Generalised Epipolar Constraints

In this paper we will discuss structure and motion problems for curved surfaces. These will be studied using the silhouettes or apparent contours in the images. The problem of determining camera motion from the apparent contours of curved three-dimensional surfaces, is studied. It will be shown how special points, called epipolar tangency points or frontier points, can be used to solve this problem. A generalised epipolar constraint is introduced, which applies to points, curves, as well as to apparent contours of surfaces. The theory is developed for both continuous and discrete motion, known and unknown orientation, calibrated and uncalibrated, perspective, weak perspective and orthographic cameras. Results of an iterative scheme to recover the epipolar line structure from real image sequences using only the outlines of curved surfaces, is presented. A statistical evaluation is performed to estimate the stability of the solution. It is also shown how the motion of the camera from a sequence of images can be obtained from the relative motion between image pairs.     

Self-Calibration of a Moving Camera from Point Correspondences and Fundamental Matrices

We address the problem of estimating three-dimensional motion, and structure from motion with an uncalibrated moving camera. We show that point correspondences between three images, and the fundamental matrices computed from these point correspondences, are sufficient to recover the internal orientation of the camera (its calibration), the motion parameters, and to compute coherent perspective projection matrices which enable us to reconstruct 3-D structure up to a similarity. In contrast with other methods, no calibration object with a known 3-D shape is needed, and no limitations are put upon the unknown motions to be performed or the parameters to be recovered, as long as they define a projective camera.The theory of the method, which is based on the constraint that the observed points are part of a static scene, thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic, is first detailed. Several algorithms are then presented, and their performances compared by means of extensive simulations and illustrated by several experiments with real images.     

Silhouette coherence for camera calibration under circular motion

We present a new approach to camera calibration as a part of a complete and practical system to recover digital copies of sculpture from uncalibrated image sequences taken under turntable motion. In this paper, we introduce the concept of the silhouette coherence of a set of silhouettes generated by a 3D object. We show how the maximization of the silhouette coherence can be exploited to recover the camera poses and focal length. Silhouette coherence can be considered as a generalization of the well-known epipolar tangency constraint for calculating motion from silhouettes or outlines alone. Further, silhouette coherence exploits all the geometric information encoded in the silhouette (not just at epipolar tangency points) and can be used in many practical situations where point correspondences or outer epipolar tangents are unavailable. We present an algorithm for exploiting silhouette coherence to efficiently and reliably estimate camera motion. We use this algorithm to reconstruct very high quality 3D models from uncalibrated circular motion sequences, even when epipolar tangency points are not available or the silhouettes are truncated. The algorithm has been integrated into a practical system and has been tested on more than 50 uncalibrated sequences to produce high quality photo-realistic models. Three illustrative examples are included in this paper. The algorithm is also evaluated quantitatively by comparing it to a state-of-the-art system that exploits only epipolar tangents     

A Linear Algorithm for Computing the Homography from Conics in Correspondence

This paper presents a study, based on conic correspondences, on the relationship between two perspective images acquired by an uncalibrated camera. We show that for a pair of corresponding conics, the parameters representing the conics satisfy a linear constraint. To be more specific, the parameters that represent a conic in one image are transformed by a five-dimensional projective transformation to the parameters that represent the corresponding conic in another image. We also show that this transformation is expressed as the symmetric component of the tensor product of the transformation based on point/line correspondences and itself. In addition, we present a linear algorithm for uniquely determining the corresponding point-based transformation from a given conic-based transformation up to a scale factor. Accordingly, conic correspondences enable us to easily handle both points and lines in uncalibrated images of a planar object.     

