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．     

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．     

A new method for camera stratified self-calibration under circular motion

We consider the stratified self-calibration (affine and metric reconstruction) problem from images acquired with a camera with unchanging internal parameters undergoing circular motion. The general stratified method (modulus constraints) is known to fail with this motion. In this paper we give a novel constraint on the plane at infinity in projective reconstruction for circular motion, the constant inter-frame motion constraint on the plane at infinity between every two adjacent views and a fixed view of the motion sequences, by making use of the facts that in many commercial systems rotation angles are constant. An initial solution can be obtained by using the first three views of the sequence, and Stratified Iterative Particle Swarm Optimization (SIPSO) is proposed to get an accurate and robust solution when more views are at hand. Instead of using the traditional optimization algorithm as the last step to obtain an accurate solution, in this paper, the whole motion sequence information is exploited before computing the camera calibration matrix, this results in a more accurate and robust solution. Once the plane at infinity is identified, the calibration matrices of the camera and a metric reconstruction can be readily obtained. Experiments on both synthetic and real image sequence are given, showing the accuracy and robustness of the new algorithm.     

Self-calibration of stationary non-rotating zooming cameras

This paper proposes a new method for self-calibrating a set of stationary non-rotating zooming cameras. This is a realistic configuration, usually encountered in surveillance systems, in which each zooming camera is physically attached to a static structure (wall, ceiling, robot, or tripod). In particular, a linear, yet effective method to recover the affine structure of the observed scene from two or more such stationary zooming cameras is presented. The proposed method solely relies on point correspondences across images and no knowledge about the scene is required. Our method exploits the mostly translational displacement of the so-called principal plane of each zooming camera to estimate the location of the plane at infinity. The principal plane of a camera, at any given setting of its zoom, is encoded in its corresponding perspective projection matrix from which it can be easily extracted. As a displacement of the principal plane of a camera under the effect of zooming allows the identification of a pair of parallel planes, each zooming camera can be used to locate a line on the plane at infinity. Hence, two or more such zooming cameras in general positions allow the obtainment of an estimate of the plane at infinity making it possible, under the assumption of zero-skew and/or known aspect ratio, to linearly calculate the camera's parameters. Finally, the parameters of the camera and the coordinates of the plane at infinity are refined through a nonlinear least-squares optimization procedure. The results of our extensive experiments using both simulated and real data are also reported in this paper.     

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.     

Zeros at infinity for affine nonlinear control systems

A definition of zeros at infinity for affine nonlinear control systems is proposed. The definition is local, which means that we exclude certain singularities. We argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling. In particular, we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity.     

Camera Autocalibration and Horopter Curves

We describe a new algorithm for the obtainment of the affine and Euclidean calibration of a camera under general motion. The algorithm exploits the relationships of the horopter curves associated to each pair of cameras with the plane at infinity and the absolute conic. Using these properties we define cost functions whose minimization by means of general purpose techniques provides the required calibration. The experiments show the good convergence properties, computational efficiency and robust performance of the new techniques.     

Quasi-Euclidean epipolar rectification of uncalibrated images

This paper deals with the problem of epipolar rectification in the uncalibrated case. First the calibrated (Euclidean) case is recognized as the ideal one, then we observe that in that case images are transformed with a collineation induced by the plane at infinity, which has a special structure. Hence, that structure is imposed to the sought transformation while minimizing a rectification error. Experiments show that this method yields images that are close to the ones produced by Euclidean rectification.     

A New Linear Method for Camera Self-Calibration with Planar Motion

We consider the self-calibration (affine and metric reconstruction) problem from images acquired with a camera with unchanging internal parameters undergoing planar motion. The general self-calibration methods (modulus constraint, Kruppa equations) are known to fail with this camera motion. In this paper we give two novel linear constraints on the coordinates of the plane at infinity in a projective reconstruction for any camera motion. In the planar case, we show that the two constraints are equivalent and easy to compute, giving us a linear version of the quartic modulus constraint. Using this fact, we present a new linear method to solve the self-calibration problem with planar motion of the camera from three or more images. This work was partly supported by project BFM2003-02914 from the Ministerio de Ciencia y Tecnología (Spain). Ferran Espuny received the MSc in Mathematics in 2002 from the Universitat de Barcelona, Spain. He is currently a PhD student and associate professor in the Departament d’àlgebra i Geometria at Universitat de Barcelona, Spain. His research, supervised by Dr. José Ignacio Burgos Gil, is focussed on self-calibration and critical motions for both pinhole and generic camera models.     

