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.     

Fitting conics to paracatadioptric projections of lines

The paracatadioptric camera is one of the most popular panoramic systems currently available in the market. It provides a wide field of view by combining a parabolic shaped mirror with a camera inducing an orthographic projection. Previous work proved that the paracatadioptric projection of a line is a conic curve, and that the sensor can be fully calibrated from the image of three or more lines. However, the estimation of the conic curves where the lines are projected is hard to accomplish because of the partial occlusion. In general only a small arc of the conic is visible in the image, and conventional conic fitting techniques are unable to accurately estimate the curve. The present work provides methods to overcome this problem. We show that in uncalibrated paracatadioptric views a set of conic curves is a set of line projections if and only if certain properties are verified. These properties are used to constrain the search space and correctly estimate the curves. The conic fitting is solved naturally by an eigensystem whenever the camera is skewless and the aspect ratio is known. For the general situation the line projections are estimated using non-linear optimization. The set of paracatadioptric lines is used in a geometric construction to determine the camera parameters and calibrate the system. We also propose an algorithm to estimate the conic locus corresponding to a line projection in a calibrated paracatadioptric image. It is proved that the set of all line projections is a hyperplane in the space of conic curves. Since the position of the hyperplane depends only on the sensor parameters, the accuracy of the estimation can be improved by constraining the search to conics lying in this subspace. We show that the fitting problem can be solved by an eigensystem, which leads to a robust and computationally efficient method for paracatadioptric line estimation.     

Calibration of an active binocular head

In this paper, we show how an active binocular head, the IIS head, can be easily calibrated with very high accuracy. Our calibration method can also be applied to many other binocular heads. In addition to the proposal and demonstration of a four-stage calibration process, there are three major contributions in this paper. First, we propose a motorized-focus lens (MFL) camera model which assumes constant nominal extrinsic parameters. The advantage of having constant extrinsic parameters is to having a simple head/eye relation. Second, a calibration method for the MFL camera model is proposed in this paper, which separates estimation of the image center and effective focal length from estimation of the camera orientation and position. This separation has been proved to be crucial; otherwise, estimates of camera parameters would be very noise-sensitive. Thirdly, we show that, once the parameters of the MFL camera model is calibrated, a nonlinear recursive least-square estimator can be used to refine all the 35 kinematic parameters. Real experiments have shown that the proposed method can achieve accuracy of one pixel prediction error and 0.2 pixel epipolar error, even when all the joints, including the left and right focus motors, are moved simultaneously. This accuracy is good enough for many 3D vision applications, such as navigation, object tracking and reconstruction     

Camera calibration by vanishing lines for 3-D computer vision

A novel approach to camera calibration by vanishing lines is proposed. Calibrated parameters include the orientation, position, and focal length of a camera. A hexagon is used as the calibration target to generate a vanishing line of the ground plane from its projected image. It is shown that the vanishing line includes useful geometric hints about the camera orientation parameters and the focal length, from which the orientation parameters can be solved easily and analytically. And the camera position parameters can be calibrated by the use of related geometric projective relationships. The simplicity of the target eliminates the complexity of the environment setup and simplifies the feature extraction in relevant image processing. The calibration formulas are also simple to compute. Experimental results show the feasibility of the proposed approach     

Camera and light calibration from reflections on a sphere

This paper introduces a novel method for recovering light directions and camera parameters using a single sphere. Traditional methods for estimating light directions using spheres either assume both the radius and center of the sphere being known precisely, or they depend on multiple calibrated views to recover these parameters. In this paper, it will be shown that light directions can be uniquely determined from specular highlights observed in a single view of a sphere without knowing or recovering the exact radius and center of the sphere. Besides, given multiple views of the sphere, it will be shown that the focal length and the relative positions and orientations of the cameras can be determined using the recovered sphere and light directions. Closed form solutions for estimation of light directions and camera poses are presented, and an optimization procedure for estimation of the focal length is introduced. Experimental results on synthetic and real data demonstrates both the accuracy and robustness of the proposed method.     

