基于无穷单应的线性多视图重构

研究了由多幅图像恢复摄像机矩阵和空间物体三维几何形状的问题,对Cross等人提出的利用无穷远平面诱导的单应进行重构的算法进行了改进,提出了一种新的算法。该算法只需要一个点和一条直线在所有视图中均可见,解决了原算法要求4个共面参考点的难题。     

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．     

基于径向基函数的图像修复技术

图像修复是指恢复图像中破损区域的颜色信息或者去除图像中的多余物体。本文提出了一种新的基于径向基函数的图像修复算法，由用户交互地指定需要修复的区域，算法自动地计算破损区域的轮廓并沿轮廓法向扩张，确定合适的径向基函数重构区域，将该区域内图像的颜色值看作规则采样点上的高度场，把二维图像修复问题转化为三维散乱点重建问题，利用径向基函数曲面重建的优势来修补破损的图像。实验表明，该算法能正确、稳定地处理各种破损区域。     

信号博弈的三维重建形变识别算法

现有双目立体视觉算法常常需要双目相机位置固定,在现实应用中,这类算法难以重构空间三维几何关系.为此,本文提出了一种不受位置限制的多视角图像三维重建与形变检测算法.该算法首先采用sift算法获取成对图像的特征点,以获取形变前后比对点对图像的特征信息;其次,利用信号博弈方法确定图像拍摄时相机的空间位置与视角,以准确获取图像的空间位置坐标;再次,依据上述信息完成物体的三维点云重建;进而,利用三维数据信息比对实现物体形变识别.最后,本文利用真实物体的实验,验证了三维重建形变识别算法的有效性.     

基于单目体系的可见手重构算法研究

首先确立单相机加单平面镜的体系结构，然后研究在该体系下实现三维重构的基本理论和基本方法，具体探讨了以下4个关键问题：（1）手边沿的提取；（2）对应关系的获取；（3）3D重构的基本方法；（4）校准算法，通过揭示出空间物点在像平面上的投影、该物点的对称点在同一像平面上的投影、镜面以及该物点本身这四者之间的关系，得到三维重构的新方法，既便于理论分析，又便于程序设计；既使校准过程简单易行，又保证了三维重构的精度．     

基于交比不变性的空间平面参数算法

为解决利用图像坐标计算交比可能出现计算故障或者引起计算精度下降的问题,从实际计算出发,采用N矢量表示视平面上的点和直线,建立交比的N矢量计算公式.列举一个应用实例,利用交比的不变性确定空间平面参数.该算法利用空间平面上不同的4个点的N矢量计算空间平面的3D方向和视点到平面的距离.实例表明该算法比传统算法实用、可靠.     

纹理映射中的平面校正技术研究

为了快速实时地进行由平面组成的结构景物的3D建模问题,文中介绍了一种在进行图像3D重构时纹理映射中的平面校正方法.介绍了三角形模型在图像处理、图形绘制、虚拟现实等技术中的重要作用.从射影几何的角度出发,给出了从两幅视图进行景物三维重构的分层重构方法.在已知欧氏重构即摄像机内参数的基础上,介绍一种基于标定的平面射影失真矫正方法.通过此方法,将矫正过的纹理映射到欧式点重构结构中,得到景物的3D模型.经实验验证,这种方法在处理由平面组成的景物的3D重构中是实时有效的.     

纹理映射中的平面校正技术研究

为了快速实时地进行由平面组成的结构景物的3D建模问题,文中介绍了一种在进行图像3D重构时纹理映射中的平面校正方法。介绍了三角形模型在图像处理、图形绘制、虚拟现实等技术中的重要作用。从射影几何的角度出发,给出了从两幅视图进行景物三维重构的分层重构方法。在已知欧氏重构即摄像机内参数的基础上,介绍一种基于标定的平面射影失真矫正方法。通过此方法,将矫正过的纹理映射到欧式点重构结构中,得到景物的3D模型。经实验验证,这种方法在处理由平面组成的景物的3D重构中是实时有效的。     

一维可重构流水线总线并行机上平面点集的凸壳算法

确定平面点集的凸壳是计算几何中的一个基本问题。一维可重构流水线总线并行机是近年提出的一种采用光连接的并行计算模型。本文在规模为n的可重构流水线总线并行机上提出了一个计算n个平面点的凸壳算法,当n个点按横坐标递增的顺序存储时,该算法的时问复杂度为O(logn)。     