A Novel Solution to the P4P Problem for an Uncalibrated Camera

We present a novel solution for the absolute camera pose and the camera calibration (effective focal length and aspect ratio) based on perspective four point (P4P) problem. By converting perspective transformation to affine transformation and using invariance to 3D affine transformation, we explore the relationship between the dual image of the absolute conic (DIAC) and the world coordinate of camera optical center and show how the coplanar and noncoplanar cases are cast into the problems of solving a quadratic polynomial equation and an eighth degree polynomial equation in a single variable respectively using only linear algebra. In particular, geometric configurations for infinite solutions of the coplanar case are explored. We also confirm the conclusion that the upper bound of eight real solutions for noncoplanar case is attainable by an example. The performance and usefulness of our novel solution are demonstrated by thorough testing on both synthetic and real data.     

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.     

Using collineations to compute motion and structure in an uncalibrated image sequence

We address the well-known problem of estimating the motion and structure of a plane, but in the case where the visual system is not calibrated and in a monocular image-sequence. We first define plane collineations and analyse some of their properties when used to analyse the retinal motion in an uncalibrated image sequence. We show how to relate them to the Euclidean parameters of the scene. In particular, we discuss how to detect and estimate the collineation of the plane at infinity and use this quantity for auto-calibration.

More precisely

- We have been able to elaborate a method to estimate robustly any collineation in the image as soon as at least four projections have been established, especially for points at infinity and the collineation of this virtual infinite plane;

- It is shown that, given at least four points of a stationary plane and two stationary points not on the plane (or equivalently 2 planes) we can compute the focus of expansion;

- A step further, we have defined a bi-ratio of distances for a point with respect to a plane which allows us to analyse not only the relative position of this point with respect to the plane but also quantify this distance;

- Moreover a necessary and sufficient condition for a collineation to correspond to a stationary plane is given in the affine case;

- It is also discussed that when given three views and the plane at infinity, the intrinsics calibration parameters of the camera can be recovered from linear equations.

Robust estimations of collineation and statistical tests are then developed and illustrated by some experimental results.     

Stereo calibration from rigid motions

We describe a method for calibrating a stereo pair of cameras using general or planar motions. The method consists of upgrading a 3D projective representation to affine and to Euclidean without any knowledge, neither about the motion parameters nor about the 3D layout. We investigate the algebraic properties relating projective representation to the plane at infinity and to the intrinsic camera parameters when the camera pair is considered as a moving rigid body. We show that all the computations can be carried out using standard linear resolutions techniques. An error analysis reveals the relative importance of the various steps of the calibration process: projective-to-affine and affine-to-metric upgrades. Extensive experiments performed with calibrated and natural data confirm the error analysis as well as the sensitivity study performed with simulated data     

Tracking While Zooming Using Affine Transfer and Multifocal Tensors

This paper presents algorithms for tracking unknown objects in the presence of zoom. Since prior models are unavailable, point and line matches in affine views are used to characterize the structure and to transfer a fixation point into new images in a sequence. Because any affine projection matrix is permitted, the intrinsic camera parameters such as focal length may change freely. Also, since the techniques do not require long feature tracks, a further desirable property is insensitivity to partial occlusion caused, for instance, by part of the object falling off the image plane while zooming in. If only point matches are available, a previous method based on factorization is applied. When also incorporating lines, the affine trifocal and quadrifocal tensors are used for tracking in monocular and stereo systems respectively. Methods for computing the tensors, minimizing algebraic error, are developed. In comparison with their projective counterparts, the affine tensors offer significant advantages in terms of computation time and convenience of parameterization, and the relations between the different tensors are shown to be much simpler. Successful tracking is demonstrated on several real image sequences.     

