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.     

Epipolar Geometry for Central Catadioptric Cameras

Central catadioptric cameras are cameras which combine lenses and mirrors to capture a very wide field of view with a central projection. In this paper we extend the classical epipolar geometry of perspective cameras to all central catadioptric cameras. Epipolar geometry is formulated as the geometry of corresponding rays in a three-dimensional space. Using the model of image formation of central catadioptric cameras, the constraint on corresponding image points is then derived. It is shown that the corresponding points lie on epipolar conics. In addition, the shape of the conics for all types of central catadioptric cameras is classified. Finally, the theory is verified by experiments with real central catadioptric cameras.     

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.     

An Efficient Approach for Dynamic Calibration of Multiple Cameras

In this paper, we propose a new algorithm for dynamic calibration of multiple cameras. Based on the mapping between a horizontal plane in the 3-D space and the 2-D image plane on a panned and tilted camera, we utilize the displacement of feature points and the epipolar-plane constraint among multiple cameras to infer the changes of pan and tilt angles for each camera. This algorithm does not require a complicated correspondence of feature points. It can be applied to surveillance systems with wide-range coverage. It also allows the presence of moving objects in the captured scenes while performing dynamic calibration. The sensitivity analysis of our algorithm with respect to measurement errors and fluctuations in previous estimations is also discussed. The efficiency and feasibility of this approach has been demonstrated in some experiments over real scenery.     

Non-Single Viewpoint Catadioptric Cameras: Geometry and Analysis

Conventional vision systems and algorithms assume the imaging system to have a single viewpoint. However, these imaging systems need not always maintain a single viewpoint. For instance, an incorrectly aligned catadioptric system could cause non-single viewpoints. Moreover, a lot of flexibility in imaging system design can be achieved by relaxing the need for imaging systems to have a single viewpoint. Thus, imaging systems with non-single viewpoints can be designed for specific imaging tasks, or image characteristics such as field of view and resolution. The viewpoint locus of such imaging systems is called a caustic. In this paper, we present an in-depth analysis of caustics of catadioptric cameras with conic reflectors. We use a simple parametric model for both, the reflector and the imaging system, to derive an analytic solution for the caustic surface. This model completely describes the imaging system and provides a map from pixels in the image to their corresponding viewpoints and viewing direction. We use the model to analyze the imaging system's properties such as field of view, resolution and other geometric properties of the caustic itself. In addition, we present a simple technique to calibrate the class of conic catadioptric cameras and estimate their caustics from known camera motion. The analysis and results we present in this paper are general and can be applied to any catadioptric imaging system whose reflector has a parametric form.     

A Framework for Augmented Reality using Non-Central Catadioptric Cameras

This paper proposes a strategy for a group of swarm robots to self-assemble into a single articulated(legged) structure in response to terrain difficulties during autonomous exploration. These articulated structures will have several articulated legs or backbones, so they are well suited to walk on difficult terrains like animals. There are three tasks in this strategy: exploration, self-assembly and locomotion. We propose a formation self-assembly method to improve self-assembly efficiency. At the beginning, a swarm of robots explore the environment using their sensors and decide whether to self-assemble and select a target configuration from a library to form some robotic structures to finish a task. Then, the swarm of robots will execute a self-assembling task to construct the corresponding configuration of an articulated robot. For the locomotion, with joint actuation from the connected robots, the articulated robot generates locomotive motions. Based on Sambot that are designed to unite swarm mobile and self-reconfigurable robots, we demonstrate the feasibility for a varying number of swarm robots to self-assemble into snake-like and multi-legged robotic structures. Then, the effectiveness and scalability of the strategy are discussed with two groups of experiments and it proves the formation self-assembly is more efficient in the end.     

基于一维标定物的反射折射摄像机标定方法

一维标定物是指一组任意两点距离已知的共线点.基于一维标定物的标定方法相对基于二维、三维标定物的方法更加灵活,在实际中有很高的应用价值.文中提出一种基于一维标定物的反射折射摄像机标定算法.如果一维标定物包含5个或5个以上的共线点,则通过一维标定物的3次或3次以上的一般刚体运动,就能够标定反射折射摄像机的参数.算法分为两步:首先,使用一维标定物的图像和主点满足的不变量计算主点;然后,通过一维标定物图像所隐含的正交消影点信息,线性地求解绝对二次曲线的像(IAC),并对IAC矩阵进行Cholesky分解确定尺度因子和畸变因子.此外,文中方法还能够给出镜面参数的解析表示以及一维标定物相对于视球中心的位置.模拟实验中,作者在两种镜面配置下比较了文中的方法和基于圆环点的方法,结果表明文中的方法在不同的镜面配置下都能得到较好的标定结果.真实实验也验证了文中方法的正确性和可行性.     

