简单、操作方便、计算简便等优点。     

Self-identifying patterns for plane-based camera calibration

Determining camera calibration parameters is a time-consuming task despite the availability of calibration algorithms and software. A set of correspondences between points on the calibration target and the camera image(s) must be found, usually a manual or manually guided process. Most calibration tools assume that the correspondences are already found. We present a system which allows a camera to be calibrated merely by passing it in front of a panel of self-identifying patterns. This calibration scheme uses an array of fiducial markers which are detected with a high degree of confidence, each detected marker provides one or four correspondence points. Experiments were performed calibrating several cameras in a short period of time with no manual intervention. This marker-based calibration system was compared to one using the OpenCV chessboard grid finder which also finds correspondences automatically. We show how our new marker-based system more robustly finds the calibration pattern and how it provides more accurate intrinsic camera parameters.     

Camera calibration and three-dimensional world reconstruction of stereo-vision using neural networks

Stereo-pair images obtained from two cameras can be used to compute three-dimensional (3D) world coordinates of a point using triangulation. However, to apply this method, camera calibration parameters for each camera need to be experimentally obtained. Camera calibration is a rigorous experimental procedure in which typically 12 parameters are to be evaluated for each camera. The general camera model is often such that the system becomes nonlinear and requires good initial estimates to converge to a solution. We propose that, for stereo vision applications in which real-world coordinates are to be evaluated, artificial neural networks be used to train the system such that the need for camera calibration is eliminated. The training set for our neural network consists of a variety of stereo-pair images and corresponding 3D world coordinates. We present the results obtained on our prototype mobile robot that employs two cameras as its sole sensors and navigates through simple regular obstacles in a high-contrast environment. We observe that the percentage errors obtained from our set-up are comparable with those obtained through standard camera calibration techniques and that the system is accurate enough for most machine-vision applications.     

A variational approach to problems in calibration of multiple cameras

This paper addresses the problem of calibrating camera parameters using variational methods. One problem addressed is the severe lens distortion in low-cost cameras. For many computer vision algorithms aiming at reconstructing reliable representations of 3D scenes, the camera distortion effects will lead to inaccurate 3D reconstructions and geometrical measurements if not accounted for. A second problem is the color calibration problem caused by variations in camera responses that result in different color measurements and affects the algorithms that depend on these measurements. We also address the extrinsic camera calibration that estimates relative poses and orientations of multiple cameras in the system and the intrinsic camera calibration that estimates focal lengths and the skew parameters of the cameras. To address these calibration problems, we present multiview stereo techniques based on variational methods that utilize partial and ordinary differential equations. Our approach can also be considered as a coordinated refinement of camera calibration parameters. To reduce computational complexity of such algorithms, we utilize prior knowledge on the calibration object, making a piecewise smooth surface assumption, and evolve the pose, orientation, and scale parameters of such a 3D model object without requiring a 2D feature extraction from camera views. We derive the evolution equations for the distortion coefficients, the color calibration parameters, the extrinsic and intrinsic parameters of the cameras, and present experimental results.     

移动机器人足目标定方法

为构建完整的移动机器人视觉导航系统，提出了一种移动机器人足目标定方法．该方法以一个带有数个已知标记点的平面反射镜为中介，分别标定出平面镜坐标系与摄像机坐标系的欧氏变换关系、镜像坐标系与摄像机坐标系的欧氏变换关系、镜像坐标系与平面镜坐标系的欧氏变换关系及机器人坐标系与平面镜坐标系的欧氏变换关系，从而确定摄像机坐标系和移动机器人车体坐标系的欧氏变换关系，实现了移动机器人足目标定．实验结果表明，该方法简单、有效，无需昂贵的标定装置和复杂的标定过程，且可实现现场标定．     

基于图像轮廓的三维重建方法

根据平面镜成像原理,提出了一种基于单幅图像的侧影轮廓线可见外壳重建方法。利用成角度平面镜装置模拟实现多相机同时拍摄,对图像中各轮廓线之间极线几何关系的分析得到对应的相机参数,实现目标物体的三维重建。实验结果表明,该方法简单有效,不需要通过实验室条件下的特殊仪器进行标定即可实现目标物体的三维重建,具有一定的实用价值。     

A Linear Approach for Depth and Colour Camera Calibration Using Hybrid Parameters

Many recent applications of computer graphics and human computer interaction have adopted both colour cameras and depth cameras as input devices. Therefore, an effective calibration of both types of hardware taking different colour and depth inputs is required. Our approach removes the numerical difficulties of using non-linear optimization in previous methods which explicitly resolve camera intrinsics as well as the transformation between depth and colour cameras. A matrix of hybrid parameters is introduced to linearize our optimization. The hybrid parameters offer a transformation from a depth parametric space (depth camera image) to a colour parametric space (colour camera image) by combining the intrinsic parameters of depth camera and a rotation transformation from depth camera to colour camera. Both the rotation transformation and intrinsic parameters can be explicitly calculated from our hybrid parameters with the help of a standard QR factorisation. We test our algorithm with both synthesized data and real-world data where ground-truth depth information is captured by Microsoft Kinect. The experiments show that our approach can provide comparable accuracy of calibration with the state-of-the-art algorithms while taking much less computation time (1/50 of Herrera’s method and 1/10 of Raposo’s method) due to the advantage of using hybrid parameters.     

