二射影对应面束与二次曲面

利用正投影法首次系统说明了固有线为底的二射影对应面束,如果平移或 旋转其中之一,可以分别形成各种二次柱面、二次锥面、单叶双曲面和双曲抛物面。二射影 对应面束,如果选择合适的截平面,可以得到两对对应合同线束。合同线束是否同向共面是 二次曲面存在圆截口的充分必要条件。     

Critical surface pairs and triplets

In this paper, we study situations where a perspective image motion field can have multiple interpretations. We show that the ambiguity in interpretation of the three-dimensional instantaneous motion of curved surfaces is at most three-fold, and can occur only in the case of certain hyperboloids of one sheet, saddle surfaces, and hyperbolic paraboloids. We also present analytical expressions for the relationship among multiple interpretations.     

Implementation of two hidden-line algorithms

Two hidden-line elimination programs are described. One removes the hidden lines from vector-type projections of planar-faced 3D objects. This program implements the Loutrel algorithm which has been extended here to solids with multiply-connected faces. The other is applicable to solids bounded by sections of quadric surfaces (i.e. cylinders, cones, spheres, ellipsoids, paraboloids and hyperboloids) and represents an implementation of the Woon algorithm. The latter can be regarded as an extension of the Loutrel algorithm to curved-surface bodies. Both programs generate true, visible-line perspective projections for output on a digital plotter or a vector-type CRT display. The implementation of these algorithms for a variety of computer systems is described.     

基于三条相互垂直直线的单目位姿估计

基于单目视觉的位姿估计是计算机视觉中的典型问题之一。文中利用目标物体上的三条相互垂直的直线特征和相机像平面上这些特征的对应获得已标定相机相对于目标物体的位姿参数,给出其闭式求解方法,并证明问题解的数量与相机光心和三条直线的相对位置有关。当光心位于两个特殊平面以外时存在唯一解,反之若在该两个平面之间则存在两个解,并且这两个解具有对称性,该性质可作为合理解的判别依据。由于三条相互垂直的直线是长方体的三条边缘,而长方体在现实世界中广泛存在,该结论为应用直线特征进行单目视觉位姿估计及合作目标设计提供理论依据。     

空间轴对称目标三维姿态测量方法的研究

提出一种双目视觉测量空间轴对称目标姿态的新方法,应用线性方法获取轴对称目标在像面的轴线,通过两像面轴线与各自光心所成的平面相交,得到被测目标的轴线的方向矢量,进行三维姿态测量,避免了传统姿态测量中左右像面目标特征点的特征匹配或灰度匹配。模拟实验结果表明:该方法姿态角测量误差小于0.5°;且计算速度快,结果稳定,能够满足实时处理的要求。     

基于一维移动物体的双目装置自标定

给出了平移运动的一维物体所在平面的虚圆点图像及其对摄像机内参数的约束，和约束方程的数值求解方法，从而获得摄像机的内参数. 进一步通过恢复空间点在摄像机坐标系中的坐标，求解出双目摄像机之间的方位，即摄像机的外参数．对于一维物体的一般刚体运动，给出了把它转化为平移运动的方法．模拟实验和真实图像实验结果表明该方法具有较高的求解精度，同时也有一定的应用价值．     

An Application of Surface Reconstruction from Rotational Motion

For surface reconstruction using motion, objects are placed on a rotating disc in front of a single camera. For camera calibration the method by Tsai was implemented, extended (calculation of distorted from undisturbed coordinates) and optimized (e.g. with respect to the number of calibration planes and points in each plane) (1). The way the calibration results can be used for this special case of surface reconstruction of objects on a rotating disc is described. Motion vectors calculated from point correspondences are used as input for this calculation of 3-D point positions. In two theorems, new reconstruction formulae are given. Experimentally, accurate depth values could be obtained for sparse object surface points. It is suggested to combine these exact values with "surface drafts" calculated by approaches based on reflectance properties.     

双摄像机系统对移动目标的跟踪

提出了一种由一个静止摄像机加上一个动态摄像机组成的双摄像机实时跟踪系统．该系统利用两种形式摄像机各自的优点，克服它们自身的不足，实现了对运动目标的实时跟踪．文中给出了双摄像机系统的组成以及功能划分．利用由近似的摄像机投影模型导出的单应性关系，实现两个摄像机图像之间的目标匹配．系统在静态摄像机的图像平面上建立目标的2D运动模型，采用卡尔曼滤波实现目标位置的预测，由单应性关系求出动态摄像机图像平面上对应目标的预测位置，然后计算摄像机动态平台的旋转角度，实现对动态平台的伺服控制．     

Flow-induced forces on two circular cylinders in proximity

Flow-induced forces on two nearby circular cylinders of equal diameter immersed in the cross flow at Re = 100 were numerically studied. We consider all possible arrangements of the two circular cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. It turns out that significant changes in the characteristics of flow-induced forces are noticed depending on how the two circular cylinders are positioned, resulting in quantitative changes of force coefficients on both cylinders. Collecting all the numerical results obtained, we propose contour diagrams for mean force coefficients and rms values of force coefficient fluctuations for each of the two cylinders. The perfect geometrical symmetry implied in the flow configuration allows one to use those diagrams to estimate flow-induced forces on two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main flow direction.     

