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     

基于共面二点一线特征的单目视觉定位

研究了根据点、线混合特征进行单目视觉定位问题,在给定物体坐标系中共面的两个特征点和一条特征直线的条件下,根据它们在像平面上的对应计算相机与物体之间的位姿参数。根据三个特征之间的几何位置关系,分两种情况给出问题求解的具体过程,最终将问题转换成求解一个二次方程问题,真实的工件定位实验验证了方法的有效性。该结果为应用单目视觉进行工件定位提供了一种新方法。     

A two‐stage sampling for robust feature matching

For any visual feature‐based SLAM (simultaneous localization and mapping) solutions, to estimate the relative camera motion between two images, it is necessary to find “correct” correspondence between features extracted from those images. Given a set of feature correspondents, one can use a n‐point algorithm with robust estimation method, to produce the best estimate to the relative camera pose. The accuracy of a motion estimate is heavily dependent on the accuracy of the feature correspondence. Such a dependency is even more significant when features are extracted from the images of the scenes with drastic changes in viewpoints and illuminations and presence of occlusions. To make a feature matching robust to such challenging scenes, we propose a new feature matching method that incrementally chooses a five pairs of matched features for a full DoF (degree of freedom) camera motion estimation. In particular, at the first stage, we use our 2‐point algorithm to estimate a camera motion and, at the second stage, use this estimated motion to choose three more matched features. In addition, we use, instead of the epipolar constraint, a planar constraint for more accurate outlier rejection. With this set of five matching features, we estimate a full DoF camera motion with scale ambiguity. Through the experiments with three, real‐world data sets, our method demonstrates its effectiveness and robustness by successfully matching features (1) from the images of a night market where presence of frequent occlusions and varying illuminations, (2) from the images of a night market taken by a handheld camera and by the Google street view, and (3) from the images of a same location taken daytime and nighttime.     

Affine Structure and Motion from Points,Lines and Conics

In this paper several new methods for estimating scene structure and camera motion from an image sequence taken by affine cameras are presented. All methods can incorporate both point, line and conic features in a unified manner. The correspondence between features in different images is assumed to be known.Three new tensor representations are introduced describing the viewing geometry for two and three cameras. The centred affine epipoles can be used to constrain the location of corresponding points and conics in two images. The third order, or alternatively, the reduced third order centred affine tensors can be used to constrain the locations of corresponding points, lines and conics in three images. The reduced third order tensors contain only 12 components compared to the 16 components obtained when reducing the trifocal tensor to affine cameras.A new factorization method is presented. The novelty lies in the ability to handle not only point features, but also line and conic features concurrently. Another complementary method based on the so-called closure constraints is also presented. The advantage of this method is the ability to handle missing data in a simple and uniform manner. Finally, experiments performed on both simulated and real data are given, including a comparison with other methods.     

3D model based tracking for omnidirectional vision: A new spherical approach

The current work addresses the problem of 3D model tracking in the context of monocular and stereo omnidirectional vision in order to estimate the camera pose. To this end, we track 3D objects modeled by line segments because the straight line feature is often used to model the environment. Indeed, we are interested in mobile robot navigation using omnidirectional vision in structured environments. In the case of omnidirectional vision, 3D straight lines are projected as conics in omnidirectional images. Under certain conditions, these conics may have singularities.In this paper, we present two contributions. We, first, propose a new spherical formulation of the pose estimation withdrawing singularities, using an object model composed of lines. The theoretical formulation and the validation on synthetic images thus show that the new formulation clearly outperforms the former image plane one. The second contribution is the extension of the spherical representation to the stereovision case. We consider in the paper a sensor which combines a camera and four mirrors. Results in various situations show the robustness to illumination changes and local mistracking. As a final result, the proposed new stereo spherical formulation allows us to localize online a robot indoor and outdoor whereas the classical formulation fails.     

Triangulation of Points,Lines and Conics

The problem of reconstructing 3D scene features from multiple views with known camera motion and given image correspondences is considered. This is a classical and one of the most basic geometric problems in computer vision and photogrammetry. Yet, previous methods fail to guarantee optimal reconstructions—they are either plagued by local minima or rely on a non-optimal cost-function. A common framework for the triangulation problem of points, lines and conics is presented. We define what is meant by an optimal triangulation based on statistical principles and then derive an algorithm for computing the globally optimal solution. The method for achieving the global minimum is based on convex and concave relaxations for both fractionals and monomials. The performance of the method is evaluated on real image data.