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.     

Identical Projective Geometric Properties of Central Catadioptric Line Images and Sphere Images with Applications to Calibration

Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. Lines and spheres in space are all projected into conics in the central catadioptric image planes, and such conics are called line images and sphere images, respectively. We discovered that there exists an imaginary conic in the central catadioptric image planes, defined as the modified image of the absolute conic (MIAC), and by utilizing the MIAC, the novel identical projective geometric properties of line images and sphere images may be exploited: Each line image or each sphere image is double-contact with the MIAC, which is an analogy of the discovery in pinhole camera that the image of the absolute conic (IAC) is double-contact with sphere images. Note that the IAC also exists in the central catadioptric image plane, but it does not have the double-contact properties with line images or sphere images. This is the main reason to propose the MIAC. From these geometric properties with the MIAC, two linear calibration methods for central catadioptric cameras using sphere images as well as using line images are proposed in the same framework. Note that there are many linear approaches to central catadioptric camera calibration using line images. It seems that to use the properties that line images are tangent to the MIAC only leads to an alternative geometric construction for calibration. However, for sphere images, there are only some nonlinear calibration methods in literature. Therefore, to propose linear methods for sphere images may be the main contribution of this paper. Our new algorithms have been tested in extensive experiments with respect to noise sensitivity.     

Catadioptric Stereo Using Planar Mirrors

By using mirror reflections of a scene, stereo images can be captured with a single camera (catadioptric stereo). In addition to simplifying data acquisition single camera stereo provides both geometric and radiometric advantages over traditional two camera stereo. In this paper, we discuss the geometry and calibration of catadioptric stereo with two planar mirrors. In particular, we will show that the relative orientation of a catadioptric stereo rig is restricted to the class of planar motions thus reducing the number of external calibration parameters from 6 to 5. Next we derive the epipolar geometry for catadioptric stereo and show that it has 6 degrees of freedom rather than 7 for traditional stereo. Furthermore, we show how focal length can be recovered from a single catadioptric image solely from a set of stereo correspondences. To test the accuracy of the calibration we present a comparison to Tsai camera calibration and we measure the quality of Euclidean reconstruction. In addition, we will describe a real-time system which demonstrates the viability of stereo with mirrors as an alternative to traditional two camera stereo.     

Calibration of Cameras with Radially Symmetric Distortion

We present algorithms for plane-based calibration of general radially distorted cameras. By this, we understand cameras that have a distortion center and an optical axis such that the projection rays of pixels lying on a circle centered on the distortion center form a right viewing cone centered on the optical axis. The camera is said to have a single viewpoint (SVP) if all such viewing cones have the same apex (the optical center); otherwise, we speak of NSVP cases. This model encompasses the classical radial distortion model [5], fisheyes, and most central or noncentral catadioptric cameras. Calibration consists in the estimation of the distortion center, the opening angles of all viewing cones, and their optical centers. We present two approaches of computing a full calibration from dense correspondences of a single or multiple planes with known euclidean structure. The first one is based on a geometric constraint linking viewing cones and their intersections with the calibration plane (conic sections). The second approach is a homography-based method. Experiments using simulated and a broad variety of real cameras show great stability. Furthermore, we provide a comparison with Hartley-Kang's algorithm [12], which, however, cannot handle such a broad variety of camera configurations, showing similar performance.     

一种中心反射折射直线像的拟合方法

直线在中心反射折射摄像机下的像是一条二次曲线.由于存在遮挡,准确地拟合直线像是非常困难的,从而影响了摄像机的标定精度.目前,这一问题仍然没有得到有效的解决.此外,根据中心反射折射摄像机成像模型发现,如果可见弧上图像点的对极点已知,可以大大提高直线像的拟合精度.为此,提出了一种新的拟合直线像的方法,该方法适用于包括抛物反射折射摄像机在内的所有中心反射折射摄像机.首先,推导出一种新的关于对极图像点与摄像机主点之间的关系;然后,通过这种关系建立目标函数,用来优化得到直线像的方程;最后,利用拟合的直线像估计摄像机的内参数,以此评价拟合算法的性能.大量模拟实验和真实实验均验证了拟合算法的有效性,即提出的拟合算法不仅鲁棒,且提高了直线像的拟合精度,进而提高了摄像机的标定精度.     

