1D camera geometry and its application to the self-calibration of circular motion sequences

This paper proposes a novel method for robustly recovering the camera geometry of an uncalibrated image sequence taken under circular motion. Under circular motion, all the camera centers lie on a circle and the mapping from the plane containing this circle to the horizon line observed in the image can be modelled as a 1D projection. A 2x2 homography is introduced in this paper to relate the projections of the camera centers in two 1D views. It is shown that the two imaged circular points of the motion plane and the rotation angle between the two views can be derived directly from such a homography. This way of recovering the imaged circular points and rotation angles is intrinsically a multiple view approach, as all the sequence geometry embedded in the epipoles is exploited in the estimation of the homography for each view pair. This results in a more robust method compared to those computing the rotation angles using adjacent views only. The proposed method has been applied to self-calibrate turntable sequences using either point features or silhouettes, and highly accurate results have been achieved.     

Using vanishing points for camera calibration

In this article a new method for the calibration of a vision system which consists of two (or more) cameras is presented. The proposed method, which uses simple properties of vanishing points, is divided into two steps. In the first step, the intrinsic parameters of each camera, that is, the focal length and the location of the intersection between the optical axis and the image plane, are recovered from a single image of a cube. In the second step, the extrinsic parameters of a pair of cameras, that is, the rotation matrix and the translation vector which describe the rigid motion between the coordinate systems fixed in the two cameras are estimated from an image stereo pair of a suitable planar pattern. Firstly, by matching the corresponding vanishing points in the two images the rotation matrix can be computed, then the translation vector is estimated by means of a simple triangulation. The robustness of the method against noise is discussed, and the conditions for optimal estimation of the rotation matrix are derived. Extensive experimentation shows that the precision that can be achieved with the proposed method is sufficient to efficiently perform machine vision tasks that require camera calibration, like depth from stereo and motion from image sequence.     

Self-calibration from one circular motion sequence and two images

This paper describes a new method for self-calibration of camera with constant internal parameters under circular motion, using one sequence and two images captured with different camera orientations. Unlike the previous method, in which three circular motion sequences are needed with known motion, the new method computes the rotation angles and the projective reconstructions of the sequence and the images with circular constraint enforced, which is called a circular projective reconstruction, using a factorization-based method. It is then shown that the images of the circular points of each circular projective reconstruction can be readily obtained. Subsequently, the image of the absolute conic and the calibration matrix of the camera can be determined. Experiments on both synthetic and real image sequence are given, showing the accuracy and robustness of the new algorithm.     

单轴运动下未标定图像序列的度量重构

提出了一种由单轴运动下的未标定运动图像序列进行三维重构的新方法。利用不变量计算出第一幅图像对应的摄像机矩阵,根据转台的旋转角度计算出其余图像对应的摄像机矩阵,再使用SIFT算法查找相邻两幅图像可见的匹配点,并利用线性三角形法对图像进行重构,最后用捆集调整优化重构的结果。真实图像序列的重构实验验证了算法的正确性和有效性。     

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...     

Epipolar geometry from profiles under circular motion

Addresses the problem of motion estimation from profiles (apparent contours) of an object rotating on a turntable in front of a single camera. A practical and accurate technique for solving this problem from profiles alone is developed. It is precise enough to reconstruct the shape of the object. No correspondences between points or lines are necessary. Symmetry of the surface of revolution swept out by the rotating object is exploited to obtain the image of the rotation axis and the homography relating epipolar lines in two views robustly and elegantly. These, together with geometric constraints for images of rotating objects, are used to obtain first the image of the horizon, which is the projection of the plane that contains the camera centers, and then the epipoles, thus fully determining the epipolar geometry of the image sequence. The estimation of this geometry by this sequential approach avoids many of the problems found in other algorithms. The search for the epipoles, by far the most critical step, is carried out as a simple 1D optimization. Parameter initialization is trivial and completely automatic at all stages. After the estimation of the epipolar geometry, the Euclidean motion is recovered using the fixed intrinsic parameters of the camera obtained either from a calibration grid or from self-calibration techniques. Finally, the spinning object is reconstructed from its profiles using the motion estimated in the previous stage. Results from real data are presented, demonstrating the efficiency and usefulness of the proposed methods     

A new method for camera stratified self-calibration under circular motion

We consider the stratified self-calibration (affine and metric reconstruction) problem from images acquired with a camera with unchanging internal parameters undergoing circular motion. The general stratified method (modulus constraints) is known to fail with this motion. In this paper we give a novel constraint on the plane at infinity in projective reconstruction for circular motion, the constant inter-frame motion constraint on the plane at infinity between every two adjacent views and a fixed view of the motion sequences, by making use of the facts that in many commercial systems rotation angles are constant. An initial solution can be obtained by using the first three views of the sequence, and Stratified Iterative Particle Swarm Optimization (SIPSO) is proposed to get an accurate and robust solution when more views are at hand. Instead of using the traditional optimization algorithm as the last step to obtain an accurate solution, in this paper, the whole motion sequence information is exploited before computing the camera calibration matrix, this results in a more accurate and robust solution. Once the plane at infinity is identified, the calibration matrices of the camera and a metric reconstruction can be readily obtained. Experiments on both synthetic and real image sequence are given, showing the accuracy and robustness of the new algorithm.     

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．     

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.     