基于未标定图像的三维重建算法

提出一种基于多幅未标定图像的三维重建算法。在标记点匹配的基础上进行射影重建,通过施加度量约束将射影重建升级为欧氏重建,即利用未标定的透视图像恢复相机的内、外部参数以及标记点的三维空间坐标,实现场景的三维重建。标记点易于进行点对精确匹配,较手动拾取匹配提高了效率。实验结果表明,利用该算法能够大幅减小再投影误差。     

Depth recovery and affine reconstruction under camera pure translation

This paper addresses the problems of depth recovery and affine reconstruction from two perspective images, which are generated by an uncalibrated translating camera. Firstly, we develop a new constraint that the homography for the plane, which is orthogonal to the optical axis, is determined only by the epipole and the plane's relative distance to the origin under camera pure translation. The algorithm of depth recovery is based on this new constraint, and it can successfully avoid the step of camera calibration. With the recovered depth, we show that affine reconstruction can be obtained readily. The proposed affine reconstruction does not need any control points, which were used to expand the affine coordinate system in existing method. Therefore, it could avoid the step of non-planarity verification as well as the errors from the control points. Error analysis is also presented to evaluate the uncertainty for the recovered depth value. Finally, we have tested the proposed algorithm with both simulated data and real image data. And the results show that the proposed algorithm is accurate and practical.     

单轴运动下未标定图像序列的度量重构

提出了一种由单轴运动下的未标定运动图像序列进行三维重构的新方法。利用不变量计算出第一幅图像对应的摄像机矩阵,根据转台的旋转角度计算出其余图像对应的摄像机矩阵,再使用SIFT算法查找相邻两幅图像可见的匹配点,并利用线性三角形法对图像进行重构,最后用捆集调整优化重构的结果。真实图像序列的重构实验验证了算法的正确性和有效性。     

Simultaneous two-view epipolar geometry estimation and motion segmentation by 4D tensor voting

We address the problem of simultaneous two-view epipolar geometry estimation and motion segmentation from nonstatic scenes. Given a set of noisy image pairs containing matches of n objects, we propose an unconventional, efficient, and robust method, 4D tensor voting, for estimating the unknown n epipolar geometries, and segmenting the static and motion matching pairs into n, independent motions. By considering the 4D isotropic and orthogonal joint image space, only two tensor voting passes are needed, and a very high noise to signal ratio (up to five) can be tolerated. Epipolar geometries corresponding to multiple, rigid motions are extracted in succession. Only two uncalibrated frames are needed, and no simplifying assumption (such as affine camera model or homographic model between images) other than the pin-hole camera model is made. Our novel approach consists of propagating a local geometric smoothness constraint in the 4D joint image space, followed by global consistency enforcement for extracting the fundamental matrices corresponding to independent motions. We have performed extensive experiments to compare our method with some representative algorithms to show that better performance on nonstatic scenes are achieved. Results on challenging data sets are presented.     

A Direct Interpretation of Dynamic Images with Camera and Object Motions for Vision Guided Robot Control

A general scheme to represent the relation between dynamic images and camera and/or object motions is proposed for applications to visual control of robots. We consider the case where a moving camera observes moving objects in a static scene. The camera obtains images of the objects moving within the scene. Then, the possible combinations of the camera and the objects' poses and the obtained images are not arbitrary but constrained to each other. Here we represent this constraint as a lower dimensional hypersurface in the product space of the whole combination of their motion control parameters and image data. The visual control is interpreted as to find a path on this surface leading to their poses where a given goal image will be obtained. In this paper, we propose a visual control method to utilize tangential properties of this surface. First, we represent images with a composition of a small number of eigen images by using K-L (Karhunen-Loève) expansion. Then, we consider to reconstruct the eigen space (the eigen image space) to achieve efficient and straightforward controls. Such reconstruction of the space results in the constraint surface being mostly flat within the eigen space. By this method, visual control of robots in a complex configuration is achieved without image processing to extract and correspond image features in dynamic images. The method also does not need camera or hand-eye calibrations. Experimental results of visual servoing with the proposed method show the feasibility and applicability of our newly proposed approach to a simultaneous control of camera self-motion and object motions.     