Extrinsic calibration of heterogeneous cameras by line images

The extrinsic calibration refers to determining the relative pose of cameras. Most of the approaches for cameras with non-overlapping fields of view (FOV) are based on mirror reflection, object tracking or rigidity constraint of stereo systems whereas cameras with overlapping FOV can be calibrated using structure from motion solutions. We propose an extrinsic calibration method within structure from motion framework for cameras with overlapping FOV and its extension to cameras with partially non-overlapping FOV. Recently, omnidirectional vision has become a popular topic in computer vision as an omnidirectional camera can cover large FOV in one image. Combining the good resolution of perspective cameras and the wide observation angle of omnidirectional cameras has been an attractive trend in multi-camera system. For this reason, we present an approach which is applicable to heterogeneous types of vision sensors. Moreover, this method utilizes images of lines as these features possess several advantageous characteristics over point features, especially in urban environment. The calibration consists of a linear estimation of orientation and position of cameras and optionally bundle adjustment to refine the extrinsic parameters.     

一种基于DLT模型和圆环点改正的摄像机定标方法

提出一种基于DLT(直接线性变换)模型和圆环点改正的摄像机定标方法.运用计算机视觉原理,通过三维DLT平面模板模型平移对摄像机进行定标,并在模板上设计一个圆环,使用圆环上的点进行定标参数改进.实验数据证明,定标方法是有效的.     

Camera calibration with distortion models and accuracy evaluation

A camera model that accounts for major sources of camera distortion, namely, radial, decentering, and thin prism distortions is presented. The proposed calibration procedure consists of two steps: (1) the calibration parameters are estimated using a closed-form solution based on a distribution-free camera model; and (2) the parameters estimated in the first step are improved iteratively through a nonlinear optimization, taking into account camera distortions. According to minimum variance estimation, the objective function to be minimized is the mean-square discrepancy between the observed image points and their inferred image projections computed with the estimated calibration parameters. The authors introduce a type of measure that can be used to directly evaluate the performance of calibration and compare calibrations among different systems. The validity and performance of the calibration procedure are tested with both synthetic data and real images taken by tele- and wide-angle lenses     

Self-calibration of an affine camera from multiple views

A key limitation of all existing algorithms for shape and motion from image sequences under orthographic, weak perspective and para-perspective projection is that they require the calibration parameters of the camera. We present in this paper a new approach that allows the shape and motion to be computed from image sequences without having to know the calibration parameters. This approach is derived with the affine camera model, introduced by Mundy and Zisserman (1992), which is a more general class of projections including orthographic, weak perspective and para-perspective projection models. The concept of self-calibration, introduced by Maybank and Faugeras (1992) for the perspective camera and by Hartley (1994) for the rotating camera, is then applied for the affine camera.This paper introduces the 3 intrinsic parameters that the affine camera can have at most. The intrinsic parameters of the affine camera are closely related to the usual intrinsic parameters of the pin-hole perspective camera, but are different in the general case. Based on the invariance of the intrinsic parameters, methods of self-calibration of the affine camera are proposed. It is shown that with at least four views, an affine camera may be self-calibrated up to a scaling factor, leading to Euclidean (similarity) shape réconstruction up to a global scaling factor. Another consequence of the introduction of intrinsic and extrinsic parameters of the affine camera is that all existing algorithms using calibrated affine cameras can be assembled into the same framework and some of them can be easily extented to a batch solution.Experimental results are presented and compared with other methods using calibrated affine cameras.     

Auto‐calibration of a projector–camera stereo system for projection mapping

Standard camera and projector calibration techniques use a checkerboard that is manually shown at different poses to determine the calibration parameters. Furthermore, when image geometric correction must be performed on a three‐dimensional (3D) surface, such as projection mapping, the surface geometry must be determined. Camera calibration and 3D surface estimation can be costly, error prone, and time‐consuming when performed manually. To address this issue, we use an auto‐calibration technique that projects a series of Gray code structured light patterns. These patterns are captured by the camera to build a dense pixel correspondence between the projector and camera, which are used to calibrate the stereo system using an objective function, which embeds the calibration parameters together with the undistorted points. Minimization is carried out by a greedy algorithm that minimizes the cost at each iteration with respect to both calibration parameters and noisy image points. We test the auto‐calibration on different scenes and show that the results closely match a manual calibration of the system. We show that this technique can be used to build a 3D model of the scene, which in turn with the dense pixel correspondence can be used for geometric screen correction on any arbitrary surface.     

The Effect of Noise on Camera Calibration Parameters

Camera calibration is the estimation of parameters (both intrinsic and extrinsic) associated with a camera being used for imaging. Given the world coordinates of a number of precisely placed points in a 3D space, camera calibration requires the measurement of the 2D projection of those scene points on the image plane. While the coordinates of the points in space can be known precisely, the image coordinates that are determined from the digital image are often inaccurate and hence noisy. In this paper, we look at the statistics of the behavior of the camera calibration parameters, which are important for stereo matching, when the image plane measurements are corrupted by noise. We derive analytically the behavior of the camera calibration matrix under noisy conditions and further show that the elements of the camera calibration matrix have a Gaussian distribution if the noise introduced into the measurement system is Gaussian. Under certain approximations we derive relationships between the camera calibration parameters and the noisy camera calibration matrix and compare it with Monte Carlo simulations.     

近距离多目标（种子）检测中摄像机系统的标定方法

在进行基于计算机视觉的排种器性能检测时，为了解决目标（种子）之间的遮挡、加快图象采集速度和节省计算机的存储空间，提出了一种近距离多目标（种子）检测中，摄像机系统的标定方法。建立了由摄像机和平面镜组成的摄像机系统标定的数学模型，并给出了恢复空间点的方法。同时在排种器实验台上进行了验证，结果表明该系统不仅能较好地检测出种子和重叠和丢失等情况，而且检测误差小于1mm，且完全可以不用粘胶带，即可检测出排种器性能。