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.     

A simulation framework for evolution on uneven terrains for synchronous drive robot

This paper presents a simulation framework for evolution on uneven terrains for a wheeled mobile robot (WMR) such as a synchronous drive robot. The framework lends itself as a tool capable of solving various problems, such as forward kinematic-based evolution, inverse kinematic-based evolution, path planning and trajectory tracking. This framework becomes particularly useful when we understand that the evolution problem (and hence, the various associated problems based on evolution) is particularly challenging on uneven terrain. Specifically, it is entailed to bring in the contact constraints posed by the interaction of the wheel and the ground as well as the holonomic constraints as the problem is formulated in a Differential Algebraic Equation setting. The problem becomes all the more crucial as vehicles moving on uneven terrain are becoming the order of the day. Nonetheless, there has not been much literature that deals in length the various aspects that go into the framework. This paper elaborates on the various aspects of the framework, presents simulation results on uneven terrain, where the vehicle evolves without slipping, and also presents substantial quantitative analysis in regard to wheel slippage. The main contributions of this paper are the motion planning using forward kinematic framework and a new formulation of inverse kinematics for wheeled robots on uneven terrains.     

Using points at infinity for parameter decoupling in camera calibration

The majority of camera calibration methods, including the gold standard algorithm, use point-based information and simultaneously estimate all calibration parameters. In contrast, we propose a novel calibration method that exploits line orientation information and decouples the problem into two simpler stages. We formulate the problem as minimization of the lateral displacement between single projected image lines and their vanishing points. Unlike previous vanishing point methods, parallel line pairs are not required. Additionally, the invariance properties of vanishing points mean that multiple images related by pure translation can be used to increase the calibration data set size without increasing the number of estimated parameters. We compare this method with vanishing point methods and the gold standard algorithm and demonstrate that it has comparable performance.     

Path planning for a tracked robot traversing uneven terrains based on tip-over stability

In the real-world environment, the path planning method of tracked robot is widely studied when driving on uneven terrain. How to solve the problem that the traditional path planning algorithm cannot adapt to uneven terrain because of the constraints of obstacle avoidance and path length is a challenge for tracked robots. In this paper, a stability-based path planning framework for tracked robot is proposed to reduce the risk of rollover when the tracked robot passes through uneven terrain. First, a virtual plane method is proposed to estimate the attitude of tracked robot. Second, on this basis, a dynamic high-stability path evaluation algorithm for tracked robot based on force angle stability margin (FASM) is proposed, which transforms the stability-based path planning problem into a hypergraph problem. Moreover, considering that the optimization problem is strongly nonlinear and nonconvex, a hybrid algorithm of covariance matrix adaptive evolution strategy (CMAES) and Levenberg–Marquardt (LM) is designed under the framework of generalized graph optimization (G2O) to improve the solution efficiency. Finally, simulation and experiments show that the stability-based path planning framework can effectively plan the high-quality path, and the maximum stability of the tracked robot is 0.9156 when the robot crosses uneven terrain using optimal path 2.     

摄像机非线性标定方法

为了有效地解决传统摄像机标定方法独立性差、附加条件繁琐的问题,提出一种基于非线性三角函数转换的摄像机标定方法.该方法无需设立参照系,仅根据摄像机架设信息,利用图像空域内的三角坐标换算、构建不同纬度之间的非线性转换模型,并通过畸变过滤手段来确定摄像机采集图像中选取点位的实际场景对应坐标,同时不降低标定的准确率.实验结果表明,该方法可以在无参考物的条件下准确的对图像进行点位标定.     

Algorithms for coplanar camera calibration

Abstract. Coplanar camera calibration is the process of determining the extrinsic and intrinsic camera parameters from a given set of image and world points, when the world points lie on a two-dimensional plane. Noncoplanar calibration, on the other hand, involves world points that do not lie on a plane. While optimal solutions for both the camera-calibration procedures can be obtained by solving a set of constrained nonlinear optimization problems, there are significant structural differences between the two formulations. We investigate the computational and algorithmic implications of such underlying differences, and provide a set of efficient algorithms that are specifically tailored for the coplanar case. More specifically, we offer the following: (1) four algorithms for coplanar calibration that use linear or iterative linear methods to solve the underlying nonlinear optimization problem, and produce sub-optimal solutions. These algorithms are motivated by their computational efficiency and are useful for real-time low-cost systems. (2) Two optimal solutions for coplanar calibration, including one novel nonlinear algorithm. A constraint for the optimal estimation of extrinsic parameters is also given. (3) A Lyapunov type convergence analysis for the new nonlinear algorithm. We test the validity and performance of the calibration procedures with both synthetic and real images. The results consistently show significant improvements over less complete camera models. Received: 30 September 1998 / Accepted: 12 January 2000     

