Registration of partially overlapping surfaces by rejection of false point correspondences

We present a new algorithm for the registration of three-dimensional partially overlapping surfaces. It is based on an efficient scheme for the rejection of false point correspondences (correspondence outliers) and does not require initial pose estimation or feature extraction. An initial list of corresponding points is first derived using the regional properties of vertices on both surfaces. From these point correspondences, pairs of corresponding rigid triplets are formed. The normal vectors at the vertices of each corresponding triplet are used to compute the candidate rotations. By clustering the candidate rotation axes and candidate rotation angles separately, a large number of false correspondences are eliminated and an approximate rotation is decided, from which an approximate translation is also obtained. Finally, the optimal transformation parameters are determined by further refining the estimated parameters in an iterative manner. Mathematical analysis and experimental results show that the registration process is fast and accurate even when the objects are regularly shaped and contain many regionally similar surface patches.     

Self-Calibration from Image Derivatives

This study investigates the problem of estimating camera calibration parameters from image motion fields induced by a rigidly moving camera with unknown parameters, where the image formation is modeled with a linear pinhole-camera model. The equations obtained show the flow to be separated into a component due to the translation and the calibration parameters and a component due to the rotation and the calibration parameters. A set of parameters encoding the latter component is linearly related to the flow, and from these parameters the calibration can be determined.However, as for discrete motion, in general it is not possible to decouple image measurements obtained from only two frames into translational and rotational components. Geometrically, the ambiguity takes the form of a part of the rotational component being parallel to the translational component, and thus the scene can be reconstructed only up to a projective transformation. In general, for full calibration at least four successive image frames are necessary, with the 3D rotation changing between the measurements.The geometric analysis gives rise to a direct self-calibration method that avoids computation of optical flow or point correspondences and uses only normal flow measurements. New constraints on the smoothness of the surfaces in view are formulated to relate structure and motion directly to image derivatives, and on the basis of these constraints the transformation of the viewing geometry between consecutive images is estimated. The calibration parameters are then estimated from the rotational components of several flow fields. As the proposed technique neither requires a special set up nor needs exact correspondence it is potentially useful for the calibration of active vision systems which have to acquire knowledge about their intrinsic parameters while they perform other tasks, or as a tool for analyzing image sequences in large video databases.     

Linear Quasi-Parallax SfM Using Laterally-Placed Eyes

A large class of visual systems in the biological world often has multiple eyes in simultaneous motion and yet has little or no overlap in the visual fields between the eyes. These systems include the lateral eyes found in many vertebrates and the compound eyes in insects. Instead of computing feature correspondences between the eyes, which might not even be possible due to the lack of overlap in the visual fields, we exploit the organizational possibility offered by the eye topography. In particular, we leverage on the pair of visual rays that are parallel to each other but opposite in direction, and compute what we call the quasi-parallax for translation recovery. Besides resulting in parsimonious visual processing, the quasi-parallax term also enhances the information pick-up for the translation, as it is almost rotation-free. The rotation is subsequently recovered from a pencil of visual rays using the individual epipolar constraints of each camera. As a result of using these different and appropriate aspects of visual rays for motion recovery, our method is numerically more effective in disambiguating the translation and rotation. In comparison to the gold standard solution obtained by the bundle adjustment (BA) technique, our method has a better Fisher information matrix for a lateral eye pair, as well as a superior experimental performance under the case of narrow field of view. For other eye configurations, the two methods achieve comparable performances, with our linear method slightly edging the nonlinear BA method when there exists imperfection in the calibration.     

