基于平面与直线的仿射重建

首先给出了无穷远平面的单应矩阵以及仿射重建算法，然后从数学上严格证明了下述命题：在变参数模型下，如果场景中含有一张平面和一对平行直线，或者场景中含有两张平行平面，则从两个平移视点下的图像均可以线性地对场景进行仿射重建；文章同时指出：如果场景中包含一对平行平面和一对平行直线，则从两个一般运动视点也可以线性地重建场景的仿射几何．大量的模拟和真实图像实验表明，该线性仿射重建算法是正确的，同时具有较高的重建精度和鲁棒性．     

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.     

基于一组对应消失线的度量重建

提出了一种由3幅图像间一组对应消失线进行度量重建的方法.首先利用对应的消失线和模值约束计算出无穷远平面的单应矩阵,然后根据无穷远平面的单应矩阵保持绝对二次曲线的像不动的性质,线性求解摄像机内参数,最后得到度量重建.模拟实验和真实图像实验均验证了这种度量重建方法的可行性和正确性.     

平面单应矩阵对摄像机内参数约束的一些性质

空间x-y坐标平面与图像平面之间的单应矩阵可以提供关于摄像机内参数的2个线性约束.文中研究表明:给定一个一般空间平面与图像平面之间的单应矩阵,如果空间平面在世界坐标系的坐标已知,则该单应矩阵同样可以提供关于摄像机内参数的2个线性约束;如果空间平面在世界坐标系的坐标未知,则该单应矩阵不能构成对摄像机内参数的任何约束.另外,仅仅知道某一个场景中的2幅图像间的单应矩阵不能对摄像机内参数构成任何约束.该结果对从事摄像机标定和三维重建的研究人员有一定的参考作用.     

一种基于平面模板的单应矩阵求解方法

在视觉测量、摄像机标定和三维重建等领域中,单应矩阵的估计都起着至关重要的作用.用平面模板代替传统的传感器进行视觉测量和摄像机标定,由于其成本低,操作快速简单等优点,已经得到了越来越广泛的应用.文中主要讨论了二维成像平面的透视投影模型,给出了一种最大似然估计法获取平面模板与成像平面的单应矩阵的求解过程,并用Levenberg-Marquardt算法对结果进行非线性优化.该方法简单、快速、易实现,在计算机视觉应用中具有一定的理论意义和应用价值.     

基于场景几何约束未标定两视图的三维模型重建

提出了一种从两幅未标定图象重建场景三维模型的方法 .这种方法充分利用了人造结构场景中大量存在的平行性和正交性几何约束 ,即利用每幅视图中三组互相垂直的平行线 ,计算出 3个影灭点 ,从而对每幅视图进行标定 .对两幅未标定图象 ,从基本矩阵只能得到射影重构 ,如果每幅图象都已标定 ,则可将基本矩阵转化为本质矩阵 .三维重构过程有两个步骤 :先是恢复相机的位置和运动 ;后是用三角测量法计算出点的三维坐标 .对多平面组成的场景进行三维重构实验 ,所得三维模型产生新的视点图象 ,与所观察的场景一致 ,重构的两个平面夹角与实际值相近 ,实验结果表明 ,该算法是行之有效的     

一种基于平面模板的单应矩阵求解方法

在视觉测量、摄像机标定和三维重建等领域中,单应矩阵的估计都起着至关重要的作用。用平面模板代替传统的传感器进行视觉测量和摄像机标定,由于其成本低,操作快速简单等优点,已经得到了越来越广泛的应用。文中主要讨论了二维成像平面的透视投影模型,给出了一种最大似然估计法获取平面模板与成像平面的单应矩阵的求解过程,并用Levenberg-Marqurdt算法对结果进行非线性优化。该方法简单、快速、易实现,在计算机视觉应用中具有一定的理论意义和应用价值。     

基于两幅图像的三维物体分层重构

文章研究在仅有两幅图像的条件下,如果摄像机内参数保持不变,如何利用场景中的结构信息实现空间物体的分层重构,研究表明,计算出无穷远平面的单应矩阵,可以仿射重构,计算出绝对二次曲线的像,就可以进一步实现欧氏重构。最后给出一个具体的实验,结果表明该算法是可行的。     

基于正交平面的摄像机自定标

提出了一种基于正交平面摄像机定标的新算法。它利用场景中的正交平面,摄像机作五次以上的平移运动,根据每次运动关于平面的单应矩阵建立内参数的线性约束方程组,从而线性地确定内参数。与以往的定标方法相比,文章对摄像机的运动不苛刻,只需控制摄像机作平移运动,这在一般的实验平台上可以很容易地实现,并且线性地确定摄像机所有的五个内参数。模拟实验和真实图象实验表明,文章给出的方法在机器人视觉中具有一定的实用价值。     

线性确定无穷远平面的单应矩阵和摄象机自标定

引入了一种新的对无穷远平面的单应性矩阵(The infinite homography)的约束方程并 据此提出了一种新的摄象机线性自标定算法.与文献中已有的方法相比,该方法对摄象机的运 动要求不苛刻(如不要求摄象机的运动为正交运动),只须摄象机作一次平移运动和两次任意刚 体运动,就可线性唯一确定内参数.该方法主要优点在于:在确定无穷远平面的单应性矩阵的过 程中,不需要射影重构,也不需要有限远平面信息,唯一所需要的信息是图象极点,从而简化了 文献中现有的算法.另外同时给出了由极点确定(运动组)关于无穷远平面单应性矩阵的充分必 要条件.模拟实验和实际图象实验验证了该方法的正确性和可行性.     