Recovery of SHGCs from a single intensity view

Generalized cylinders are a flexible, loosely-defined class of parametric shapes capable of modeling many real-world objects. Straight homogeneous generalized cylinders are an important subclass of generalized cylinders, whose cross-sections are scaled versions of a reference curve. Although there has been considerable research into recovering the shape of SHGCs from their contour, this work has almost exclusively involved methods that couple contour and heuristic constraints. A rigorous approach to the problem of recovering solid parametric shape from a single intensity view should involve at least two stages: (1) deriving the contour constraints, and (2) determining if additional image constraints, e.g., intensity, can be used to uniquely determine the 3D object shape. In this paper, the authors follow the approach just described. This methodology is also important for the recovery of object classes like tubes, where contour and heuristic constraints are shown to be insufficient for shape recovery. First, the authors prove that SHGC contours generated under orthography have exactly two degrees of freedom. Next, the authors show that the remaining free parameters can be resolved using reflectance-based constraints, without knowledge of the number of light sources, their positions, intensities, the amount of ambient light; or the surface albedo. Finally, the reflectance-based recovery algorithm is demonstrated on both synthetic and real SHGC images     

Linear Multi View Reconstruction and Camera Recovery Using a Reference Plane

This paper presents a linear algorithm for simultaneous computation of 3D points and camera positions from multiple perspective views based on having a reference plane visible in all views. The reconstruction and camera recovery is achieved in a single step by finding the null-space of a matrix built from image data using Singular Value Decomposition. Contrary to factorization algorithms this approach does not need to have all points visible in all views. This paper investigates two reference plane configurations: Finite reference planes defined by four coplanar points and infinite reference planes defined by vanishing points. A further contribution of this paper is the study of critical configurations for configurations with four coplanar points. By simultaneously reconstructing points and views we can exploit the numerical stabilizing effect of having wide spread cameras with large mutual baselines. This is demonstrated by reconstructing the outsideand inside (courtyard) of a building on the basis of 35 views in one single Singular Value Decomposition.     

从单幅正轴测投影线图建立平面立体的模型

提出了一种从单幅二维正轴测投影线图建立平面立体线框模型的新方法。提出一种新的空间直线坐标表示法，根据正轴测投影线图中隐含的直线与平面之间的从属关系建立约束方程。考虑画出隐藏线的正轴测投影线图，根据线画图中隐含的约束条件，建立一个线性系统，通过求解该线性系统，得到平面立体的三维信息。证明解释平面立体正轴测投影线图至少有4个自由度。     

基于约束关系的平面立体三维重建

提出一种基于约束的平面立体三维重建算法。该算法采用参数化方式来表示空间直线及其投影,这种参数化方式能满足数字图像中直线提取所需的唯一性、有界性及均匀性条件。依据平面立体投影线图的拓扑结构隐含的三维信息,建立平面立体上棱线、表面空间位置参数之间的约束方程,联立约束方程组求其最小二乘解,恢复出平面立体的三维结构。研究成果可用于计算机视觉和智能CAD系统。     

A Comprehensive and Versatile Camera Model for Cameras with Tilt Lenses

We propose camera models for cameras that are equipped with lenses that can be tilted in an arbitrary direction (often called Scheimpflug optics). The proposed models are comprehensive: they can handle all tilt lens types that are in common use for machine vision and consumer cameras and correctly describe the imaging geometry of lenses for which the ray angles in object and image space differ, which is true for many lenses. Furthermore, they are versatile since they can also be used to describe the rectification geometry of a stereo image pair in which one camera is perspective and the other camera is telecentric. We also examine the degeneracies of the models and propose methods to handle the degeneracies. Furthermore, we examine the relation of the proposed camera models to different classes of projective camera matrices and show that all classes of projective cameras can be interpreted as cameras with tilt lenses in a natural manner. In addition, we propose an algorithm that can calibrate an arbitrary combination of perspective and telecentric cameras (no matter whether they are tilted or untilted). The calibration algorithm uses a planar calibration object with circular control points. It is well known that circular control points may lead to biased calibration results. We propose two efficient algorithms to remove the bias and thus obtain accurate calibration results. Finally, we perform an extensive evaluation of the proposed camera models and calibration algorithms that establishes the validity and accuracy of the proposed models.     

