基于局部邻域多流形度量的人脸识别

针对人脸识别中特征的提取,提出了一种基于局部邻域多流形度量的人脸识别方法。针对人脸识别的小样本问题,用特征脸对人脸图像预处理。对预处理后的人脸数据集中每个流形内的数据点采用欧氏距离来选择各数据点的近邻点,由此得到局部权重矩阵,并计算重构数据点与原始数据点之间的误差距离;同时,采用图像集建模流形,用affine hull表示流形对应的数据集信息,计算多流形间的距离度量矩阵。通过最大化流形间距离以及最小化数据点与重构数据点误差距离来寻找投影降维矩阵。在人脸数据集上的大量比较实验,验证了该方法的准确性和有效性。     

正投影模型下基于秩1的遮挡点恢复方法

为了有效地恢复遮挡点,假设相机为正投影模型,提出了一种基于秩1的遮挡点恢复方法.该方法利用所有图像点组成一个秩的矩阵,并利用该特性构造一个投影矩阵,利用该投影矩阵求到遮挡点,再将求到的遮挡点代替图像中的遮挡点,经过多次迭代,最后求到遮挡点的真实图像位置.模拟实验和真实实验表明:该方法具有鲁棒性好、收敛性好及误差小等优点.     

最小化TPE一元回归分类在人脸识别中的应用

针对人脸识别中现有回归分类方法不能很好地考虑总类内投影误差的问题,提出了一种基于最小化总投影误差（TPE）的一元回归分类方法。通过各个类投影矩阵计算所有训练数据的类内投影误差矩阵,并且借助特征分解找到一元旋转矩阵;利用一元旋转矩阵将每个训练图像向量转换为新的向量空间,并计算出每个类的特定投影矩阵;根据一元旋转子空间中各个类的最小投影误差来完成人脸的识别。在两大通用人脸数据库FEI和FERET上的实验验证了所提方法的有效性及鲁棒性,实验结果表明,相比其他几种先进的回归分类方法,所提方法取得了更好的识别效果。     

基于秩4约束的遮挡点恢复方法

提出了一种基于秩4约束的遮挡点恢复方法.该方法 首先假设所有的遮挡点及深度因子已知,利用所有遮挡点及深度因子组成一个秩4矩阵的特 性,构造一个投影矩阵,并利用该投影矩阵求得所有的遮挡点及深度因子.然后将求得的遮 挡点及深度因子代替图像中的遮挡点和深度因子,再求投影矩阵.经过多次迭代,最后求得 遮挡点的真实图像位置.该方法的优点是平等地看待所有的图像及图像点.模拟实验和真实实 验表明,该方法具有鲁棒性好、收敛性好及误差小等优点.     

立体视觉中基本矩阵的改进投影M估计方法

在立体视觉与图像运动分析中，需要排除特征误配点的影响进而得到精确的基本矩阵估计。针对EIV(Error In Variables)模型中基于投影的M估计方法存在的核密度估计和正常点与异常点阈值确定的局限性，提出一种改进的投影M估计算法：首先给出新的用于搜索极值点的自适应核密度估计函数，然后改进了正常点的确定方法。对模拟及真实数据进行了实验，验证了改进投影M估计方法的有效性及稳健性。     

一种基于最大边界投影和l2,1 范数正则化的属性选择算法

当数据含有噪声或标签错误时,传统的属性选择方法(如粗糙集)无法得到正确结果,为此提出一种针对含噪、标签错误数据的属性选择方法。首先用最大边界投影方法获得数据的最佳投影;然后通过对投影矩阵进行L2,1范数正则化操作,进而获得行稀疏的投影矩阵,据此获得对关键属性的挖掘;最后给出方法的收敛性和针对标签错误数据的有效性证明。实验结果表明,所提出的算法克服了噪声和标签错误的影响,较好地实现了针对含噪、标签错误数据的属性选择。     

透视和透视投影变换 --论图形变换和投影的若干问题之三

讨论了透视变换的基本原理．由于与画面成一角度的平行线簇经透视变换后交于灭点,因此可采用两种不同的方法来获得透视图：一是保持画面铅垂,通过旋转物体使之与画面构成角度达到透视变换效果,得到了三种最佳透视变换矩阵;二是通过倾斜投影画面达到透视变换效果,给出了通过倾斜画面得到三灭点透视图的齐次透视变换矩阵．两种方法的灭点都是可预先控制(即可先决定灭点再决定变换矩阵)的,比较彻底地解决了透视变换矩阵元素的产生方法．给出了“对一个空间物体,一定存在另一个空间物体,使前者在画面上的透视投影与后者的平行投影是一样的,且保留了深度方向的对应关系”的证明．这个性质可使复杂的透视投影转化成简单的平行投影,使得立体图形的处理大为简化．     