Circular motion geometry using minimal data

Circular motion or single axis motion is widely used in computer vision and graphics for 3D model acquisition. This paper describes a new and simple method for recovering the geometry of uncalibrated circular motion from a minimal set of only two points in four images. This problem has been previously solved using nonminimal data either by computing the fundamental matrix and trifocal tensor in three images or by fitting conics to tracked points in five or more images. It is first established that two sets of tracked points in different images under circular motion for two distinct space points are related by a homography. Then, we compute a plane homography from a minimal two points in four images. After that, we show that the unique pair of complex conjugate eigenvectors of this homography are the image of the circular points of the parallel planes of the circular motion. Subsequently, all other motion and structure parameters are computed from this homography in a straighforward manner. The experiments on real image sequences demonstrate the simplicity, accuracy, and robustness of the new method.     

Globally Optimal Algorithms for Stratified Autocalibration

We present practical algorithms for stratified autocalibration with theoretical guarantees of global optimality. Given a projective reconstruction, we first upgrade it to affine by estimating the position of the plane at infinity. The plane at infinity is computed by globally minimizing a least squares formulation of the modulus constraints. In the second stage, this affine reconstruction is upgraded to a metric one by globally minimizing the infinite homography relation to compute the dual image of the absolute conic (DIAC). The positive semidefiniteness of the DIAC is explicitly enforced as part of the optimization process, rather than as a post-processing step.     

基于仿射点对应的分层重构

提出了一种基于仿射点对应的分层重构方法,所谓仿射点对应是指相差一个仿射变换的两个空间点集的图像对应．该方法主要分为以下三个步骤：首先,从点对应计算准仿射重构;然后,由仿射点对应的准仿射重构建立一个三维射影变换,并利用这个射影变换的特征向量来确定无穷远平面,从而得到仿射重构;最后,从仿射重构所获得的无穷远平面单应矩阵标定摄像机内参数,进而得到度量重构．在上述三个步骤中,第二个步骤是最关键的,即如何确定对应于无穷远平面的特征向量,这也是该文的新思想和主要贡献所在．仿真和真实图像实验均表明,该文的方法是有效的,并且有很好的鲁棒性．     

Multiple homographies with omnidirectional vision for robot homing

Two relevant issues in vision-based navigation are the field-of-view constraints of conventional cameras and the model and structure dependency of standard approaches. A good solution of these problems is the use of the homography model with omnidirectional vision. However, a plane of the scene will cover only a small part of the omnidirectional image, missing relevant information across the wide range field of view, which is the main advantage of omnidirectional sensors. The interest of this paper is in a new approach for computing multiple homographies from virtual planes using omnidirectional images and its application in an omnidirectional vision-based homing control scheme. The multiple homographies are robustly computed, from a set of point matches across two omnidirectional views, using a method that relies on virtual planes independently of the structure of the scene. The method takes advantage of the planar motion constraint of the platform and computes virtual vertical planes from the scene. The family of homographies is also constrained to be embedded in a three-dimensional linear subspace to improve numerical consistency. Simulations and real experiments are provided to evaluate our approach.     

The Geometry and Matching of Lines and Curves Over Multiple Views

This paper describes the geometry of imaged curves in two and three views. Multi-view relationships are developed for lines, conics and non-algebraic curves. The new relationships focus on determining the plane of the curve in a projective reconstruction, and in particular using the homography induced by this plane for transfer from one image to another. It is shown that given the fundamental matrix between two views, and images of the curve in each view, then the plane of a conic may be determined up to a two fold ambiguity, but local curvature of a curve uniquely determines the plane. It is then shown that given the trifocal tensor between three views, this plane defines a homography map which may be used to transfer a conic or the curvature from two views to a third. Simple expressions are developed for the plane and homography in each case.A set of algorithms are then described for automatically matching individual line segments and curves between images. The algorithms use both photometric information and the multiple view geometric relationships. For image pairs the homography facilitates the computation of a neighbourhood cross-correlation based matching score for putative line/curve correspondences. For image triplets cross-correlation matching scores are used in conjunction with line/curve transfer based on the trifocal geometry to disambiguate matches. Algorithms are developed for both short and wide baselines. The algorithms are robust to deficiencies in the segment extraction and partial occlusion.Experimental results are given for image pairs and triplets, for varying motions between views, and for different scene types. The methods are applicable to line/curve matching in stereo and trinocular rigs, and as a starting point for line/curve matching through monocular image sequences.     

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.     

摄像机自标定的线性理论与算法

文中提出一种新的摄像机线性自标定的算法和理论。与文献中已有的方法相比,该文方法的主要优点是对摄像机的运动要求不苛刻,如不要求摄像机的运动为正交运动。该方法的关键步骤是确定无穷远平面的单应性矩阵（Homography)。文中从理论上严格证明了下述结论：摄像机作两组运动参数未知的运动M1＝{（R1,t^11),(R1,t^12)},M2={(R2,t^21),(R2,t^22)},若下述两个条件满足：（1）T1＝{t^11,t^12},T2={t^21,t^22}是两个线性无关组（即本组内的两个平移向量线性无关）;（2）R1,R2的旋转轴不同,则可线性地唯一确定摄像机的内参矩阵和运动参数。另外,在四参数摄像机模型下,严格证明了一组运动可线性地唯一确定摄像机的内参数矩阵和运动参数。模拟实验和实际图像实验验证了本文方法的正确性和可行性。     

单幅图像测量的一种新方法

本文方法表明,由一空间平面(参考平面)与其图像间的单应性矩阵(Homography)不仅 此参考平面上的距离可以测量,而且可以测量与此参考平面垂直的平面上的距离.同时,分别位 于两平面上的点间的距离也可以测量.这样就可以得到关于场景的更多的几何信息,此结果是在 前人的基础上又向前跨了一步.另外,本文提出一种新的基于平面单应性矩阵的摄像机标定方 法.模拟和真实图像试验均表明本文方法是可行的,并得到了令人满意的结果.