A loop-consistency measure for dense correspondences in multi-view video

Many applications in computer vision and computer graphics require dense correspondences between images of multi-view video streams. Most state-of-the-art algorithms estimate correspondences by considering pairs of images. However, in multi-view videos, several images capture nearly the same scene. In this article we show that this redundancy can be exploited to estimate more robust and consistent correspondence fields. We use the multi-video data structure to establish a confidence measure based on the consistency of the correspondences in a loop of three images. This confidence measure can be applied after flow estimation is terminated to find the pixels for which the estimate is reliable. However, including the measure directly into the estimation process yields dense and highly accurate correspondence fields. Additionally, application of the loop consistency confidence measure allows us to include sparse feature matches directly into the dense optical flow estimation. With the confidence measure, spurious matches can be successfully suppressed during optical flow estimation while correct matches contribute to increase the accuracy of the flow.     

Determination of camera location from 2-D to 3-D line and pointcorrespondences

A method for the determination of camera location from two-dimensional (2-D) to three-dimensional (3-D) straight line or point correspondences is presented. With this method, the computations of the rotation matrix and the translation vector of the camera are separable. First, the rotation matrix is found by a linear algorithm using eight or more line correspondences, or by a nonlinear algorithm using three or more line correspondences, where the line correspondences are either given or derived from point correspondences. Then, the translation vector is obtained by solving a set of linear equations based on three or more line correspondences, or two or more point correspondences. Eight 2-D to 3-D line correspondences or six 2-D to 3-D point correspondences are needed for the linear approach; three 2-D to 3-D line or point correspondences for the nonlinear approach. Good results can be obtained in the presence of noise if more than the minimum required number of correspondences are used     

基于图像视觉伺服的二维运动优化控制

基于图像的视觉伺服方法,图像的变化直接解释为摄像机的运动,而不是直接对机械手末端实现笛卡尔速度控制,导致机械手的运动轨迹迂回,产生摄像机回退现象.针对这一问题,提出了将旋转和平移分离并先实现旋转的视觉伺服方案.该方案计算量小,系统响应时间短,解决了图像旋转和平移间的干扰,克服了传统基于图像视觉伺服产生的摄像机回退现象,实现了时间和路径的最优控制.并用传统IBVS的控制律和摄像机成像模型解释了回退现象的产生原因.二维运动仿真说明了提出方案的有效性.     

Self-Calibration of Turntable Sequences from Silhouettes

This paper addresses the problem of recovering both the intrinsic and extrinsic parameters of a camera from the silhouettes of an object in a turntable sequence. Previous silhouette-based approaches have exploited correspondences induced by epipolar tangents to estimate the image invariants under turntable motion and achieved a weak calibration of the cameras. It is known that the fundamental matrix relating any two views in a turntable sequence can be expressed explicitly in terms of the image invariants, the rotation angle, and a fixed scalar. It will be shown that the imaged circular points for the turntable plane can also be formulated in terms of the same image invariants and fixed scalar. This allows the imaged circular points to be recovered directly from the estimated image invariants, and provide constraints for the estimation of the imaged absolute conic. The camera calibration matrix can thus be recovered. A robust method for estimating the fixed scalar from image triplets is introduced, and a method for recovering the rotation angles using the estimated imaged circular points and epipoles is presented. Using the estimated camera intrinsics and extrinsics, a Euclidean reconstruction can be obtained. Experimental results on real data sequences are presented, which demonstrate the high precision achieved by the proposed method.     

Stereo geometry from 3D ego-motion streams

This paper addresses the problem of geometry determination of a stereo rig that undergoes general rigid motions. Neither known reference objects nor stereo correspondence are required. With almost no exception, all existing online solutions attempt to recover stereo geometry by first establishing stereo correspondences. We first describe a mathematical framework that allows us to solve for stereo geometry, i.e., the rotation and translation between the two cameras, using only motion correspondence that is far easier to acquire than stereo correspondence. Second, we show how to recover the rotation and present two linear methods, as well as a nonlinear one to solve for the translation. Third, we perform a stability study for the developed methods in the presence of image noise, camera parameter noise, and ego-motion noise. We also address accuracy issues. Experiments with real image data are presented. The work allows the concept of online calibration to be broadened, as it is no longer true that only single cameras can exploit structure-from-motion strategies; even the extrinsic parameters of a stereo rig of cameras can do so without solving stereo correspondence. The developed framework is applicable for estimating the relative three-dimensional (3D) geometry associated with a wide variety of mounted devices used in vision and robotics, by exploiting their scaled ego-motion streams.     