Globally Optimal Point Set Registration by Joint Symmetry Plane Fitting

The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of symmetry. By reflecting the points of each set with respect to the plane of symmetry, we can largely increase the overlap between the sets and therefore boost the registration process. However, prior knowledge about the plane of symmetry is generally unavailable or at least very hard to find, especially with limited partial views. Finding this plane could strongly benefit from a prior alignment of the partial point sets. We solve this chicken-and-egg problem by jointly optimizing the relative pose and symmetry plane parameters. We present a globally optimal solver by employing the branch-and-bound paradigm and thereby demonstrate that joint symmetry plane fitting leads to a great improvement over the current state of the art in globally optimal point set registration for common objects. We conclude with an interesting application of our method to dense 3D reconstruction of scenes with repetitive objects.

     

由平行平面的投影确定无穷远平面的单应矩阵

在三维计算机视觉中,无穷远平面的单应矩阵扮演了极其重要的角色,可使众多视觉问题的求解得到简化.主要讨论如何利用平行平面的投影来求解两个视点间的无穷远平面的单应矩阵,用代数方法构造性地证明了下述结论:(1) 如果场景中含有一组平行平面,则可以通过求解一个一元4次方程来确定两个视点间的无穷远平面对应的单应矩阵;(2) 如果场景中含有两组平行平面,则可以线性地确定两个视点间的无穷远平面对应的单应矩阵.并对上述结果给出了相应的几何解释和具体算法.所给出的结果在三维计算机视觉,特别是摄像机自标定中具有一定的理论意义和应用价值.     

Affine reconstruction from perspective image pairs with a relativeobject-camera translation in between

A method is described to recover the three-dimensional affine structure of a scene consisting of at least five points identified in two perspective views with a relative object-camera translation in between. When compared to the results for arbitrary stereo views, a more detailed reconstruction is possible using less information. The method presented only assumes that the two images are obtained by identical cameras, but no knowledge about the intrinsic parameters of the camera(s) or about the performed translation is assumed. By the same method, affine 3D reconstruction from a single view can be achieved for parallel structures. In that case, four points suffice for affine reconstruction     

Global,Dense Multiscale Reconstruction for a Billion Points

We present a variational approach for surface reconstruction from a set of oriented points with scale information. We focus particularly on scenarios with nonuniform point densities due to images taken from different distances. In contrast to previous methods, we integrate the scale information in the objective and globally optimize the signed distance function of the surface on a balanced octree grid. We use a finite element discretization on the dual structure of the octree minimizing the number of variables. The tetrahedral mesh is generated efficiently with a lookup table which allows to map octree cells to the nodes of the finite elements. We optimize memory efficiency by data aggregation, such that robust data terms can be used even on very large scenes. The surface normals are explicitly optimized and used for surface extraction to improve the reconstruction at edges and corners.     

Design of an improved framework for stratified 3D reconstruction from a pair of images,with reduced ambiguity

Reconstruction of three dimensional (3D) object structure from multiple images is a fundamental problem in computational vision. Many applications in computer vision require the use of structure information of 3D objects. The objective of this work is to develop a stable method of 3D reconstruction of an object, which works without the availability of camera parameters, once the plane at infinity is obtained using the approximate scene information. First, a framework has been designed based on a modification of the auto-calibration procedure for 3D structure computation using singular value decomposition. In the second part of the work, ambiguities present at the various stages of 3D reconstruction have been analysed. Error norms have been proposed, and studied to quantify the ambiguity in the reconstruction process. We attempt to analyse the effect of pose difference between camera views and focal length parameters on the reconstruction process, using experimentation with simulated and real-world data.     

非线性系统的自适应实用输出跟踪控制

研究了一类具有不可控不稳定线性化和线性化参数的非线性系统的全局自适应实用输 出跟踪控制问题,这类系统既不具有反馈线性化性质,对输入也没有仿射特性.因为这类系统的 线性化系统具有不可控模式且该模式在右半平面内有根,所以全局渐近输出跟踪是不可能的(甚 至是局部的).应用修正的自适应增加幂积分方法,设计了一种光滑状态反馈控制器,保证闭环系 统所有信号全局一致最终有界,且使跟踪误差进入零的小邻域内.仿真结果表明该控制器是可行 的并且是有效的.