Automatic geometric reasoning in structure and motion estimation

We present a system for doing automatic surveying or structure and motion analysis given 1D images of a 2D surrounding. Nothing is known about the structure of the scene features or of the motion of the camera. The system automatically identifies and tracks the image of new points and solves the structure and motion problem. One key feature of the system is the ability to hypothesize, test and incorporate simple constraints on the scene, e.g. that two object points are the same, that several points are coplanar. In this paper we develop and test the theory for automatic geometric reasoning. Ideas on hypothesis generation and testing are presented. It is also shown how to update the uncertainty representation of the database.     

一种非定标图像高精度三维重建算法

由非定标图像重建三维场景有着广泛的应用。给出了一种非定标多视图像三维重建算法。该算法主要基于因子分解和光束法平差技术。首先用因子分解方法得到射影空间下相机投影矩阵和物点坐标,以旋转矩阵的正交性以及对偶绝对二次曲面秩为3为约束,将射影空间升级到欧式空间,最后用光束法平差进行优化。该方法可同时获得相机的内外参数、畸变系数和场景的三维坐标。仿真实验表明,在1000 mm×1000 mm×400mm的范围内,当像点检测误差在0-1pixel和0-2pixel内,所重建三维点的误差分别为0.1530 mm和0.6712 mm。在500 mm×500 m×200 mm下,真实实验重构三维点的误差在0.3 mm以内。所提出的算法稳定可靠,可对实际工程进行指导。     

一种新的摄像机自定标的方法

本文给出一种由未定标图像进行摄像机自定标的方法．通过分析基础矩阵关系式及方 差之间关系,得出一种新的计算摄像机内部参数及运动参数的准则．在计算中采用单个摄 像机并且假设摄像机像主点的位置已知,大大简化了运算量．     

基于图像序列的交互式快速建模系统

给出了一个基于图像序列的交互式三维建模系统.通过输入一段未标定的图像或视频序列,系统能够自动地恢复出摄像机参数;然后用户只需要在少量几帧图像上简单勾画出物体的形态结构,系统就能自动解析出多帧之间用户交互的对应关系,从而迅速、逼真地重建出场景的三维模型.该系统提供了点与线段的重建、直线与平面的重建、曲线与曲面的重建等功能,能够满足对现实世界中的复杂场景的快速高精度的重建要求.几组真实拍摄的图像序列的建模实验表明:该系统高效、实用.能够很好地满足实际建模需求.     

Visual Modeling with a Hand-Held Camera

In this paper a complete system to build visual models from camera images is presented. The system can deal with uncalibrated image sequences acquired with a hand-held camera. Based on tracked or matched features the relations between multiple views are computed. From this both the structure of the scene and the motion of the camera are retrieved. The ambiguity on the reconstruction is restricted from projective to metric through self-calibration. A flexible multi-view stereo matching scheme is used to obtain a dense estimation of the surface geometry. From the computed data different types of visual models are constructed. Besides the traditional geometry- and image-based approaches, a combined approach with view-dependent geometry and texture is presented. As an application fusion of real and virtual scenes is also shown.     

一种鲁棒的基于两个特征点的深度估计方法

This paper presents a novel depth estimation method based on feature points. Two points are selected arbitrarily from an object and their distance in the space is assumed to be known.The proposed technique can estimate simultaneously their depths according to two images taken before and after a camera moves and the motion parameters of the camera may be unknown. In addition, this paper analyzes the ways to enhance the precision of the estimated depths and presents a feature point image coordinates search algorithm to increase the robustness of the proposed method.The search algorithm can find automatically more accurate image coordinates of the feature points based on their detected image coordinates. Experimental results demonstrate the efficiency of the presented method.     