Pose estimation-based path planning for a tracked mobile robot traversing uneven terrains

A novel path-planning algorithm is proposed for a tracked mobile robot to traverse uneven terrains, which can efficiently search for stability sub-optimal paths. This algorithm consists of combining two RRT-like algorithms (the Transition-based RRT (T-RRT) and the Dynamic-Domain RRT (DD-RRT) algorithms) bidirectionally and of representing the robot–terrain interaction with the robot’s quasi-static tip-over stability measure (assuming that the robot traverses uneven terrains at low speed for safety). The robot’s stability is computed by first estimating the robot’s pose, which in turn is interpreted as a contact problem, formulated as a linear complementarity problem (LCP), and solved using the Lemke’s method (which guarantees a fast convergence). The present work compares the performance of the proposed algorithm to other RRT-like algorithms (in terms of planning time, rate of success in finding solutions and the associated cost values) over various uneven terrains and shows that the proposed algorithm can be advantageous over its counterparts in various aspects of the planning performance.     

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     

CCD摄像机标定

在基于单目视觉的农业轮式移动机器人自主导航系统中,CCD摄像机标定是农业轮式移动机器人正确和安全导航的前提和关键。摄像机标定确立了地面某点的三维空间坐标与计算机图像二维坐标之间的对应关系,机器人根据该关系计算出车体位姿值自主导航。因此,根据CCD摄像机针孔成像模型,利用大地坐标系中平面模板上已知的各点坐标,建立与计算机图像空间中各对应像素值之间的关系方程组,在Matlab环境下拟合出摄像机各内外参数。实验结果表明：该方法可以正确完成CCD摄像机标定。     

CCD摄像机标定的研究

在计算机视觉中,二维计算机坐标和三维物体空间坐标的关系可通过摄像机模型来建立.模型中的参数包括:摄像机几何、光学特性参数(内参数)及摄像机空间位置参数(外参数).摄像机的标定就是要确定这些参数.本文分析了三维空间点投影在像平面的像点产生畸变的原因:在大视场摄像机镜头各向同性,而且物像空间媒质均匀的情况下,像素单位元面积产生的变化引起像点畸变,并在实际图像坐标到计算机图像(帧存)坐标标定过程中推导出CCD传感器单元N方向的比例系数N<,x>的表达式,并进行了实验测量分析,取得的结果对提高标定精度具有意义.     

基于交比不变性的摄像机标定方法

针对传统棋盘格模板制作过程复杂、精度要求高的问题,提出了一种动态的基于交比不变性的摄像机标定方法。对两幅同源图像中的直线信息进行提取,运用顶点交比序列的唯一性来完成两图像中直线的匹配,从而准确实现了点与点的动态标定。实验结果表明,该方法鲁棒性较好,在自然环境下,对于标定固定位置的摄像机也能运用,表现出了良好的效果,具有广泛的应用性。     

机器视觉标定中的亚像素中心定位算法

双目视觉检测系统中,圆形标志的中心定位精度直接影响标定的精度和整体测量的精度。传统算法定位精度较低,不能满足高精度测量的要求。采用Canny算子对标定板图像进行边缘检测,Zernike矩定位亚像素边缘,用最小二乘拟合标志中心。实验表明:该方法对圆形标志中心点提取精确且稳定,中心定位精度优于0.1个像素,系统测量平均误差小于0.02 mm,满足高精度视觉测量要求。     

Self-identifying patterns for plane-based camera calibration

Determining camera calibration parameters is a time-consuming task despite the availability of calibration algorithms and software. A set of correspondences between points on the calibration target and the camera image(s) must be found, usually a manual or manually guided process. Most calibration tools assume that the correspondences are already found. We present a system which allows a camera to be calibrated merely by passing it in front of a panel of self-identifying patterns. This calibration scheme uses an array of fiducial markers which are detected with a high degree of confidence, each detected marker provides one or four correspondence points. Experiments were performed calibrating several cameras in a short period of time with no manual intervention. This marker-based calibration system was compared to one using the OpenCV chessboard grid finder which also finds correspondences automatically. We show how our new marker-based system more robustly finds the calibration pattern and how it provides more accurate intrinsic camera parameters.     

