关于分层三维重建中模约束的一点讨论

在分层三维重建中,从射影重建到仿射重建是一个关键步骤,而模约束是从射影重建提升到仿射重建的一种重要方法,其本质在于确定无穷远平面对应的三维向量.模约束成立的前提是三维重建中所有图像对应的摄像机的内参数相同,针对当无任何关于待重建场景的先验信息或摄像机运动的先验信息时,模约束是唯一的对无穷远平面的可行约束的提法,文中指出,保持摄像机的一个或多个内参数不变,进而对摄像机进行标定,是三维重建从射影重建到度量重建的本质,而模约束不过是这种本质属性当所有内参数均保持不变下的一种特殊形式.     

基于图像的三维分层重构算法研究

文章研究在摄像机内参数不变的情况下,利用图像中场景的结构信息实现分层重构的方法.通过求解基础矩阵实现射影重构,通过求解无穷远平面单应矩阵实现仿射重构,利用虚圆点约束求解绝对二次曲线的像实现欧氏重构.实验表明所研究的算法是有效可行的.     

基于图像的三维分层重构算法研究

文章研究在摄像机内参数不变的情况下,利用图像中场景的结构信息实现分层重构的方法。通过求解基础矩阵实现射影重构,通过求解无穷远平面单应矩阵实现仿射重构,利用虚圆点约束求解绝对二次曲线的像实现欧氏重构。实验表明所研究的算法是有效可行的。     

线性多视图重构的新算法

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这一多视图三维重构问题,改进了由Hartley和Rother等人分别给出的基于由无穷远平面诱导的单应进行射影重构的算法,提出了一种新的线性算法,它仅需要空间中3个点在每幅图像上均可见。因为空间中不在同一直线上的3个点恰好确定一个平面,所以它避免了Hartley和Rother等方法中需要确定空间4个点是否共面这一比较棘手的问题。大量实验结果表明,这种方法快速、准确且受噪声影响小。     

改进的基于凸壳仿射不变量的图像识别和配准算法

提出了一种新的基于凸壳和仿射不变量的图像识别和配准的方法。该方法利用从参考图和测试图中得到的特征点提取其凸壳,并计算凸壳的仿射不变特征向量。通过比较参考图和测试图特征向量的一致性,建立它们的仿射变换关系,最后利用凸壳内特征点的匹配来实现识别和配准。该方法的优点是即使目标物体被部分覆盖或者缺损,其图像也能够达到较好的识别和配准效果。     

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．     

基于三维模型和仿射对应原理的人脸姿态估计方法

该文提出了一种基于人脸三维模型和仿射对应原理从单目视频图像序列中估计人脸空间姿态的方法．其主要思想是利用人脸的三维模型生成特征点正面平行投影,并估算输入帧和该正面平行投影之间的仿射变换参数,然后根据圆一椭圆之间的仿射对应关系得到描述人脸空间姿态的6个参数(3个旋转分量,3个平移分量)的粗略估计值,最后通过基于ICP(Iterative Closest Points：反复最近点)算法的优化迭代过程得到精确值．对石膏像和真实人脸进行的实验结果表明该算法能在较大的姿态变化范围内实现精确的人脸姿态估计．     

一种多视图分层重构算法研究

本文介绍了基于奇异值分解的射影重构算法的一般框架,以测量矩阵的秩为4作为约束,以仿射投影逼近透视投影,利用共轭梯度法估计射影深度,通过奇异值分解实现射影重构.利用共轭梯度法确定Kruppa方程中的未知比例因子,然后利用所确定的比例因子线性求解Kruppa方程,进而标定摄像机内参数.在摄像机内参数已知的情况下,求解一个满足欧氏重构条件的非奇异矩阵,然后通过此矩阵将射影重构变换为欧氏重构.实验结果表明所给出的算法是行之有效的.     

具有仿射不变性的视网膜图像配准方法

为解决眼底照相机视角发生变化的视网膜图像的配准问题,提出一种具有仿射不变性的局部特征配准方法.首先通过寻找连通的血管交点对应的最小包围矩形得到仿射不变的各向异性图像结构;然后通过旋转、采样和压缩操作将各向异性的图像结构变为含不同角度因素的各向同性的图像结构;最后使用尺度不变特征变换算法在各向同性的图像结构上提取特征点,并对特征点坐标进行匹配.在包含83组视网膜图像的私有样本集中的实验结果表明,该方法的均方根误差为1.247±0.251像素,能很好地解决视角和尺度变化问题.     