基于自适应投影矩阵的实时视频拼接算法

提出一种快速的算法用于高质量的实时拼接视频。算法分为两个阶段:后台阶段和实时阶段。后台阶段每隔一定周期运行,从同步的视频流中提取图像特征,采用RANSAC和LM算法计算投影矩阵。在实时阶段,采用从前一帧中得到的特征点点对,用光流法跟踪匹配点对的方法,对跟踪得到的点对由投影矩阵计算得到图像误差。若误差超过一定阈值或跟踪到点对数目太少,后台阶段就会再次执行。一旦得到了投影矩阵,就采取一种非线性的融合算法对视频进行融合。通过以上步骤,即使摄像头移动,算法也能运行快速。实验结果显示该算法大大改善了速度,而且拼接质量也很好。     

误差云映射的深度融合3维重建

描述了一种应用于视频序列的3维稠密重建方法,主要针对基于多深度图恢复3维物体时存在的多对一映射重复投影问题,提出基于误差云概念的3维定点优化方法.该方法首先通过深度矫正,增加视频序列深度图的一致性;其次利用投影过滤分类算法,把所有投影点按照多对一映射的关系,以3维空间中所有不同点为类型,进行投影点依次映射,将每一点划分在各自的误差云类中以求得投影点与3维点的对应关系;随后采用空间高斯分布求出每个误差云所恢复出来的点坐标.最后通过多边形技术对恢复的点云数据进行网格化,使其重建出精确的目标物体或场景的3维轮廓.从实验结果可以观察到,本文3维重建方法可以有效减少深度图融合多对一映射重复投影问题所带来的负面影响,使重建结果更加接近于真实物体,达到较好的效果.     

稳态过程的数据校正和大误差侦破方法的集成研究

针对实际数据校正问题中同时含有未测变量和带大误差已测变量的情况，提出利用两步投影矩阵方法来进行数据分类，先将稳态模型变换为统计检验所需要的标准形式（只含已测变量），用广义似然比方法侦破出大误差并予以补偿后再对数据校正问题进行求解计算，从而为数据校正及大误差侦破的集成提出了一种通用的策略，并且减少了计算量。     

基于ORB特征的单目视觉定位算法研究

针对大范围室外场景和具有重复、高频纹理特征(例如水泥地、草坪)的场景,提出了一种鲁棒性强、定位精度高、速度更快的视觉定位算法。采用8级图像金字塔的ORB (Oriented FAST and Rotated BRIEF)特征描述子提取图像特征点,通过K近邻(KNN)匹配相邻图像序列的特征点对,依次解算基础矩阵F和本质矩阵E,采用自适应法利用单应矩阵和本质矩阵进行位姿估计,最后解算两帧图像间相机刚体运动的旋转R和平移t,利用三角测量法则求解出匹配点的三维坐标,重建相机运动轨迹。为了提高算法性能,提出采用最小化基于点特征的非线性重投影误差优化三维点。通过调用OpenCV在C++中实现,对所采集的数据集进行测试,测试结果表明,该方法比传统的3D位姿估计更优,实时可行。由于其基于单目而实现,因此无法得到尺度信息。     

Fundamental matrix estimation: A study of error criteria

The fundamental matrix (FM) describes the geometric relations that exist between two images of the same scene. Different error criteria are used for estimating FMs from an input set of correspondences. In this paper, the accuracy and efficiency aspects of the different error criteria are studied. We mathematically and experimentally proved that the most popular error criterion, the symmetric epipolar distance, is biased. It was also shown that despite the similarity between the algebraic expressions of the symmetric epipolar distance and Sampson distance, they have different accuracy properties. In addition, a new error criterion, Kanatani distance, was proposed and proved to be the most effective for use during the outlier removal phase from accuracy and efficiency perspectives. To thoroughly test the accuracy of the different error criteria, we proposed a randomized algorithm for Reprojection Error-based Correspondence Generation (RE-CG). As input, RE-CG takes an FM and a desired reprojection error value d. As output, RE-CG generates a random correspondence having that error value. Mathematical analysis of this algorithm revealed that the success probability for any given trial is 1 − (2/3)² at best and is 1 − (6/7)² at worst while experiments demonstrated that the algorithm often succeeds after only one trial.     

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.     

