基于空间透视不变量的摄象机标定方法

本文给出了一种以空间不变量的数据来计算摄象机外部参数的方法．空间透视不变量是指在几何变换中如投影或改变观察点时保持不变的形状描述．由于它可以得到一个相对于外界来讲独立的物体景物的特征描述，故可以很广泛的应用到计算机视觉等方面．摄象机标定是确定摄象机摄取的２Ｄ图象信息及其３Ｄ实际景物的信息之间的变换关系，它包括内部参数和外部参数两个部分．内部参数表征的是摄象机的内部特征和光学特征参数，包括图象中心（Ｃｘ，Ｃｙ）坐标、图象尺度因子Ｓｘ、有效的焦距长度ｆ和透镜的畸变失真系数Ｋ；外部参数表示的是摄象机的位置和方向在世界坐标中的坐标参数，它包括平移矩阵Ｔ和旋转矩阵Ｒ３×３，一般情况下可以写成一个扩展矩阵［ＲＴ］３×４．本文基于空间透视不变量的计算数据，给出了一种标定摄象机外部参数的方法，实验结果表明该方法具有很强的鲁棒性．     

Autocalibration with the Minimum Number of Cameras with Known Pixel Shape

In 3D reconstruction, the recovery of the calibration parameters of the cameras is paramount since it provides metric information about the observed scene, e.g., measures of angles and ratios of distances. Autocalibration enables the estimation of the camera parameters without using a calibration device, but by enforcing simple constraints on the camera parameters. In the absence of information about the internal camera parameters such as the focal length and the principal point, the knowledge of the camera pixel shape is usually the only available constraint. Given a projective reconstruction of a rigid scene, we address the problem of the autocalibration of a minimal set of cameras with known pixel shape and otherwise arbitrarily varying intrinsic and extrinsic parameters. We propose an algorithm that only requires 5 cameras (the theoretical minimum), thus halving the number of cameras required by previous algorithms based on the same constraint. To this purpose, we introduce as our basic geometric tool the six-line conic variety (SLCV), consisting in the set of planes intersecting six given lines of 3D space in points of a conic. We show that the set of solutions of the Euclidean upgrading problem for three cameras with known pixel shape can be parameterized in a computationally efficient way. This parameterization is then used to solve autocalibration from five or more cameras, reducing the three-dimensional search space to a two-dimensional one. We provide experiments with real images showing the good performance of the technique.     

Camera calibration for a mobile robot prototype

Stereovision is an effective technique to use a CCD video camera to determine the 3D position of a target object from two or more simultaneous views of the scene. Camera calibration is a central issue in finding the position of objects in a stereovision system. This is usually carried out by calibrating each camera independently, and then applying a geometric transformation of the external parameters to find the geometry of the stereo setting. After calibration, the distance of various target objects in the scene can be calculated with CCD video cameras, and recovering the 3D structure from 2D images becomes simpler. However, the process of camera calibration is complicated. Based on the ideal pinhole model of a camera, we describe formulas to calculate intrinsic parameters that specify the correct camera characteristics, and extrinsic parameters that describe the spatial relationship between the camera and the world coordinate system. A simple camera calibration method for our CCD video cameras and corresponding experiment results are also given. This work was presented in part at the 7th International Symposium on Artificial Life and Robotics, Oita, Japan, January 16–18, 2002     

