Camera calibration and light source orientation from solar shadows

In this paper, we describe a method for recovering camera parameters from perspective views of daylight shadows in a scene, given only minimal geometric information determined from the images. This minimal information consists of two 3D stationary points and their cast shadows on the ground plane. We show that this information captured in two views is sufficient to determine the focal length, the aspect ratio, and the principal point of a pinhole camera with fixed intrinsic parameters. In addition, we are also able to compute the orientation of the light source. Our method is based on exploiting novel inter-image constraints on the image of the absolute conic and the physical properties of solar shadows. Compared to the traditional methods that require images of some precisely machined calibration patterns, our method uses cast shadows by the sun, which are common in natural environments, and requires no measurements of any distance or angle in the 3D world. To demonstrate the accuracy of the proposed algorithm and its utility, we present the results on both synthetic and real images, and apply the method to an image-based rendering problem.     

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     

未知主点条件的相机焦距自标定方法

对于双目相机焦距自标定,当前研究方法均假定相机主点位置已知,而相机主点在实际中却通常是未知的,提出一种主点和场景均未知的条件下相机焦距自标定的新方法,通过严格的数学分析表明相机的坐标系尺度对焦距标定具有重要影响,并在坐标系尺度影响的定量分析的基础上提出了一种选择合适的坐标系尺度算法。模拟和实际实验都验证了坐标系尺度的重要性,且该方法较传统方法可获得更好的标定精度。     

Paracatadioptric camera calibration

Catadioptric sensors refer to the combination of lens-based devices and reflective surfaces. These systems are useful because they may have a field of view which is greater than hemispherical, providing the ability to simultaneously view in any direction. Configurations which have a unique effective viewpoint are of primary interest, among these is the case where the reflective surface is a parabolic mirror and the camera is such that it induces an orthographic projection and which we call paracatadioptric. We present an algorithm for the calibration of such a device using only the images of lines in space. In fact, we show that we may obtain all of the intrinsic parameters from the images of only three lines and that this is possible without any metric information. We propose a closed-form solution for focal length, image center, and aspect ratio for skewless cameras and a polynomial root solution in the presence of skew. We also give a method for determining the orientation of a plane containing two sets of parallel lines from one uncalibrated view. Such an orientation recovery enables a rectification which is impossible to achieve in the case of a single uncalibrated view taken by a conventional camera. We study the performance of the algorithm in simulated setups and compare results on real images with an approach based on the image of the mirror's bounding circle     

Characterization of Errors in Compositing Panoramic Images

A panoramic image has a 360° horizontal field of view, and it can provide the viewer the impression of being immersed in the scene. A panorama is created by first taking a sequence of images while rotating the camera about a vertical axis. These images are then projected onto a cylindrical surface before being seamlessly composited. The cross-sectional circumference of the cylindrical panorama is called thecompositing length. This work characterizes the error in compositing panoramic images due to errors in some of the intrinsic parameters. The intrinsic camera parameters that are considered are the camera focal length and the radial distortion coefficient. We show that the error in the compositing length is more sensitive to the error in the camera focal length. Especially important is the discovery that the relative error in compositing length is always smaller than the relative error in the focal length. This means that the error in focal length can be corrected by iteratively using the composited length to compute a new and more correct focal length. Thiscompositing approach to camera calibrationhas the advantages of not requiring both feature detection and separate prior calibration.     

基于空间共线点的单光心反射折射摄像机标定

一条空间直线的单光心反射折射图像是一个二次曲线段, 大多数利用直线进行单光心反射折射摄像机标定的方法都需要对直线的像进行二次曲线拟合, 曲线拟合的精度严重影响着标定的精度. 然而, 一条空间直线的像仅占整个二次曲线的一小段, 这使得曲线拟合的效果非常差. 本文利用空间三个共线点的反射折射投影给出了摄像机内参数的一个非线性约束. 当反射镜面为抛物面时, 在主点已知的情况下, 该约束变为线性约束. 如其他参数已知, 该约束变为关于有效焦距的多项式约束. 由此, 本文提出了三种不同条件下的标定算法, 算法中无需对直线的像进行二次曲线拟合, 无需场景的任何信息, 标定精度较高. 实验验证了算法的有效性.     

Camera re-calibration after zooming based on sets of conics

We describe a method to compute the internal parameters (focal and principal point) of a camera with known position and orientation, based on the observation of two or more conics on a known plane. The conics can even be degenerate (e.g., pairs of lines). The proposed method can be used to re-estimate the internal parameters of a fully calibrated camera after zooming to a new, unknown, focal length. It also allows estimating the internal parameters when a second, fully calibrated camera observes the same conics. The parameters estimated through the proposed method are coherent with the output of more traditional procedures that require a higher number of calibration images. A deep analysis of the geometrical configurations that influence the proposed method is also reported.     