On the Importance of Being Asymmetric in Stereopsis—Or Why We Should Use Skewed Parallel Cameras

This paper presents a new clever camera sensor, where relative pose determination is not needed, and the sensor is simultaneously capable of using vergence micromovements. Sweeping depth using vergence micromovements promises subpixel depth precision, measuring zero disparity at each time instant. We show that curves preserving zero disparity are exactly conics, nondegenerate or degenerate. Oddly enough, only circles (Vieth-Müller circles) are routinely considered, either theoretically or in practical work, in vergence stereo. Horopters in human vision, cf. Ogle (1932), closely resemble conics.We introduce translational vergence by suggesting the use of a pair of shift-optics CCD cameras. The nonrigidity causes zero disparity curves to become planes, for each fixation. (They are degenerate conics.) We have parallel optical axes, but slanting left and right primary lines of sight. During vergence movements, the primary lines of sight move over time. This has farreaching consequences: Binocular head-eye systems all involve relative camera rotation, to fixate. But, camera rotation is unnecessary. Hence, for relative depth maps, there is no need for measuring camera rotation (relative camera pose) from mechanical sources. Nor are algorithms needed for calculating epipolar lines. The suggested technique removes the need for camera rotations about the optical centers in a binocular head-eye system.     

基于共面圆的距离传感器与相机的相对位姿标定

近年来, 距离传感器与摄像机的组合系统标定在无人车环境感知中得到了广泛的研究与应用, 其中基于平面特征的方法简单易行而被广泛采用. 然而, 目前多数方法基于点匹配进行, 易错且鲁棒性较低. 本文提出了一种基于共面圆的距离传感器与相机的组合系统相对位姿估计方法. 该方法使用含有两个共面圆的标定板, 可以获取相机与标定板间的位姿, 以及距离传感器与标定板间的位姿. 此外, 移动标定板获取多组数据, 根据计算得到两个共面圆的圆心在距离传感器和相机下的坐标, 优化重投影误差与3D对应点之间的误差, 得到距离传感器与相机之间的位姿关系. 该方法不需要进行特征点的匹配, 利用射影不变性来获取相机与三维距离传感器的位姿. 仿真实验与真实数据实验结果表明, 本方法对噪声有较强的鲁棒性, 得到了精确的结果.     

A versatile homography computation method based on two real points

In this paper, we present a novel 2D homography computation method based on two real points. The homography is thus decomposed into three parts. The two real points and their images can be utilized to compute the first and the last parts respectively, while other primitives (could be point(s), line(s) and conic) can be utilized to compute the middle part which is a hyperbolic similarity transformation. We introduce the proposed method in a 2D pattern with a conic and a coplanar line, and apply the method in various other geometric patterns. Subsequently, many plane-based vision tasks, such as camera calibration, pose estimation and metric rectification can be solved in a unified way as polynomial systems. The experiments with simulated and real data verify the correctness and the versatility of our algorithm.     

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。     

基于直线和二次曲线的多回路平面曲线分割

提出了一种多回路平面曲线的分割算法。算法以直线段和二次曲线段作为拟合的基本单元，通过边缘跟踪把多回路的平面曲线分割成曲线段或单回路的封闭曲线，然后在曲线曲率不连续处继续分割。针对一次分割时可能会产生的迷向问题，提出了基于对偶原理的线段合并技术。该算法的结果能简单有效地描述场景中的物体，使高级视觉任务更简单。实验结果表明算法能取得较好的效果。     

基本矩阵的5点和4点算法

基本矩阵(Fundamental Matrix)是两幅图像之间的基本约束,在摄像机标定和三维重建 中起着至关重要的作用.本文证明,当摄像机在两幅图像之间的运动为纯平移运动时,给定5对 图像对应点,如果其中的4对对应点为共面空间点的投影(称为共面对应点),则可以线性确定基 本矩阵.另外,如果摄像机不是5参数模型(完全针孔模型),而是4参数模型(畸变因子为零),则 此时仅使用该4对共面对应点即可线性确定基本矩阵.据我们所知,这些结果在文献中还没有类 似的报导.     

单目视觉中基于IEKF,DD1及DD2滤波器的位姿和运动估计

用单摄像机所获取的二维(2D)图像来估计两坐标之间的相对位姿和运动在实际应用中是可取的,其难点是从物体的三维(3D)特征投影到2D图像特征的过程是一个非线性变换,把基于单目视觉的位姿和运动估计系统定义为一个非线性随机模型,分别以迭代扩展卡尔曼滤波器(IEKF)、一阶斯梯林插值滤波器(DD1)和二阶斯梯林插值滤波器(DD2)作非线性状态估计器来估计位姿和运动.为了验证每种估计器的相对优点,用文中所提方法对每种估计器都作了仿真实验,实验结果表明DD1和DD2滤波器的特性要比IEKF好.     