Self-calibration of hybrid central catadioptric and perspective cameras

Hybrid central catadioptric and perspective cameras are desired in practice, because the hybrid camera system can capture large field of view as well as high-resolution images. However, the calibration of the system is challenging due to heavy distortions in catadioptric cameras. In addition, previous calibration methods are only suitable for the camera system consisting of perspective cameras and catadioptric cameras with only parabolic mirrors, in which priors about the intrinsic parameters of perspective cameras are required. In this work, we provide a new approach to handle the problems. We show that if the hybrid camera system consists of at least two central catadioptric and one perspective cameras, both the intrinsic and extrinsic parameters of the system can be calibrated linearly without priors about intrinsic parameters of the perspective cameras, and the supported central catadioptric cameras of our method can be more generic. In this work, an approximated polynomial model is derived and used for rectification of catadioptric image. Firstly, with the epipolar geometry between the perspective and rectified catadioptric images, the distortion parameters of the polynomial model can be estimated linearly. Then a new method is proposed to estimate the intrinsic parameters of a central catadioptric camera with the parameters in the polynomial model, and hence the catadioptric cameras can be calibrated. Finally, a linear self-calibration method for the hybrid system is given with the calibrated catadioptric cameras. The main advantage of our method is that it cannot only calibrate both the intrinsic and extrinsic parameters of the hybrid camera system, but also simplify a traditional nonlinear self-calibration of perspective cameras to a linear process. Experiments show that our proposed method is robust and reliable.     

Plane-Based Calibration for Linear Cameras

Linear or 1D cameras are used in several areas such as industrial inspection and satellite imagery. Since 1D cameras consist of a linear sensor, a motion (usually perpendicular to the sensor orientation) is performed in order to acquire a full image. In this paper, we present a novel linear method to estimate the intrinsic and extrinsic parameters of a 1D camera using a planar object. As opposed to traditional calibration scheme based on 3D-2D correspondences of landmarks, our method uses homographies induced by the images of a planar object. The proposed algorithm is linear, simple and produces good results as shown by our experiments.     

Some aspects of zoom lens camera calibration

Zoom lens camera calibration is an important and difficult problem for two reasons at least. First, the intrinsic parameters of such a camera change over time, it is difficult to calibrate them on-line. Secondly, the pin-hole model for single lens system can not be applied directly to a zoom lens system. In this paper, we address some aspects of this problem, such as determining principal point by zooming, modeling and calibration of lens distortion and focal length, as well as some practical aspects. Experimental results on calibrating cameras with computer controlled zoom, focus and aperture are presented     

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.     

一种反射折射摄像机的简易标定方法

Central catadioptric cameras are widely used in virtual reality and robot navigation, and the camera calibration is a prerequisite for these applications. In this paper, we propose an easy calibration method for central catadioptric cameras with a 2D calibration pattern. Firstly, the bounding ellipse of the catadioptric image and field of view (FOV) are used to obtain the initial estimation of the intrinsic parameters. Then, the explicit relationship between the central catadioptric and the pinhole model is used to initialize the extrinsic parameters. Finally, the intrinsic and extrinsic parameters are refined by nonlinear optimization. The proposed method does not need any fitting of partial visible conic, and the projected images of 2D calibration pattern can easily cover the whole image, so our method is easy and robust. Experiments with simulated data as well as real images show the satisfactory performance of our proposed calibration method.     

一种反射折射摄像机的简易标定方法

Central catadioptric cameras are widely used in virtual reality and robot navigation,and the camera calibration is a prerequisite for these applications.In this paper,we propose an easy calibration method for central catadioptric cameras with a 2D calibration pattern.Firstly,the bounding ellipse of the catadioptric image and field of view (FOV) are used to obtain the initial estimation of the intrinsic parameters.Then,the explicit relationship between the central catadioptric and the pinhole model is used to initialize the extrinsic parameters.Finally,the intrinsic and extrinsic parameters are refined by nonlinear optimization.The proposed method does not need any fitting of partial visible conic,and the projected images of 2D calibration pattern can easily cover the whole image,so our method is easy and robust.Experiments with simulated data as well as real images show the satisfactory performance of our proposed calibration method.     

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.     