反射折射几何元统一成像及标定性讨论

基于圆的摄像机标定有着无可比拟的优势,然而由于反射折射摄像机存在大畸变,在该摄像机下对这一问题的研究还很不透彻且存在很多困难.文中研究了圆在反射折射摄像机下的像,并在此基础上统一了几何元的成像理论,为基于圆的反射折射摄像机标定方法奠定了理论基础.首先证明了圆在反射折射摄像机下的像为四次曲线;之后根据圆的大小或所在位置的不同,发现此四次曲线可约化为点、直线及球在反射折射摄像机下的像,这与已有的结论是等价的,从而统一了几何元在反射折射摄像机下的成像理论;并在该统一成像理论下讨论了不同几何元在反射折射摄像机标定方面的应用.最后通过模拟实验验证了一种基于圆的抛物反射折射摄像机的标定结果.     

Tracking in a Dense Crowd Using Multiple Cameras

Tracking people in a dense crowd is a challenging problem for a single camera tracker due to occlusions and extensive motion that make human segmentation difficult. In this paper we suggest a method for simultaneously tracking all the people in a densely crowded scene using a set of cameras with overlapping fields of view. To overcome occlusions, the cameras are placed at a high elevation and only people’s heads are tracked. Head detection is still difficult since each foreground region may consist of multiple subjects. By combining data from several views, height information is extracted and used for head segmentation. The head tops, which are regarded as 2D patches at various heights, are detected by applying intensity correlation to aligned frames from the different cameras. The detected head tops are then tracked using common assumptions on motion direction and velocity. The method was tested on sequences in indoor and outdoor environments under challenging illumination conditions. It was successful in tracking up to 21 people walking in a small area (2.5 people per m²), in spite of severe and persistent occlusions.     

基于二次曲线的线阵相机标定技术

针对绕固定轴旋转的线阵相机,提出一种基于二次曲线的相机标定方法。该方法只需要相机在2个或更多不同的方位拍摄图像,通过相机的转动在每个方位拍摄多帧图像。靶标采用一个包含3个或更多二次曲线的平板。相机和靶标可以自由移动,不需要知道运动参数。通过坐标变换,把每个方位所拍摄的多帧线阵图像排列成面阵图像。从面阵图像中提取二次曲线作为标定基元,以此简化基元对应问题。仿真实验结果表明,该方法精度较高,鲁棒性较好。     

Photogeometric Direct Visual Tracking for Central Omnidirectional Cameras

The fundamental task of visual tracking is considered in this work as a direct image registration problem. Direct methods refer to those that exploit the pixel intensities without intermediate steps, e.g., no extraction of image features. This article proposes new photogeometric transformation models and nonlinear optimization methods for directly registering central omnidirectional images. The proposed models ensure robustness to arbitrary illumination changes, as well as encompass all classes of projective deformations of planar objects within those images. Experimental results show that visual tracking can indeed be highly robust and accurate even for this type of vision systems.     

一种扩展小孔成像模型的鱼眼相机矫正与标定方法

鱼眼相机由于其超宽的视场范围（Field of view,FOV）（可以达到180°以上）,得到越来越广泛的应用. 常规的基于小孔成像模型的相机矫正与标定算法在超宽视场的鱼眼成像系统中已经不太适用,为了兼顾小孔模型的特点,本文提出了一种扩展小孔成像模型的鱼眼相机矫正与标定方法. 此方法是对小孔成像模型的进一步拓展,不仅具备小孔模型实现简单、适合人眼视觉效果以及相机标定方便等优点,同时将小孔成像模型适用的视场范围扩展到超宽视场领域. 其基本思路是：在利用小孔成像模型对鱼眼相机90°左右视场范围进行矫正与标定的基础上,使用非等间距的点阵模板,并结合直线拟合以及自然邻点插值算法,扩展小孔模型适用的视场范围. 本文使用鱼眼相机从不同的角度拍摄多幅模板图,完成鱼眼相机的矫正与标定. 通过求取的小孔成像模型参数实现相机的标定;对鱼眼相机拍摄的实际场景图进行畸变矫正测试,结果表明此方法能够很好地矫正鱼眼相机存在的畸变,得到符合人眼视觉效果的矫正图;单幅矫正图视场范围达到130°,结合不同角度拍摄的多幅模板图,可把矫正的视场范围扩展到180°.     

四路摄像头协同的多重触控系统

为解决多重触控系统中多触点遮挡问题,提出一个基于四路摄像头协同工作的多重触控系统,其中包括硬件层、图像处理层、图像理解层和应用层.硬件层由四路摄像头与多个红外二极管围成的矩形边框组成;图像处理层完成图像的获取和触点检测;图像理解层实现触点的定位与跟踪;应用层完成与具体应用基于手势的交互.图片管理应用实验结果表明,该系统能实现基于多指的复杂操作,在公共信息查询、指挥决策等领域具有很好的应用前景.