一种基于TOF相机与CCD相机的联合标定算法研究

针对基于Time-of-Flight(TOF)相机的彩色目标三维重建需标定CCD相机与TOF相机联合系统的几何参数,在研究现有的基于彩色图像和TOF深度图像标定算法的基础上,提出了一种基于平面棋盘模板的标定方法。拍摄了固定在平面标定模板上的彩色棋盘图案在不同角度下的彩色图像和振幅图像,改进了Harris角点提取,根据棋盘格上角点与虚拟像点的共轭关系,建立了相机标定系统模型,利用Levenberg-Marquardt算法求解,进行了标定实验。获取了TOF与CCD相机内参数,并利用像平面之间的位姿关系估计两相机坐标系的相对姿态,最后进行联合优化,获取了相机之间的旋转矩阵与平移向量。实验结果表明,提出的算法优化了求解过程,提高了标定效率,能够获得较高的精度。     

基于全周多视角的三维重建技术

提出一种基于圆分度台的三维模型拼接技术，其核心是把双目立体测量系统安装在步进电机控制的旋转平台上，旋转拍摄多视角下的场景影像，由所记录的相应角度值，通过坐标变换将不同视角场景模型进行三维拼接．论述了旋转装置的参数标定以及同一视点下不同视角的坐标转换关系．该方法只需一次标定，自动完成测量数据的采集与拼合，非常适合于近景场景下的三维数据采集与重建．实验结果表明,系统具有较高的拼合精度．     

基于单平面模板的摄像机定标研究

提出了一种摄像机定标方法，只需要摄像机从不同方向拍摄平面模板的多幅图像，摄像机与平面模板间可以自由地移动，运动的参数无需已知。对于每个视点获得图像，提取图像上的网格角点；平面模板与图像间的网格角点对应关系，确定了单应性矩阵；对每幅图像，就可确定一个单应性矩阵，这样就能够进行摄像机定标。该算法先有一个线性解法，然后基于极大似然准则对线性结果进行非线性优化求精。该方法同时也考虑了镜头畸变的影响。实验结果表明该算法简单易用。     

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     

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。     

Outward-looking circular motion analysis of large image sequences

This work presents a novel and simple method of analyzing the motion of a large image sequence captured by a calibrated outward-looking video camera moving on a circular trajectory for large-scale environment applications. Previous circular motion algorithms mainly focus on inward-looking turntable-like setups. They are not suitable for outward-looking motion where the conic trajectory of corresponding points degenerates to straight lines. The circular motion of a calibrated camera essentially has only one unknown rotation angle for each frame. The motion recovery for the entire sequence computes only one fundamental matrix of a pair of frames to extract the angular motion of the pair using Laguerre's formula and then propagates the computation of the unknown rotation angles to the other frames by tracking one point over at least three frames. Finally, a maximum-likelihood estimation is developed for the optimization of the whole sequence. Extensive experiments demonstrate the validity of the method and the feasibility of the application in image-based rendering.     

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.     

一种简易的线结构光投影三维形状获取方法

利用普通的LCD投影仪和数码相机获得物体的三维形状.投影仪作为光源,投射线结构光在物体表面,从数码相机拍摄的照片序列中,恢复物体的形状.提出了根据已经标定好的相机参数,继续对投影仪进行标定的方法;同时,针对物体表面颜色/纹理较为复杂的情况,提出了一次投射三色线结构光的改进方法,克服了不易恢复此类物体形状的困难.实验结果表明,该方法可以获得物体的稠密点云用于进一步的重建,适于组建一个廉价但却保持相对精度的扫描系统.     

Structure and motion estimation from apparent contours under circular motion

In this paper, we address the problem of recovering structure and motion from the apparent contours of a smooth surface. Fixed image features under circular motion and their relationships with the intrinsic parameters of the camera are exploited to provide a simple parameterization of the fundamental matrix relating any pair of views in the sequence. Such a parameterization allows a trivial initialization of the motion parameters, which all bear physical meaning. It also greatly reduces the dimension of the search space for the optimization problem, which can now be solved using only two epipolar tangents. In contrast to previous methods, the motion estimation algorithm introduced here can cope with incomplete circular motion and more widely spaced images. Existing techniques for model reconstruction from apparent contours are then reviewed and compared. Experiment on real data has been carried out and the 3D model reconstructed from the estimated motion is presented.     

基于场景几何约束未标定两视图的三维模型重建

提出了一种从两幅未标定图象重建场景三维模型的方法 .这种方法充分利用了人造结构场景中大量存在的平行性和正交性几何约束 ,即利用每幅视图中三组互相垂直的平行线 ,计算出 3个影灭点 ,从而对每幅视图进行标定 .对两幅未标定图象 ,从基本矩阵只能得到射影重构 ,如果每幅图象都已标定 ,则可将基本矩阵转化为本质矩阵 .三维重构过程有两个步骤 :先是恢复相机的位置和运动 ;后是用三角测量法计算出点的三维坐标 .对多平面组成的场景进行三维重构实验 ,所得三维模型产生新的视点图象 ,与所观察的场景一致 ,重构的两个平面夹角与实际值相近 ,实验结果表明 ,该算法是行之有效的     

激光异物清除器装置研究

目前清除架空输电线路上异物的方法主要是依靠人工方式或者借助无人机等遥控操作装置,这些操作耗时耗力且带电作业有一定的危险性,不能适应复杂的输电线路环境。随着激光技术的应用越来越广泛,利用激光清除电线异物已经成为现实。为了更好地实现切割效果,提高切割效率,文章结合数字图像处理技术,提出了一种基于转台伺服控制的激光除异物系统。通过架设在双自由度转台上相对固定的摄像头和激光发射装置达到识别跟踪并切除异物的效果,以图像解析结果为反馈,控制转台的转动方向和角度,从而确定激光发射的位置。为了有效确定切割目标,利用图像处理技术中的特征识别法进行异物识别与跟踪,并通过Hough直线检测识别出线缆,确定切割方向。实验表明,在转台满足精度指标的情况下可以有效清除规定范围内的目标异物,切割速度较快,适用范围较广。