面向全自主智能机器人的无标定图像视觉伺服控制研究

在利用全自主智能机器人检测、搬运目标物的过程中,为了提高主机元件对机器人的伺服控制效果,设计了一种无标定图像视觉伺服控制方法。首先,根据机器人轨迹的无标定估计结果,计量目标物的位姿点,推导出机器人无标定图像中的目标物检测与追踪条件。按需连接视觉伺服控制器,通过求解机器人无标定运动内积的方式,计算图像视觉特征的伺服选择标准,实现对机器人无标定图像视觉特征的伺服选择。然后,在无标定图像中定义雅克比矩阵,根据图像视觉分割原则,完成机器人图像角点的伺服匹配处理,再通过确定强化控制参数的取值范围,实现无标定图像的视觉伺服控制。根据实验可知,应用该方法可以解决智能机器人难以运动至标定区域的问题,为提高伺服控制指令的执行有效性提供了保障。     

Chirality

It is known that a set of points in three-dimensions is determined up to projectivity from two views with uncalibrated cameras. It is shown in this paper that this result may be improved by distinguishing between points in front of and behind the camera. Any point that lies in an image must lie in front of the camera producing that image. Using this idea, it is shown that the scene is determined from two views up to a more restricted class of mappings known as quasi-affine transformations, which are precisely those projectivities that preserve the convex hull of an object of interest. An invariant of quasi-affine transformation known as the chiral sequence of a set of points is defined and it is shown how the chiral sequence may be computed using two uncalibrated views. As demonstrated theoretically and by experiment the chiral sequence may distinguish between sets of points that are projectively equivalent. These results lead to necessary and sufficient conditions for a set of corresponding pixels in two images to be realizable as the images of a set of points in three dimensions.Using similar methods, a necessary and sufficient condition is given for the orientation of a set of points to be determined by two views. If the perspective centres are not separated from the point set by a plane, then the orientation of the set of points is determined from two views.     

Self-calibration from one circular motion sequence and two images

This paper describes a new method for self-calibration of camera with constant internal parameters under circular motion, using one sequence and two images captured with different camera orientations. Unlike the previous method, in which three circular motion sequences are needed with known motion, the new method computes the rotation angles and the projective reconstructions of the sequence and the images with circular constraint enforced, which is called a circular projective reconstruction, using a factorization-based method. It is then shown that the images of the circular points of each circular projective reconstruction can be readily obtained. Subsequently, the image of the absolute conic and the calibration matrix of the camera can be determined. Experiments on both synthetic and real image sequence are given, showing the accuracy and robustness of the new algorithm.     

摄像机位姿的高精度快速求解

目的 针对对应点个数大于等于6的摄像机位姿估计问题,提出一种既适用于已标定也适用于未标定摄像机的时间复杂度为 的高精度快速算法。 方法 首先选取四个非共面虚拟控制点,并根据空间点和虚拟控制点的空间关系以及空间点的图像建立线性方程组,以此求解虚拟控制点的图像坐标及摄像机内参,再由POSIT算法根据虚拟控制点及其图像坐标求解旋转矩阵和平移向量。 结果 模拟数据实验和真实图像实验表明该算法时间复杂度和计算精度均优于现有的已标定摄像机位姿的高精度快速求解算法EPnP。 结论 该算法能够同时估计摄像机内外参数,而且比现有算法具有更好的速度和精度。     

Recovery of the 3-D location and motion of a rigid object through camera image (An Extended Kalman Filter Approach)

This paper deals with the problem of locating a rigid object and estimating its motion in three dimensions. This involves determining the position and orientation of the object at each instant when an image is captured by a camera, and recovering the motion of the object between consecutive frames.In the implementation scheme used here, a sequence of camera images, digitized at the sample instants, is used as the initial input data. Measurements are made of the locations of certain features (e.g., maximum curvature points of an image contour, corners, edges, etc.) on the 2-D images. To measure the feature locations a matching algorithm is used, which produces correspondences between the features in the image and the object.Using the measured feature locations on the image, an algorithm is developed to solve the location and motion problem. The algorithm is an extended Kalman filter modeled for this application.Department of Electrical Engineering and Alberta Center for Machine Intelligence and Robotics, University of Alberta