手眼立体视觉的算法与实现

传统的定位方法要求标定出摄像机的内外参数,本文基于直接将图像坐标映射到机器 人参考坐标的“黑箱”思想,提出了末端执行器到机器人参考坐标系的一个恒定旋转矩阵． 使用恒定旋转矩阵使得目标三维定位的算法与标定参数的过程大大简化,同时具有较高的定 位精度．本文提出的三维目标定位方法同样可应用于移动式装配机器人和移动式操作手臂中 ．     

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.     

Camera calibration using one-dimensional information and its applications in both controlled and uncontrolled environments

Camera model and its calibration are required in many applications for coordinate conversions between the two-dimensional image and the real three-dimensional world. Self-calibration method is usually chosen for camera calibration in uncontrolled environments because the scene geometry could be unknown. However when no reliable feature correspondences can be established or when the camera is static in relation to the majority of the scene, self-calibration method fails to work. On the other hand, object-based calibration methods are more reliable than self-calibration methods due to the existence of the object with known geometry. However, most object-based calibration methods are unable to work in uncontrolled environments because they require the geometric knowledge on calibration objects. Though in the past few years the simplest geometry required for a calibration object has been reduced to a 1D object with at least three points, it is still not easy to find such an object in an uncontrolled environment, not to mention the additional metric/motion requirement in the existing methods. Meanwhile, it is very easy to find a 1D object with two end points in most scenes. Thus, it would be very worthwhile to investigate an object-based method based on such a simple object so that it would still be possible to calibrate a camera when both self-calibration and existing object-based calibration fail to work. We propose a new camera calibration method which requires only an object with two end points, the simplest geometry that can be extracted from many real-life objects. Through observations of such a 1D object at different positions/orientations on a plane which is fixed in relation to the camera, both intrinsic (focal length) and extrinsic (rotation angles and translations) camera parameters can be calibrated using the proposed method. The proposed method has been tested on simulated data and real data from both controlled and uncontrolled environments, including situations where no explicit 1D calibration objects are available, e.g. from a human walking sequence. Very accurate camera calibration results have been achieved using the proposed method.     

Conic reconstruction and correspondence from two views

Conics are widely accepted as one of the most fundamental image features together with points and line segments. The problem of space reconstruction and correspondence of two conics from two views is addressed in this paper. It is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views, given the relative orientation of the two views. These two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics. A unified closed-form solution is also developed for both projective reconstruction of conics in space from two uncalibrated camera views and metric reconstruction from two calibrated camera views. Experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images     

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.     

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。     

一种基于主动视觉的线性自标定方法

基于主动视觉的摄像机自标定是摄像机标定的一个重要分支，通过控制摄像机做严格的运动，可以发现一些比较简单的算法，本文提出了一种新的基于主动视觉的摄像机自标定方法，通过控制摄像机作3次不共面的平移运动．可以线性标定摄像机的五个内参数．大量的仿真实验表明该算法精度很高，且鲁棒性很强．     

Computing camera parameters using vanishing-line information from a rectangular parallelepiped

A new approach to camera calibration using vanishing line information for three-dimensional computer vision is proposed. Calibrated parameters include the orientation, the position, the focal length, and the image plane center of a camera. A rectangular parallelepiped is employed as the calibration target to generate three principal vanishing points and then three vanishing lines from the projected image of the parallelepiped. Only a monocular image is required for solving these camera parameters. It is shown that the image plane center is the orthocenter of a triangle formed by the three vanishing lines. From the slopes of the vanishing lines the camera orientation parameters can be determined. The focal length can be computed by the area of the triangle. The camera position parameters can then be calibrated by using related geometric projective relationships. The derived results show the geometric meanings of these camera parameters. The calibration formulas are analytic and simple to compute. Experimental results show the feasibility of the proposed approach for a practical application—autonomous land vehicle guidance.This work was supported by National Science Council, Republic of China under Grant NSC-77-0404-E-009-31.     