Egomotion estimation of a range camera using the space envelope

In this paper we present a method to compute the egomotion of a range camera using the space envelope. The space envelope is a geometric model that provides more information than a simple segmentation for correspondences and motion estimation. We describe a novel variation of the maximal matching algorithm that matches surface normals to find correspondences. These correspondences are used to compute rotation and translation estimates of the egomotion. We demonstrate our methods on two image sequences containing 70 images. We also discuss the cases where our methods fail, and additional possible methods for exploiting the space envelope.     

Intrinsic and extrinsic active self-calibration of multi-camera systems

We present a method for active self-calibration of multi-camera systems consisting of pan-tilt zoom cameras. The main focus of this work is on extrinsic self-calibration using active camera control. Our novel probabilistic approach avoids multi-image point correspondences as far as possible. This allows an implicit treatment of ambiguities. The relative poses are optimized by actively rotating and zooming each camera pair in a way that significantly simplifies the problem of extracting correct point correspondences. In a final step we calibrate the entire system using a minimal number of relative poses. The selection of relative poses is based on their uncertainty. We exploit active camera control to estimate consistent translation scales for triplets of cameras. This allows us to estimate missing relative poses in the camera triplets. In addition to this active extrinsic self-calibration we present an extended method for the rotational intrinsic self-calibration of a camera that exploits the rotation knowledge provided by the camera’s pan-tilt unit to robustly estimate the intrinsic camera parameters for different zoom steps as well as the rotation between pan-tilt unit and camera. Quantitative experiments on real data demonstrate the robustness and high accuracy of our approach. We achieve a median reprojection error of $0.95$ pixel.     

关于视觉运动分析中凝视与跟踪作用的研究

提出主动观察者利用摄象机旋转,凝视并跟踪环境点使视场中心保持固定,能提供求解 问题所需的许多有用信息,从而缩减待解问题的维数及运动参数数目,把不适定问题转变为适定 问题,大大简化计算的复杂性,有效地进行3-D运动估计、自运动复原及TTC的计算.     

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.     

A camera calibration technique using three sets of parallel lines

This paper presents a new method for three-dimensional camera calibration in which the rotation parameters are decoupled from the translation parameters. First, the rotation parameters are obtained by projecting three sets of parallel lines independently of the translation parameters and the imaging distance from the lens to the image plane. The virtual line passing through the image center, which is calculated by perspective projection of a set of parallel lines, depends only on the rotation parameters. Next, the translation parameters and the imaging distance are analytically obtained. Experimental results are used to show how the camera model can be accurately reconstructed in an easily prepared environment.     

Multilinear Factorizations for Multi-Camera Rigid Structure from Motion Problems

Camera networks have gained increased importance in recent years. Existing approaches mostly use point correspondences between different camera views to calibrate such systems. However, it is often difficult or even impossible to establish such correspondences. But even without feature point correspondences between different camera views, if the cameras are temporally synchronized then the data from the cameras are strongly linked together by the motion correspondence: all the cameras observe the same motion. The present article therefore develops the necessary theory to use this motion correspondence for general rigid as well as planar rigid motions. Given multiple static affine cameras which observe a rigidly moving object and track feature points located on this object, what can be said about the resulting point trajectories? Are there any useful algebraic constraints hidden in the data? Is a 3D reconstruction of the scene possible even if there are no point correspondences between the different cameras? And if so, how many points are sufficient? Is there an algorithm which warrants finding the correct solution to this highly non-convex problem? This article addresses these questions and thereby introduces the concept of low-dimensional motion subspaces. The constraints provided by these motion subspaces enable an algorithm which ensures finding the correct solution to this non-convex reconstruction problem. The algorithm is based on multilinear analysis, matrix and tensor factorizations. Our new approach can handle extreme configurations, e.g. a camera in a camera network tracking only one single point. Results on synthetic as well as on real data sequences act as a proof of concept for the presented insights.     