面向建筑物重建的相机标定方法研究

由于灭点具有很多独特的几何属性且大量地存在于建筑物场景中,因此针 对建筑物重建,提出了一种基于灭点的相机标定方法。首先通过构造各种几何约束关系,如 灭点与相机矩阵间的关系、世界坐标原点和相机矩阵间的关系,逐步实现相机矩阵的度量重 建和欧氏重建,获得相机矩阵的值,然后通过分解相机矩阵得到相机的内外部参数。该方法 在标定过程中无须借助任何标定物,求解过程简单,标定速度快。实验结果表明,该方法可 以满足虚拟现实中建筑物场景重建的需要。     

Automatic detection of pedestrians from stereo camera images

We propose a technique for detecting pedestrians by employing stereo camera images and based on probabilistic voting. From a disparity map, each pixel on the image is voted on a depth map employing a 2-D Gaussian distribution. The region having the peak value in the vote is chosen as the foot of an object. The object is specified by a rectangle on the right image, which is referred to as the region of interest (ROI). This ROI is described by HOG features, and is judged by SVM if it contains a person. With an ROI containing a person, a Kalman filter is applied to track the person through successive image frames. The performance of the detection of people was evaluated by employing ground truth data. The ratio of people detected to the ground truth data, called the recall rate, was 80%. This is a satisfactory result.     

一种简单的基于共面的摄像机参数标定方法

共面摄像机标定就是采用平面式模板来确定摄像机内外参数的过程,在此过程中图像像素和二维特征点是已知的。对于共面标定提出了一种简单及有效的方法去标定摄像机参数。即使用帧缓存中的计算机阵列图像直接来标定参数。首先采用预标定的方法标定出图像中心位置,然后根据帧存图像坐标和世界坐标之间的对应关系使用正交矩阵的约束条件来求解,在此算法中假设尺度因子为1,并且不考虑透镜畸变。所提出的算法用数字仿真图像及真实的图像检验。结果显示,所提出的算法具有较好的精度,是一种简单有效的标定方法。     

Dry camera calibration for underwater applications

Is it possible to calibrate a camera in the air and then use the calibration results to infer a new calibration corresponding to the embedding of the camera in another fluid (possibly water)? This problem is dealt within the paper. It is important to avoid direct underwater calibration, as it is much more inconvenient for experiments than the usual (air) calibration by human workers. Optical laws that must be considered when using underwater cameras are investigated. Both theoretical and experimental point of views are described, and it is shown that relationships can be found between results of air and water (or any other isotropic fluid in which the camera can be submerged) calibration. Received: 22 April 2000 / Accepted: 13 May 2002 Correspondence to: J.M. Lavest     

基于MATLAB中calibration toolbox的相机标定应用研究

相机标定的目的是确定相机的几何和光学参数以及相机相对于世界坐标系的方位。cal-ibration toolbox作为一个标定工具,容纳了如Tsai、Faugeras等多种经典的标定方法,从自主标定的使用方面详细介绍了calibration toolbox的使用方法。     

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。     

一种改进的相机标定方法

摄像机标定与图像畸变修正是摄影测量、视觉检测、计算机视觉等领域的重点研究课题之一,在测绘、工业控制、导航、军事等领域得到了极大的应用。研究了摄像机模型,摄像机标定等内容。对DLT的标定方法进行了改进,在摄像机模型中全面考虑了镜头的畸变,利用图像中心附近点畸变量较小的性质,提出一种摄像机内外部参数和像差修正参数分离的标定方法。并举例说明了基于同一物体的两幅图画三维重构的具体实验步骤和方法,分析了影响精度的因素。