二维点模式图像的仿射变换配准

提出了一种图像特征点配准算法．该算法为二维点模式图像仿射配准建立了新的求解模型,此模型对参考图像的特征点集和浮动图像的特征点集分别进行Whitening变换,将点集间的一般仿射变换问题转换为刚性变换问题;在对刚性变换求解时,采用平滑性好、局部极值较少的新的目标函数;并引入了形变程度分量,使该算法更能符合实际应用．结合文中提出的新的仿射不变量,目标函数只需在平分法的基础上加入随机因素便能快速求解．实验结果证明,该算法在处理特征点仿射配准问题上具有速度快、精度高的特点．     

An Approach to the Vanishing Line Identification Based on Normalized Barycentric Coordinates

The vanishing line is useful information for recovering affine properties of the plane in computer vision. This paper describes how to determine analytically the vanishing line from a single perspective view of a plane containing the four points of known normalized barycentric coordinates in a general position, and further how to compute the vanishing line via the eigenvector representation. We also propose that the projectivity may be expressed directly and analytically from the vanishing line and three 3D–2D point correspondences. It is shown that plane affine properties may be computed and the metric may be recovered from known metric information, which includes an angle, two equal but unknown angles, and a length ratio of two non-parallel line segments, without using the image of the circular points as an intermediate step. The correctness and performance of the novel results are demonstrated by thorough testing on both synthetic and real data.     

Planar Segment Based Three‐dimensional Point Cloud Registration in Outdoor Environments

We present an odometry‐free three‐dimensional (3D) point cloud registration strategy for outdoor environments based on area attributed planar patches. The approach is split into three steps. The first step is to segment each point cloud into planar segments, utilizing a cached‐octree region growing algorithm, which does not require the 2.5D image‐like structure of organized point clouds. The second step is to calculate the area of each segment based on small local faces inspired by the idea of surface integrals. The third step is to find segment correspondences between overlapping point clouds using a search algorithm, and compute the transformation from determined correspondences. The transformation is searched globally so as to maximize a spherical correlation‐like metric by enumerating solutions derived from potential segment correspondences. The novelty of this step is that only the area and plane parameters of each segment are employed, and no prior pose estimation from other sensors is required. Four datasets have been used to evaluate the proposed approach, three of which are publicly available and one that stems from our custom‐built platform. Based on these datasets, the following evaluations have been done: segmentation speed benchmarking, segment area calculation accuracy and speed benchmarking, processing data acquired by scanners with different fields of view, comparison with the iterative closest point algorithm, robustness with respect to occlusions and partial observations, and registration accuracy compared to ground truth. Experimental results confirm that the approach offers an alternative to state‐of‐the‐art algorithms in plane‐rich environments.     

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.     

Reconstruction of General Curves,Using Factorization and Bundle Adjustment

In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to curves. The extension makes it possible to reconstruct 3D-curves up to projective transformations, from a number of their 2D-projections. We also extend the bundle adjustment technique from point features to curves.The first step of the curve reconstruction algorithm is based on affine shape. It is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that, except for a small set of curves (e.g. a moving line), a solution is given to the aperture problem of finding point correspondences between curves. The second step takes advantage of any knowledge of measurement errors in the images. This is possible by extending the bundle adjustment technique to curves.Finally, experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm.     

基于仿射迭代模型的特征点匹配算法

图像序列中的特征点匹配是计算机视觉中的一个基本问题,也是目标识别、图像检索以及3维重建等问题的基础。为了提高图像匹配的精度,提出了一种针对两幅图像的高精度特征点自动匹配算法。该算法首先分析并提出两幅图像中相应特征点的邻域窗口之间的单应映射可以用仿射变换模型来近似;然后通过快速的基于仿射变换模型的迭代优化方法,不仅估计并矫正了相应邻域窗口之间的透视畸变,同时还补偿了在特征点检测阶段对相应特征点的定位误差,从而使匹配结果达到子像素级精度;最后通过真实图像的实验以及与现有算法的比较结果表明,该算法不仅得到了更多的匹配关系,还提高了特征点匹配的精度。     

Extension of Affine Shape

In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to more general sets. It turns out to be possible to generalize most of the theory. The extension makes it possible to reconstruct, for example, 3D-curves up to projective transformations, from a number of their 2D-projections. An algorithm is presented, which is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that a solution is given to the aperture problem of finding point correspondences between curves.     

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.     

Reconstructing camera projection matrices from multiple pairwise overlapping views

In this work we address the problem of projective reconstruction from multiple views with missing data. Factorization based algorithms require point correspondences across all the views. In many applications this is an unrealistic assumption. Current methods that solve the problem of projective reconstruction with missing data require correspondence information across triplets of images. We propose a projective reconstruction method that yields a consistent camera set given the fundamental matrices between pairs of views without directly using the image correspondences. The algorithm is based on breaking the reconstruction problem into small steps. In each step, we eliminate as much uncertainty as possible.     

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.