基于平面二次曲线的摄像机标定

提出了一种基于平面二次曲线的摄像机标定方法 .该方法只需要摄像机在 2个或 2个以上不同的方位摄取一个含有 3个或 3个以上同心二次曲线的平面模板的图像 ,摄像机和平面模板都可以自由移动 .所提出的摄像机标定方法在求解过程中不需要非线性迭代 ,可以直接获得解析解 .由于该方法利用二次曲线作为标定基元 ,简化了基元对应问题 ,并且精度和稳定性都比较高 .另外该方法原理简单 ,对设备的要求比较低 ,非常适合对计算机视觉不太熟悉的人员使用 .     

Euclidean structure from confocal conics: Theory and application to camera calibration

We propose confocal conics as a new planar pattern for camera calibration with poses. We show that confocal conics encode the metric information which can be easily extracted with their generalized eigenvalues. The proposed method is tested with synthetic and real data, and shows comparable performances with conventional algorithms, while it still has all virtues of curved features.     

Easy Calibration of a Multi-projector Display System

In this paper, we present a method for the geometric calibration of a multi-projector display system. The method is such that in order to calibrate the system, the user is only required to place the projectors and capture a single image of the images projected from them onto a planar screen using a hand-held camera. The problem to be solved is divided into the image registration for stitching different projector images into a single seamless image and the image rectification for making the image have the correct rectangular shape. The proposed method is characterized by simultaneously solving both of them from only a single image, which makes the calibration procedures easy. The method assumes an uncalibrated camera and partially calibrated projectors in which only focal lengths are unknown among the internal parameters. In the paper, we first prove the uniqueness of solutions to the problem, which was unclear in the previous studies, and then present a stable numerical algorithm for actually finding the solution. We present several experimental results for synthetic data, in which we show the relation between the calibration accuracy and several factors, and also present experimental results for real data, in which we demonstrate that the proposed method can calibrate a real system with sufficient accuracy for a number of layouts of the projectors.     

一种基于图像序列和外部平移数据的摄像机自定标方法

摄像机标定是从二维图像获取三维信息必不可少的步骤。本文提出了一种新的基于图像序列的自定标方法。通过控制摄像机平台作3次平移运动（其中任意2次均不在同一平面上）且不需要读取运动平台的平移数据，即可线性地标定摄像机的内参数。大量的模拟实验表明该算法精度高和鲁棒性强。     

视觉导航中的单目摄像机标定改进算法

在基于单目视觉的智能车自主导航系统中,摄像机标定是智能车实现安全准确视觉导航的前提和关键。研究摄像机理想模型和实际模型,提出一种改进的标定方法。结合线性模型和非线性模型的优点,在求解摄像机内外参数的过程中,先采用线性模型标定摄像机的一部分参数,进一步考虑简化畸变模型,将非线性方程组转化为线性方程组迭代求解,最终获得摄像机全部参数。该方法既保证了标定精度,又简化了复杂的摄像机实际模型。实验结果表明该方法能满足视觉导航要求。     

Hypercatadioptric line images for 3D orientation and image rectification

In central catadioptric systems 3D lines are projected into conics. In this paper we present a new approach to extract conics in the raw catadioptric image, which correspond to projected straight lines in the scene. Using the internal calibration and two image points we are able to compute analytically these conics which we name hypercatadioptric line images. We obtain the error propagation from the image points to the 3D line projection in function of the calibration parameters. We also perform an exhaustive analysis on the elements that can affect the conic extraction accuracy. Besides that, we exploit the presence of parallel lines in man-made environments to compute the dominant vanishing points (VPs) in the omnidirectional image. In order to obtain the intersection of two of these conics we analyze the self-polar triangle common to this pair. With the information contained in the vanishing points we are able to obtain the 3D orientation of the catadioptric system. This method can be used either in a vertical stabilization system required by autonomous navigation or to rectify images required in applications where the vertical orientation of the catadioptric system is assumed. We use synthetic and real images to test the proposed method. We evaluate the 3D orientation accuracy with a ground truth given by a goniometer and with an inertial measurement unit (IMU). We also test our approach performing vertical and full rectifications in sequences of real images.