Implicit and explicit camera calibration: theory and experiments

By implicit camera calibration, we mean the process of calibrating a camera without explicitly computing its physical parameters. Implicit calibration can be used for both three-dimensional (3-D) measurement and generation of image coordinates. In this paper, we present a new implicit model based on the generalized projective mappings between the image plane and two calibration planes. The back-projection and projection processes are modelled separately to ease the computation of distorted image coordinates from known world points. A set of constraints of perspectivity is derived to relate the transformation parameters of the two calibration planes. Under the assumption of the radial distortion model, we present a computationally efficient method for explicitly correcting the distortion of image coordinates in frame buffer without involving the computation of camera position and orientation. By combining with any linear calibration techniques, this method makes explicit the camera physical parameters. Extensive experimental comparison of our methods with the classic photogrammetric method and Tsai's (1986) method in the aspects of 3-D measurement (both absolute and relative errors), the prediction of image coordinates, and the effect of the number of calibration points, is made using real images from 15 different depth values     

Projection matrix by orthogonal vanishing points

Calculation of camera projection matrix, also called camera calibration, is an essential task in many computer vision and 3D data processing applications. Calculation of projection matrix using vanishing points and vanishing lines is well suited in the literature; where the intersection of parallel lines (in 3D Euclidean space) when projected on the camera image plane (by a perspective transformation) is called vanishing point and the intersection of two vanishing points (in the image plane) is called vanishing line. The aim of this paper is to propose a new formulation for easily computing the projection matrix based on three orthogonal vanishing points. It can also be used to calculate the intrinsic and extrinsic camera parameters. The proposed method reaches to a closed-form solution by considering only two feasible constraints of zero-skewness in the internal camera matrix and having two corresponding points between the world and the image. A nonlinear optimization procedure is proposed to enhance the computed camera parameters, especially when the measurement error of input parameters or the skew factor are not negligible. The proposed method has been run on real and synthetic data for more precise evaluations. The provided experimental results demonstrate the superiority of the proposed method.     

A unified approach to the linear camera calibration problem

The camera calibration process relates camera system measurements (pixels) to known reference points in a three-dimensional world coordinate system. The calibration process is viewed as consisting of two independent phases: the first is removing geometrical camera distortion so that rectangular calibration grids are straightened in the image plane, and the second is using a linear affine transformation as a map between the rectified camera coordinates and the geometrically projected coordinates on the image plane of known reference points. Phase one is camera-dependent, and in some systems may be unnecessary. Phase two is concerned with a generic model that includes 12 extrinsic variables and up to five intrinsic parameters. General methods handling additional constraints on the intrinsic variables in a manner consistent with explicit satisfaction of all six constraints on the orthogonal rotation matrix are presented. The use of coplanar and noncoplanar calibration points is described     

点云下地平面检测的RGB-D相机外参自动标定

目的 RGB-D相机的外参数可以被用来将相机坐标系下的点云转换到世界坐标系的点云,可以应用在3维场景重建、3维测量、机器人、目标检测等领域。 一般的标定方法利用标定物（比如棋盘）对RGB-D彩色相机的外参标定,但并未利用深度信息,故很难简化标定过程,因此,若充分利用深度信息,则极大地简化外参标定的流程。基于彩色图的标定方法,其标定的对象是深度传感器,然而,RGB-D相机大部分则应用基于深度传感器,而基于深度信息的标定方法则可以直接标定深度传感器的姿势。方法 首先将深度图转化为相机坐标系下的3维点云,利用MELSAC方法自动检测3维点云中的平面,根据地平面与世界坐标系的约束关系,遍历并筛选平面,直至得到地平面,利用地平面与相机坐标系的空间关系,最终计算出相机的外参数,即相机坐标系内的点与世界坐标系内的点的转换矩阵。结果 实验以棋盘的外参标定方法为基准,处理从PrimeSense相机所采集的RGB-D视频流,结果表明,外参标定平均侧倾角误差为-1.14°,平均俯仰角误差为4.57°,平均相机高度误差为3.96 cm。结论 该方法通过自动检测地平面,准确估计出相机的外参数,具有很强的自动化,此外,算法具有较高地并行性,进行并行优化后,具有实时性,可应用于自动估计机器人姿势。     

基于投影仪和摄像机的结构光视觉标定方法

为实现基于投影仪和摄像机的结构光视觉系统连续扫描,需要计算投影仪投影的任意光平面与摄像机图像平面的空间位置关系,进而需要求取摄像机光心与投影仪光心之间的相对位置关系。求取摄像机的内参数,在标定板上选取四个角点作为特征点并利用摄像机内参数求取该四个特征点的外参数,从而知道四个特征点在摄像机坐标系中的坐标。利用投影仪自身参数求解特征点在投影仪坐标系中的坐标,从而计算出摄像机光心与投影仪光心之间的相对位置关系,实现结构光视觉标定。利用标定后的视觉系统,对标定板上的角点距离进行测量,最大相对误差为0.277%,表明该标定算法可以应用于基于投影仪和摄像机的结构光视觉系统。     