Generalized Camera Calibration Including Fish-Eye Lenses

A method is described for accurately calibrating cameras including radial lens distortion, by using known points such as those measured from a calibration fixture. Both the intrinsic and extrinsic parameters are calibrated in a single least-squares adjustment, but provision is made for including old values of the intrinsic parameters in the adjustment. The distortion terms are relative to the optical axis, which is included in the model so that it does not have to be orthogonal to the image sensor plane. These distortion terms represent corrections to the basic lens model, which is a generalization that includes the perspective projection and the ideal fish-eye lens as special cases. The position of the entrance pupil point as a function of off-axis angle also is included in the model. (The complete camera model including all of these effects often is called CAHVORE.) A way of adding decentering distortion also is described. A priori standard deviations can be used to apply weight to given initial approximations (which can be zero) for the distortion terms, for the difference between the optical axis and the perpendicular to the sensor plane, and for the terms representing movement of the entrance pupil, so that the solution for these is well determined when there is insufficient information in the calibration data. For the other parameters, initial approximations needed for the nonlinear least-squares adjustment are obtained in a simple manner from the calibration data and other known information. (Weight can be given to these also, if desired.) Outliers among the calibration points that disagree excessively with the other data are removed by means of automatic editing based on analysis of the residuals. The use of the camera model also is described, including partial derivatives for propagating both from object space to image space and vice versa. These methods were used to calibrate the cameras on the Mars Exploration Rovers.     

一种摄像机复合标定方法及其在汽车碰撞实验中的应用

提出了一种摄像机的复合标定方法:基于共面点分步标定摄像机的初始内外参数;基于最小二乘法求解径向畸变参数,进而迭代优化。标定点的识别中,中心点的识别采用了Hough直线检测及直线求交法,避免通常的Hough椭圆检测法带来的测量误差。应用于汽车碰撞过程的定性和定量分析,结果表明了其有效性与稳定性。     

Recent Developments in 3D Multi-modal Laser Imaging Applied to Cultural Heritage

This paper proposes a novel multi-modal three-dimensional (3D) laser scanning system that combines high-accuracy 3D laser imaging, very high-resolution perspective color projection, and on-site geometric calibration of the intrinsic and extrinsic parameters. Motion compensation directly from the range measurements using ICP and a 6-DOF self-built model tracking is also used to eliminate the need for stable mechanical structures and external positioning sensors. We show that scanner performances, modeling, and visualization are intimately linked and must be considered as an integral part of the modeling chain. This is particularly important in the field of heritage where the acquisition must adapt to the environment. Equations and charts are presented to compute the optimum color camera and laser scanner configuration for a given 3D modeling application in terms of camera settings such as optimum lens aperture, focal length, optimum range, and total range depth. These equations are general and can be used for most 3D acquisition systems including time-of-flight laser scanners. Experimental results are presented to demonstrate the validity of the approach.     

基于一维移动物体的双目装置自标定

给出了平移运动的一维物体所在平面的虚圆点图像及其对摄像机内参数的约束，和约束方程的数值求解方法，从而获得摄像机的内参数. 进一步通过恢复空间点在摄像机坐标系中的坐标，求解出双目摄像机之间的方位，即摄像机的外参数．对于一维物体的一般刚体运动，给出了把它转化为平移运动的方法．模拟实验和真实图像实验结果表明该方法具有较高的求解精度，同时也有一定的应用价值．     

基于单幅图片的相机完全标定

现有相机标定方法的标定过程比较繁琐,不利于标定相机的广泛使用。为此,从摄像机镜头畸变矫正着手,结合标定板信息及消失点约束,提出一种基于单张图片的相机标定方法。利用非线性迭代得到相机镜头的畸变系数,通过线性求解得出相机的内参,直接计算得到相机的外参,从而实现仅需拍摄单张标定板图片的相机完全标定。实验结果表明,该方法在标定板与视平面夹角小于45°的情况下均能成功标定,并且重投影误差小于0.3像素。     

一种基于校正误差的立体相机标定算法

立体相机的标定是一个精确求解各个相机内参数以及相机之间关系参数的过程.它是三维重建的基础,其标定精度的好坏直接影响立体重建的结果.为此提出了一种使用校正误差作为代价函数的立体相机标定算法.该算法首先使用传统的基于重投影误差的方法对单个相机的内参数进行标定,然后利用校正误差完成对相机之间关系参数的标定求解.由于校正误差的计算只与相机内参数以及关系参数有关,可以避免在标定过程中使用难以精确标定的相机外参数.实验结果表明本算法能够有效的提高立体相机标定的精度.     