Toward a model-based Bayesian theory for estimating and recognizingparameterized 3-D objects using two or more images taken from differentpositions

A parametric modeling and statistical estimation approach is proposed and simulation data are shown for estimating 3-D object surfaces from images taken by calibrated cameras in two positions. The parameter estimation suggested is gradient descent, though other search strategies are also possible. Processing image data in blocks (windows) is central to the approach. After objects are modeled as patches of spheres, cylinders, planes and general quadrics-primitive objects, the estimation proceeds by searching in parameter space to simultaneously determine and use the appropriate pair of image regions, one from each image, and to use these for estimating a 3-D surface patch. The expression for the joint likelihood of the two images is derived and it is shown that the algorithm is a maximum-likelihood parameter estimator. A concept arising in the maximum likelihood estimation of 3-D surfaces is modeled and estimated. Cramer-Rao lower bounds are derived for the covariance matrices for the errors in estimating the a priori unknown object surface shape parameters     

基于射影不变量的摄像机自标定方法

为了方便而精确地进行摄像机标定,提出了一种基于射影不变量的求解摄像机内参数的方法,该方法利用交比在射影变换中不变的性质,通过同一平面中相交直线的无穷远点与虚圆点的交比,先求出同一模板的不同方位的3幅图像中的虚圆点的像;然后利用绝对二次曲线的像在摄像机做刚体运动时保持不变的性质,进而求出绝对二次曲线的像;最后对结果进行Cholesky分解,就可以得到摄像机的内参数。实验表明,该方法行之有效,可以达到较高的精度。     

Toward coherent object detection and scene layout understanding

Detecting objects in complex scenes while recovering the scene layout is a critical functionality in many vision-based applications. In this work, we advocate the importance of geometric contextual reasoning for object recognition. We start from the intuition that objects' location and pose in the 3D space are not arbitrarily distributed but rather constrained by the fact that objects must lie on one or multiple supporting surfaces. We model such supporting surfaces by means of hidden parameters (i.e. not explicitly observed) and formulate the problem of joint scene reconstruction and object recognition as the one of finding the set of parameters that maximizes the joint probability of having a number of detected objects on K supporting planes given the observations. As a key ingredient for solving this optimization problem, we have demonstrated a novel relationship between object location and pose in the image, and the scene layout parameters (i.e. normal of one or more supporting planes in 3D and camera pose, location and focal length). Using a novel probabilistic formulation and the above relationship our method has the unique ability to jointly: i) reduce false alarm and false negative object detection rate; ii) recover object location and supporting planes within the 3D camera reference system; iii) infer camera parameters (view point and the focal length) from just one single uncalibrated image. Quantitative and qualitative experimental evaluation on two datasets (desk-top dataset [1] and LabelMe [2]) demonstrates our theoretical claims.     

Stereo with Oblique Cameras

Mosaics acquired by pushbroom cameras, stereo panoramas, omnivergent mosaics, and spherical mosaics can be viewed as images taken by non-central cameras, i.e. cameras that project along rays that do not all intersect at one point. It has been shown that in order to reduce the correspondence search in mosaics to a one-parametric search along curves, the rays of the non-central cameras have to lie in double ruled epipolar surfaces. In this work, we introduce the oblique stereo geometry, which has non-intersecting double ruled epipolar surfaces. We analyze the configurations of mutually oblique rays that see every point in space. These configurations, called oblique cameras, are the most non-central cameras among all cameras. We formulate the assumption under which two oblique cameras posses oblique stereo geometry and show that the epipolar surfaces are non-intersecting double ruled hyperboloids and two lines. We show that oblique cameras, and the correspondingoblique stereo geometry, exist and give an example of a physically realizable oblique stereo geometry. We introduce linear oblique cameras as those which can be generated by a linear mapping from points in space to camera rays and characterize those collineations which generate them. We show that all linear oblique cameras are obtained by a collineation from one example of an oblique camera. Finally, we relate oblique cameras to spreads known from incidence geometries.     

多平面多视点单应矩阵间的约束

用代数方法系统地讨论了多平面多视点下单应矩阵间的约束关系.主要结论有(A)如 果视点间摄像机的运动为纯平移运动,则1)对于所有平面关于两视点间的单应矩阵的集合,或 单个平面关于所有视点的单应矩阵的集合的秩均等于4,2)对于多平面多视点的标准单应矩阵 的集合其秩仍等于4,3)根据以上结论可推出现有文献中关于"相对单应矩阵"约束的所有结 果;(B)如果视点间摄像机的运动为一般运动,则1)对于所有平面关于两个视点间的单应矩阵 集合的秩等于4的结论仍成立,2)对于其它情况其秩不再等于4而是等于9.     

Extensions of Plane-Based Calibration to the Case of Translational Motion in a Robot Vision Setting

In this paper, a technique for calibrating a camera using a planar calibration object with known metric structure, when the camera (or the calibration plane) undergoes pure translational motion, is presented. The study is an extension of the standard formulation of plane-based camera calibration where the translational case is considered as degenerate. We derive a flexible and straightforward way of using different amounts of knowledge of the translational motion for the calibration task. The theory is mainly applicable in a robot vision setting, and the calculation of the hand–eye orientation and the special case of stereo head calibration are also being addressed. Results of experiments on both computer-generated and real image data are presented. The paper covers the most useful instances of applying the technique to a real system and discusses the degenerate cases that needs to be considered. The paper also presents a method for calculating the infinite homography between the two image planes in a stereo head, using the homographies estimated between the calibration plane and the image planes. Its possible usage and usefulness for simultaneous calibration of the two cameras in the stereo head are discussed and illustrated using experiments.