一种基于MATLAB的摄象机标定方法的实现

使用MATLAB实现了一种简便的摄象机参数的标定方法。先由四个标定点的坐标计算出透视投影矩阵，从而计算出标定模板上其它节点的图象坐标，之后进行内部参数和外部参数的计算。此方法具有易于实施、速度较快、精度较高等特点，是一种简便实用的方法。     

一种简单快速的相机标定新方法

本文提出了一种新的相机自标定方法,该方法要求摄像机在3个(或3个以上)不同方位摄取一个包含其内接正三角形的圆的新型标定模板的图像.首先,从模板图像中推导得到圆环点的像点坐标;然后通过得到的圆环点像点坐标,可线性求解摄像机内参数.与传统方法不同的是,该方法避免了复杂的椭圆拟合和直线拟合,降低了计算复杂度,提高了标定速度和...     

Decomposition of transformation matrices for robot vision

The relationship between the three-dimensional coordinates of a point and the corresponding two-dimensional coordinates of its image, as seen by a camera, can be expressed in terms of a 3 by 4 matrix using the homogeneous coordinate system. This matrix is known more generally as the transformation matrix and it is well known that such a matrix can be determined experimentally by measuring the image coordinates of six or more points in space, whose three-dimensional coordinates are known.Such a transformation matrix can be derived analytically from knowledge of the camera position, orientation, focal length and scaling and translation parameters in the image plane. However, the inverse problem of computing the camera location and orientation from the transformation matrix involves solution of simultaneous nonlinear equations in several variables and is considered difficult.In this paper we present a new and simple analytical technique that accomplishes this inversion rather easily. This technique is quite powerful and has applications to a wide variety of problems in Computer Vision for both static and dynamic scenes. The technique has been implemented as a C program running under Unix and works well on real data.     

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.     

基于平面格网的非量测CCD相机自标定

传统的相机标定方法通常需要建立复杂3维标定块或高精度3维控制场,在实际应用中受到了一定的限制。本文采用平面控制格网作为标定块,根据相机的理想模型确定内方位元素,利用2维直接线性变换和共线方程分解出相机的外方位元素初值,采用改进的Hough变换算法检测标定图像中的格网直线并利用最小二乘法拟合出最佳直线,通过求直线的交点得到标定格网点的像坐标。最后利用自检校光线束法平差进行相机的精确标定。实际图像数据实验结果表明,主点和焦距的标定精度分别达到了0.2像素和0.3像素左右。可以满足高精度近景3维量测的要求。     

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.     

采用棋盘格靶标的全自动相机标定方法

为了去除相机标定过程中的人为干预,提出了一种采用改进的棋盘格靶标的全自动相机标定方法。识别出每幅标定图像中的四个标志圆,利用四个标志圆圆心的图像坐标和物理坐标计算二维射影变换矩阵。依据该射影变换矩阵计算出棋盘格角点的初始图像位置,接着提取亚像素精度的角点位置。迭代求解需要标定的相机参数。由实验可知,该全自动相机标定方法的棋盘格角点识别能力和相机标定精度,与Bouguet的相机标定工具箱相当,且可以显著地减少标定时间和工作量。利用20幅分辨率为640×480的靶标图像标定相机仅需16 s。     

Dynamic Visual Tracking for Manipulators Using an Uncalibrated Fixed Camera

This paper presents a new controller for controlling a number of feature points on a robot manipulator to trace desired trajectories specified on the image plane of a fixed camera. It is assumed that the intrinsic and extrinsic parameters of the camera are not calibrated. A new adaptive algorithm is developed to estimate the unknown parameters online, based on three original ideas. First, we use the pseudoinverse of the depth-independent interaction matrix to map the image errors onto the joint space of the manipulator. By eliminating the depths in the interaction matrix, we can linearly parameterize the closed-loop dynamics of the manipulator. Second, to guarantee the existence of the pseudoinverse, the adaptive algorithm introduces a potential force to drive the estimated parameters away from the values that result in a singular Jacobian matrix. Third, to ensure that the estimated parameters are convergent to their true values up to a scale, we combine the Slotine-Li method with an online algorithm for minimizing the error between the estimated projections and real image coordinates of the feature points. We have proved asymptotic convergence of the image errors to zero by the Lyapunov theory based on the nonlinear robot dynamics. Experiments have been carried out to verify the performance of the proposed controller.     