基于SFM算法的三维人脸模型重建

提出了一种根据两幅正面人脸图像和一幅侧面图像重建人脸三维模型的算法，该算法主要包括4个步骤：寻找匹配点；采用SFM算法计算出特征点的三维坐标，并组成稀疏的三维网格结构；采用分步紧支撑径向基函数进行三维插值，得到三维模型；最后根据多分辨图像拼接算法生成纹理图像并将其映射到三维模型上，从而增强真实感，与其它算法相比，该算法最大的不同之处在于匹配点的寻找，匹配点的准确与否直接影响SFM算法结果的正确性，许多寻找匹配点的算法如角点匹配算法，在处理人脸图像时得到的结果并不稳定，这是因为人脸图像上包含了许多低纹理和重复纹理区域，大多数算法将代表人脸结构基本特征的基准模型运用在重建过程的最后一步，通过三维逼近运算，得到最终的重建模型，而该算法将反映人脸共性特征的几何对称性和规律性运用到匹配点的寻找中，能够快速准确地找出SFM算法需要的匹配点，用户使用普通照相机拍摄到的图像经本算法的处理后就可以得到相应的三维人脸结构。     

Linear Multi View Reconstruction and Camera Recovery Using a Reference Plane

This paper presents a linear algorithm for simultaneous computation of 3D points and camera positions from multiple perspective views based on having a reference plane visible in all views. The reconstruction and camera recovery is achieved in a single step by finding the null-space of a matrix built from image data using Singular Value Decomposition. Contrary to factorization algorithms this approach does not need to have all points visible in all views. This paper investigates two reference plane configurations: Finite reference planes defined by four coplanar points and infinite reference planes defined by vanishing points. A further contribution of this paper is the study of critical configurations for configurations with four coplanar points. By simultaneously reconstructing points and views we can exploit the numerical stabilizing effect of having wide spread cameras with large mutual baselines. This is demonstrated by reconstructing the outsideand inside (courtyard) of a building on the basis of 35 views in one single Singular Value Decomposition.     

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。     

Self-Calibration Under the Cayley Framework

The Cayley framework here is meant to tackle the vision problems under the infinite Cayley transformation (ICT), its main advantage lies in its numerical stability. In this work, the stratified self-calibration under the Cayley framework is investigated. It is well known that the main difficulty of the stratified self-calibration in multiple view geometry is to upgrade a projective reconstruction to an affine one, in other words, to estimate the unknown 3-vector of the plane at infinity, called the normal vector. To our knowledge, without any prior knowledge about the scene or the camera motion, the only available constraint on a moving camera with constant intrinsic parameters is the well-known Modulus Constraint in the literature. Do other kinds of constraints exist? If yes, what they are? How could they be used? In this work, such questions will be systematically investigated under the Cayley framework. Our key contributions include: 1. The original projective expression of the ICT is simplified and a new projective expression is derived to make the upgrade easier from a projective reconstruction to a metric reconstruction. 2. The constraints on the normal vector are systematically investigated. For two views, two constraints on the normal vector are derived; one of them is the well-known modulus constraint, while the other is a new inequality constraint. There are only these two constraints for two views. For three views, besides the constraints for two views, two groups of new constraints are derived and each of them contains three constraints. In other words, there are 12 constraints in total for three views. 3. Based on our projective expression and these constraints, a stratified Cayley algorithm and a total Cayley algorithm are proposed for the metric reconstruction from images. It is experimentally shown that they both improve significantly the numerical stability of the classical algorithms. Compared with the global optimal algorithm under the infinite homography framework, the Cayley algorithms have comparable calibration accuracy, but substantially reduce the computational load.     

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．     

Maximum likelihood autocalibration

This paper addresses the problem of autocalibration, which is a critical step in existing uncalibrated structure from motion algorithms that utilize an initialization to avoid the local minima in metric bundle adjustment. Currently, all known direct (not non-linear) solutions to the uncalibrated structure from motion problem solve for a projective reconstruction that is related to metric by some unknown homography, and hence a necessary step in obtaining a metric reconstruction is the subsequent estimation of the rectifying homography, known as autocalibration. Although autocalibration is a well-studied problem, previous approaches have relied upon heuristic objective functions, and have a reputation for instability. We propose a maximum likelihood objective and show that it can be implemented robustly and efficiently and often provides substantially greater accuracy, especially when there are fewer views or greater noise.     

Projective Reconstruction from Multiple Views with Minimization of 2D Reprojection Error

The problem of projective reconstruction by minimization of the 2D reprojection error in multiple images is considered. Although bundle adjustment techniques can be used to minimize the 2D reprojection error, these methods being based on nonlinear optimization algorithms require a good starting point. Quasi-linear algorithms with better global convergence properties can be used to generate an initial solution before submitting it to bundle adjustment for refinement. In this paper, we propose a factorization-based method to integrate the initial search as well as the bundle adjustment into a single algorithm consisting of a sequence of weighted least-squares problems, in which a control parameter is initially set to a relaxed state to allow the search of a good initial solution, and subsequently tightened up to force the final solution to approach a minimum point of the 2D reprojection error. The proposed algorithm is guaranteed to converge. Our method readily handles images with missing points.     

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.     

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.