Optic flow estimation by a Hopfield neural network using geometrical constraints

Sparse optic flow maps are general enough to obtain useful information about camera motion. Usually, correspondences among features over an image sequence are estimated by radiometric similarity. When the camera moves under known conditions, global geometrical constraints can be introduced in order to obtain a more robust estimation of the optic flow. In this paper, a method is proposed for the computation of a robust sparse optic flow (OF) which integrates the geometrical constraints induced by camera motion to verify the correspondences obtained by radiometric-similarity-based techniques. A raw OF map is estimated by matching features by correlation. The verification of the resulting correspondences is formulated as an optimization problem that is implemented on a Hopfield neural network (HNN). Additional constraints imposed in the energy function permit us to achieve a subpixel accuracy in the image locations of matched features. Convergence of the HNN is reached in a small enough number of iterations to make the proposed method suitable for real-time processing. It is shown that the proposed method is also suitable for identifying independently moving objects in front of a moving vehicle. Received: 26 December 1995 / Accepted: 20 February 1997     

一种新的机器人手眼关系标定方法

通过控制装有摄像机的机械手的运动,给出了一种新的机器人手眼系统标定方法．与以往算法的不同之处在于,在计算手眼关系的平移向量时,对摄像机坐标系进行虚设旋转变换使旋转转化为平移问题．该方法需要机械手平台做两次平移运动和一次旋转运动,只需要场景中两个特征点,所以具有方便性和实用性．同时,也给出了基于主动视觉的空间点深度值计算方法．     

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.     

Automatic ice motion retrieval from ERS-1 SAR images using the optical flow method

The optical flow method is an approach to motion analysis in the field of computer vision. This method is implemented here to deal with rotational and deformational ice motion, for which the area correlation method shows deficiencies. The results show that the optical flow method has the capacity to cope with the rotation and deformation of an ice cover, while requiring less computing time than the area correlation method. For better representation of the discontinuities of a motion field, a modified version of the optical flow method is presented with the aid of image segmentation. The paper also includes a technique for detecting mean rotation and translation in terms of FFT transformation. In most cases, this technique can simplify and speed up the process of motion retrieval in the Arctic central pack ice area. The algorithm has been applied to fourteen pairs of images acquired in the Arctic Ocean and the Baltic Sea. Three of them are illustrated here to demonstrate the accuracy and other capacities of the algorithm.     

Structure from motion with wide circular field of view cameras

This paper presents a method for fully automatic and robust estimation of two-view geometry, autocalibration, and 3D metric reconstruction from point correspondences in images taken by cameras with wide circular field of view. We focus on cameras which have more than 180/spl deg/ field of view and for which the standard perspective camera model is not sufficient, e.g., the cameras equipped with circular fish-eye lenses Nikon FC-E8 (183/spl deg/), Sigma 8 mm-f4-EX (180/spl deg/), or with curved conical mirrors. We assume a circular field of view and axially symmetric image projection to autocalibrate the cameras. Many wide field of view cameras can still be modeled by the central projection followed by a nonlinear image mapping. Examples are the above-mentioned fish-eye lenses and properly assembled catadioptric cameras with conical mirrors. We show that epipolar geometry of these cameras can be estimated from a small number of correspondences by solving a polynomial eigenvalue problem. This allows the use of efficient RANSAC robust estimation to find the image projection model, the epipolar geometry, and the selection of true point correspondences from tentative correspondences contaminated by mismatches. Real catadioptric cameras are often slightly noncentral. We show that the proposed autocalibration with approximate central models is usually good enough to get correct point correspondences which can be used with accurate noncentral models in a bundle adjustment to obtain accurate 3D scene reconstruction. Noncentral camera models are dealt with and results are shown for catadioptric cameras with parabolic and spherical mirrors.