Using pedestrians walking on uneven terrains for camera calibration

A calibrated camera is essential for computer vision systems: the prime reason being that such a camera acts as an angle measuring device. Once the camera is calibrated, applications like three-dimensional reconstruction or metrology or other applications requiring real world information from the video sequences can be envisioned. Motivated by this, we address the problem of calibrating multiple cameras, with an overlapping field of view observing pedestrians in a scene walking on an uneven terrain. This problem of calibration on an uneven terrain has so far not been addressed in the vision community. We automatically estimate vertical and horizontal vanishing points by observing pedestrians in each camera and use the corresponding vanishing points to estimate the infinite homography existing between the different cameras. This homography provides constraints on intrinsic (or interior) camera parameters while also enabling us to estimate the extrinsic (or exterior) camera parameters. We test the proposed method on real as well as synthetic data, in addition to motion capture dataset and compare our results with the state of the art.     

一种基于平面模板的多摄像机标定方法*

对于均匀环绕四周的多台摄像机,先对每个摄像机利用Zhang的平面模板标定方法单独获得内参;在外参计算方面,提出了一种多摄像机外参标定的新方法,该方法在ICP(iterative closest point)算法的基础上,结合了VR(view registration)算法的约束优化思想,先通过两两相邻像机间自由移动平面模板计算两者的位置关系,最后将每一个摄像机统一到一个世界坐标系。标定过程操作简便,易于实现。实验结果表明,本方法能够满足后续三维重建所需的精度要求。     

三维视觉测量技术中的双目纹理映射技术

设计了基于双目摄像机的三维纹理映射系统,单色和彩色摄像机分别负责三维坐标和颜色信息的采集;建立了双目摄像机的像素匹配模型,并设计了简单的标定方法,确定模型中的内部和结构参数,建立高精度的像素对应关系,配合实现三维数据的纹理映射。还对双目纹理映射方法的测量过程进行了详细描述。经过实验验证,该方法不仅简单易用,还具有高于0.1个像素的匹配精度。     

Model-driven active visual tracking

We have previously demonstrated that the performance of tracking algorithms can be improved by integrating information from multiple cues in a model-driven Bayesian reasoning framework. Here we extend our work to active vision tracking, with variable camera geometry. Many existent active tracking algorithms avoid the problem of variable camera geometry by tracking view independent features, such as corners and lines. However, the performance of algorithms based on those single features will greatly deteriorate in the presence of specularities and dense clutter. We show, by integrating multiple cues and updating the camera geometry on-line, that it is possible to track a complicated object moving arbitrarily in three-dimensional (3D) space.We use a four degree-of-freedom (4-DoF) binocular camera rig to track three focus features of an industrial object, whose complete model is known. The camera geometry is updated by using the rig control commands and kinematic model of the stereo head. The extrinsic parameters are further refined by interpolation from a previously sampled calibration of the head work space.The 2D target position estimates are obtained by a combination of blob detection, edge searching and gray-level matching, with the aid of model geometrical structure projection using current estimates of camera geometry. The information is represented in the form of a probability density distribution, and propagated in a Bayes Net. The Bayesian reasoning that is performed in the 2D image is coupled by the rigid model geometry constraint in 3D space.An αβ filter is used to smooth the tracking pursuit and to predict the position of the object in the next iteration of data acquisition. The solution of the inverse kinematic problem at the predicted position is used to control the position of the stereo head.Finally, experiments show that the target undertaking arbitrarily 3D motion can be successfully tracked in the presence of specularities and dense clutter.