A determination method of initial camera parameters for coplanar calibration

Most coplanar calibration algorithms determine the initial camera parameters from a single image under the assumption that the principal point is known in advance. However, the camera orientations, the shifted principal point and the noise corrupted on images have an influence on the estimated initial camera parameters under the above assumption. This paper proposes a useful method to determine the initial camera parameters for coplanar calibration. The proposed method can determine the initial camera parameters from the single image, wherein the principal point is considered as a parameter. In our experiments, both synthetic and real images are used. The experimental results show that the proposed method provides both stable initial camera parameters and noise robustness for changes of camera orientations, noise levels and shifts of principal point.     

一种新的摄像机自定标的方法

本文给出一种由未定标图像进行摄像机自定标的方法．通过分析基础矩阵关系式及方 差之间关系,得出一种新的计算摄像机内部参数及运动参数的准则．在计算中采用单个摄 像机并且假设摄像机像主点的位置已知,大大简化了运算量．     

Computing camera focal length by zooming a single point

In this paper we present a novel simple procedure to compute the focal length of a camera. The method is based on zooming in and out only a single point. The same approach allows computing the principal point when only two points are available on a pair of images surveyed with a different focal length. Experimental results show that the method is as accurate as classical full calibration methods. Moreover, its application to augmented reality produces more accurate results than those obtained when the simple pin-hole model is considered.     

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.     

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．     

Simplified Active Calibration

We present a new mathematical formulation to estimate the intrinsic parameters of a camera in active or robotic platforms. We show that the focal lengths can be estimated using only one point correspondence that relates images taken before and after a degenerate rotation of the camera. The estimated focal lengths are then treated as known parameters to obtain a linear set of equations to calculate the principal point. Assuming that the principal point is close to the image center, the accuracy of the linear equations are increased by integrating the image center into the formulation. We extensively evaluate the formulations on a simulated camera, 3D scenes and real-world images. Our error analysis over simulated and real images indicates that the proposed Simplified Active Calibration method estimates the parameters of a camera with low error rates that can be used as an initial guess for further non-linear refinement procedures. Simplified Active Calibration can be employed in real-time environments for automatic calibrations given the proposed closed-form solutions.     

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。     

Stratified self-calibration with the modulus constraint

In computer vision and especially for 3D reconstruction, one of the key issues is the retrieval of the calibration parameters of the camera. These are needed to obtain metric information about the scene from the camera. Often these parameters are obtained through cumbersome calibration procedures. There is a way to avoid explicit calibration of the camera. Self-calibration is based on finding the set of calibration parameters which satisfy some constraints (e.g., constant calibration parameters). Several techniques have been proposed but it often proved difficult to reach a metric calibration at once. Therefore, in the paper, a stratified approach is proposed, which goes from projective through affine to metric. The key concept to achieve this is the modulus constraint. It allows retrieval of the affine calibration for constant intrinsic parameters. It is also suited for use in conjunction with scene knowledge. In addition, if the affine calibration is known, it can also be used to cope with a changing focal length     

基于Huang-Faugeras约束的相机分步自标定方法

提出一种运动变焦相机分步自标定的方法。因相机在运动过程中其纵横比、主点固定不变，可以事先标定；在假设像素无扭曲的情况下基于Huang-Faugeras约束线性求解焦距，只需输入基础矩阵，不必须进行任务类型的投影阵分解或投影束校正。线性求解焦距避免了非线性法的不稳定性，实际数值实验表明文中方法简单实用。     

基于环视图象的数字相机内参数自定标方法

描述了一种适用于IBR系统的数字相机内参数自定标方法。该方法基于跟踪机机旋转得到的图象系列的特征匹配点以,而不需要标定物。认定在相机旋转过程中,其光学中心是稳定不变的,也即图象中心是固定的,可以事先定标;但容许相机的焦距在各幅图象间有变化,利用真实图象序列进行了实验验证,表明该方法能鲁棒地估算相机内参数。     

散焦模糊量估计的相机加权标定方法

相机标定在计算机视觉领域中有着至关重要的作用.绝大多数相机标定方法假设相机为针孔模型,且需要良好聚焦的图像来保证相机内外参估计的准确性.然而,这些条件会受到相机景深的影响.在薄透镜相机模型假设下,提出了一种加权相机标定的方法,其权重考虑了控制点的模糊量信息.首先对棋盘格标定物上的每一个角点进行散焦模糊量估计,在标定过程中,将散焦模糊量的大小作为一个权重加入到标定能量函数最小化过程中,使得标定精度得到提高.该方法简单高效,不需要额外的数码设备或者特别定做的标定物.在Intel Core i7处理器的计算机下,使用合成数据以及真实数据上进行的实验结果表明,文中方法能够有效减小重投影误差,提高张正友标定方法的标定精度.