Automatic feature point extraction and tracking in image sequences for arbitrary camera motion

An automatic egomotion compensation based point correspondence algorithm is presented. A basic problem in autonomous navigation and motion estimation is automatically detecting and tracking features in consecutive frames, a challenging problem when camera motion is significant. In general, feature displacements between consecutive frames can be approximately decomposed into two components: (i) displacements due to camera motion which can be approximately compensated by image rotation, scaling, and translation; (ii) displacements due to object motion and/or perspective projection. In this paper, we introduce a two-step approach: First, the motion of the camera is compensated using a computational vision based image registration algorithm. Then consecutive frames are transformed to the same coordinate system and the feature correspondence problem is solved as though tracking moving objects for a stationary camera. Methods of subpixel accuracy feature matching, tracking and error analysis are introduced. The approach results in a robust and efficient algorithm. Results on several real image sequences are presented.The support of the Advanced Research Projects Agency (ARPA Order No. 8459) and the U.S. Army Engineer Topographic Laboratories under Contract DACA 76-92-C-0009 is gratefully acknowledged.     

Linear N-point camera pose determination

The determination of camera position and orientation from known correspondences of 3D reference points and their images is known as pose estimation in computer vision and space resection in photogrammetry. It is well-known that from three corresponding points there are at most four algebraic solutions. Less appears to be known about the cases of four and five corresponding points. We propose a family of linear methods that yield a unique solution to 4- and 5-point pose determination for generic reference points. We first review the 3-point algebraic method. Then we present our two-step, 4-point and one-step, 5-point linear algorithms. The 5-point method can also be extended to handle more than five points. Finally, we demonstrate our methods on both simulated and real images. We show that they do not degenerate for coplanar configurations and even outperform the special linear algorithm for coplanar configurations in practice     

一种基于旋转体的摄像机定位方法

基于旋转体的摄像机定位是单目合作目标定位领域中的涉及较少并且较为困难的一个问题,传统的基于点基元、直线基元及曲线基元的定位方法在用于旋转体定位过程中都存在相应的问题.文中设计了一种由4个相切椭圆构成的几何模型,该模型环绕于圆柱体表面,利用二次曲线的投影仍然是二次曲线的特性和椭圆的相应性质能够得到唯一确定模型位置的3个坐标点,从而将旋转体定位问题转化为P3P问题.在对P3P的解模式区域进行分析后,推导了根据模型上可视曲线的弯曲情况来确定P3P问题解模式的判别方法,并给出证明过程.仿真实验表明了这种模型定位方法的有效性.最后利用这个模型引导机械手完成目标定位的实验.     

Motion recovery from image sequences using only first order optical flow information

The primary goal in motion vision is to extract information about the motion and shape of an object in a scene that is encoded in the optic flow. While many solutions to this problem, both iterative and in closed form, have been proposed, practitioners still view the problem as unsolved, since these methods, for the most part, cannot deal with some important aspects of realistic scenes. Among these are complex unsegmented scenes, nonsmooth objects, and general motion of the camera. In addition, the performance of many methods degrades ungracefully as the quality of the data deteriorates.Here, we will derive a closed-form solution for motion estimation based on thefirst-order information from two image regions with distinct flow structures. A unique solution is guaranteed when these corespond to two surface patches with different normal vectors. Given an image sequence, we will show how the image may be segmented into regions with the necessary properties, optical flow is computed for these regions, and motion parameters are calculated. The method can be applied to arbitrary scenes and any camera motion. We will show theoretically why the method is more robust than other proposed techniques that require the knowledge of the full flow or information up to the second-order terms of it. Experimental results are presented to support the theoretical derivations.     

Motion from occlusions

In computer vision, occlusions are almost always seen as undesirable singularities that pose difficult challenges to image motion analysis problems, such as optic flow computation, motion segmentation, disparity estimation, or egomotion estimation. However, it is well known that occlusions are extremely powerful cues for depth or motion perception, and could be used to improve those methods.

In this paper, we propose to recover camera motion information based uniquely on occlusions, by observing two specially useful properties: occlusions are independent of the camera rotation, and reveal direct information about the camera translation.

We assume a monocular observer, undergoing general rotational and translational motion in a static environment. We present a formal model for occlusion points and develop a method suitable for occlusion detection. Through the classification and analysis of the detected occlusion points, we show how to retrieve information about the camera translation (FOE). Experiments with real images are presented and discussed in the paper.     

Solving the orientation-duality problem for a circular feature inmotion

Circular features have been commonly used in numerous computer vision application areas for 3D pose estimation. However, although the 3D position of the circle's center can be uniquely identified, the solution process yields two different feasible orientations, of which only one is the true solution. In this paper, two methods are presented for the solution of the orientation-duality problem for circular features that are in motion. The first approach is applicable to those features moving on a 3D line with constant orientation or to those which are moving on a plane with general motion. The second approach relies on the existence of additional object features, such as points or lines, which are coplanar to the circular feature. In this case, the circular feature can undergo an arbitrary 3D motion. Experimental results verify the validity of the proposed methods