Monitoring activities from multiple video streams: establishing acommon coordinate frame

Monitoring of large sites requires coordination between multiple cameras, which in turn requires methods for relating events between distributed cameras. This paper tackles the problem of automatic external calibration of multiple cameras in an extended scene, that is, full recovery of their 3D relative positions and orientations. Because the cameras are placed far apart, brightness or proximity constraints cannot be used to match static features, so we instead apply planar geometric constraints to moving objects tracked throughout the scene. By robustly matching and fitting tracked objects to a planar model, we align the scene's ground plane across multiple views and decompose the planar alignment matrix to recover the 3D relative camera and ground plane positions. We demonstrate this technique in both a controlled lab setting where we test the effects of errors in the intrinsic camera parameters, and in an uncontrolled, outdoor setting. In the latter, we do not assume synchronized cameras and we show that enforcing geometric constraints enables us to align the tracking data in time. In spite of noise in the intrinsic camera parameters and in the image data, the system successfully transforms multiple views of the scene's ground plane to an overhead view and recovers the relative 3D camera and ground plane positions     

Calibration of Central Catadioptric Cameras Using a DLT-Like Approach

In this study, we present a calibration technique that is valid for all single-viewpoint catadioptric cameras. We are able to represent the projection of 3D points on a catadioptric image linearly with a 6×10 projection matrix, which uses lifted coordinates for image and 3D points. This projection matrix can be computed from 3D–2D correspondences (minimum 20 points distributed in three different planes). We show how to decompose it to obtain intrinsic and extrinsic parameters. Moreover, we use this parameter estimation followed by a non-linear optimization to calibrate various types of cameras. Our results are based on the sphere camera model which considers that every central catadioptric system can be modeled using two projections, one from 3D points to a unitary sphere and then a perspective projection from the sphere to the image plane. We test our method both with simulations and real images, and we analyze the results performing a 3D reconstruction from two omnidirectional images.     

近景大视场角分区域标定方法研究

针对飞行试验测量视场大相机标定精度低的问题,提出一种高精度CCD相机分区域标定方法。该方法首先通过将标靶均匀布置在摄像机视场内,使得标靶尽可能均匀错落地充满整个视场范围,再结合人眼判读的方式求解靶标的像面位置,最终与全站仪三维坐标形成精确的空间标定点集。接着,将像平面按横向方向等间距分割成Ｎ个区域,并结合后方交会的方法分别对每个子区域进行相机参数的计算。实验结果表明：经过分区域标定,相机采集点的总误差比单区域标定法降低了4％(Ｎ＝3)。算法可实现指定区域的相机参数计算,基本满足中高等精度的工业测量要求。所本文研究可应用于位置相对固定不变的工业视觉测量,特别是大工件测量领域。     

基于图形变换的人体经络可视化

提出了一种可以检测并直观表示人体经络分布的实时定位和显示方法。首先,利用多通道经络阻抗检测仪和磁定位跟踪仪确定人体体表经络点的位置,获取经络点的三维信息;其次,对场景摄像机进行标定,并将其结果和经络点的三维信息通过图形变换技术变换到统一的世界坐标系下,获取摄像机的投影矩阵H;最后,根据该投影矩阵H,将经络点三维信息投影到二维图像上,形成二维经络线,并将其融合于场景摄像机拍摄的人体体表实时图像上,实现人体经络的可视化。测试结果表明,该方法能够准确有效地定位和显示人体经络。     

基于视频的静止虚拟摄像机生成

虚拟摄像机的生成是虚拟广告系统中一项关键技术,提出一种静止虚拟摄像机生成方法。首先,在视频图像中自动检测比赛场地的特征点,然后根据特征点在图像坐标系与世界坐标系上的匹配关系,利用摄像机定标技术计算出真实摄像机的内外参数,接着把摄像机的内参数和外参数分别转换为虚拟摄像机的视点转换矩阵和投影矩阵,最后在此虚拟摄像机下对虚拟场景进行渲染,把渲染出的图像插入到视频中。实验结果表明该方法简单、有效、易实现。     

A Stochastic Kinematic Model of Class Averaging in Single-Particle Electron Microscopy

Single-particle electron microscopy is an experimental technique that is used to determine the 3D structure of biological macromolecules and the complexes that they form. In general, image processing techniques and reconstruction algorithms are applied to micrographs, which are two-dimensional (2D) images taken by electron microscopes. Each of these planar images can be thought of as a projection of the macromolecular structure of interest from an a priori unknown direction. A class is defined as a collection of projection images with a high degree of similarity, presumably resulting from taking projections along similar directions. In practice, micrographs are very noisy and those in each class are aligned and averaged in order to reduce the background noise. Errors in the alignment process are inevitable due to noise in the electron micrographs. This error results in blurry averaged images. In this paper, we investigate how blurring parameters are related to the properties of the background noise in the case when the alignment is achieved by matching the mass centers and the principal axes of the experimental images. We observe that the background noise in micrographs can be treated as Gaussian. Using the mean and variance of the background Gaussian noise, we derive equations for the mean and variance of translational and rotational misalignments in the class averaging process. This defines a Gaussian probability density on the Euclidean motion group of the plane. Our formulation is validated by convolving the derived blurring function representing the stochasticity of the image alignments with the underlying noiseless projection and comparing with the original blurry image.     

线结构光视觉传感器直接标定方法

分析了传感器测量模型,推导了摄像机畸变模型下的像坐标与像素坐标变换关系,在此基础上,提出了一种基于二元五次多项式拟合的线结构光视觉传感器物像标定模型。在数控平台上,利用锯齿形标定块获取一组标定点,应用最小二乘方法实现参数标定。标定与测量实验表明：本方法实现简单,精度较高,满足测量要求。