基于空间几何结构的特征跟踪算法

针对传统的基于标记的增强现实系统场景受限等缺点,提出一种基于特征空间几何结构的无标记跟踪算法。在传统的金字塔Kanade-Lucas-Tomasi(KLT)跟踪算法基础上,通过建立图像的多尺度空间模型并在多尺度空间模型中对图像进行实时跟踪,同时根据图像特征间特有的空间几何结构信息优选跟踪特征点,解决了在多尺度变化情况下视频图像特征跟踪稳定性问题。实验结果表明,提出的跟踪算法在给定的数据库上性能高效稳定,与同类跟踪算法相比跟踪精度大幅提高,每帧重投影错误率均小于1像素,保持在亚像素级别。     

Global Optimization through Rotation Space Search

This paper introduces a new algorithmic technique for solving certain problems in geometric computer vision. The main novelty of the method is a branch-and-bound search over rotation space, which is used in this paper to determine camera orientation. By searching over all possible rotations, problems can be reduced to known fixed-rotation problems for which optimal solutions have been previously given. In particular, a method is developed for the estimation of the essential matrix, giving the first guaranteed optimal algorithm for estimating the relative pose using a cost function based on reprojection errors. Recently convex optimization techniques have been shown to provide optimal solutions to many of the common problems in structure from motion. However, they do not apply to problems involving rotations. The search method described in this paper allows such problems to be solved optimally. Apart from the essential matrix, the algorithm is applied to the camera pose problem, providing an optimal algorithm. The approach has been implemented and tested on a number of both synthetically generated and real data sets with good performance. NICTA is funded by the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian Research Council.     

Multi-stage 3D reconstruction under circular motion

In this paper, we propose a new method for 3D reconstruction from an image sequence captured by a camera with constant intrinsic parameters undergoing circular motion. We introduce a method, called circular projective reconstruction, for enforcing the circular constraint in a factorization-based projective reconstruction. To deal with the missing data problem, our method uses a multi-stage approach to reconstructing the objects and cameras, which first computes a circular projective reconstruction of a sub-sequence and then extends the reconstruction to the complete sequence. Camera matrix, rotation angles, and 3D structure are computed iteratively in a way that the 2D reprojection error is minimized. The algorithm is evaluated using real image sequences.     

Quasiconvex optimization for robust geometric reconstruction

Geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show that, for various geometric reconstruction problems, their reprojection error functions share a common and quasiconvex formulation. Based on the quasiconvexity, we present a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of small-scale convex programs that are ready to solve. Our final reconstruction algorithm is simple and has intuitive geometric interpretation. In contrast to existing local minimization approaches, our algorithm is deterministic and guarantees a predefined accuracy of the minimization result.The quasiconvexity also provides an intuitive method to handle directional uncertainties and outliers in measurements. When there are outliers in the measurements, our method provides a mechanism to locate the global minimum of a robust error function. For large scale problems and when computational resources are constrained, we provide an efficient approximation that gives a good upper bound (but not global minimum) on the reconstruction error. We demonstrate the effectiveness of our algorithm by experiments on both synthetic and real data.     

最短路径距离矩阵修正的多维标度定位算法

为了减小最短路径距离矩阵与欧氏距离矩阵之间的差异,提高MDS-MAP(C)算法的节点定位精度,提出一种改进的多维标度节点定位算法.该算法对MDS-MAP(C)算法进行了以下改进:采用启发式的搜索策略对最短路径距离矩阵进行修正,以减少最短路径距离矩阵与实际的欧氏距离矩阵之间的误差;利用smacof算法迭代误差函数代替SVD分解来求解节点的定位问题,以优化和改善节点定位的求解过程.实验结果表明,与MDS-MAP(C)算法相比,改进算法能够减少最短路径距离的误差,有效提高节点的定位精度,并且对不规则网络具有更好的适应性.     

基于异常匹配点去除的基本矩阵优化估计

提出了一种基于异常匹配点去除的基本矩阵优化估计算法。第一,去除异常匹配点,并得到基本矩阵的初值;第二,根据对极距离最小准则非线性优化求解基本矩阵。实验结果从平均余差和平均对极距离两方面表明,该算法消除了异常匹配点对基本矩阵的影响,精度较高,具有一定的优势。     

Outlier correction from uncalibrated image sequence using the Triangulation method

We propose a robust algorithm for estimating the projective reconstruction from image features using the RANSAC-based Triangulation method. In this method, we select input points randomly, separate the input points into inliers and outliers by computing their reprojection error, and correct the outliers so that they can become inliers. The reprojection error and correcting outliers are computed using the Triangulation method. After correcting the outliers, we can reliably recover projective motion and structure using the projective factorization method. Experimental results showed that errors can be reduced significantly compared to the previous research as a result of robustly estimated projective reconstruction.