Kruppa's equations derived from the fundamental matrix

The purpose of this paper is to give a specific form for Kruppa's equations in terms of the fundamental matrix. Kruppa's equations can be written explicitly in terms of the singular value decomposition (SVD) of the fundamental matrix     

Uncalibrated visual servoing using the fundamental matrix

This paper describes a new algorithm for visual control of an uncalibrated 3 DOF joint system, using two weakly calibrated fixed cameras. The algorithm estimates on-line the Image Jacobian, a matrix which linearly relates joint velocity and image feature velocity. In our experiments we prove that by using the fundamental matrix, robustness of the estimation in the presence of noise is significantly increased with respect to already existing algorithms in specialized literature.     

一个基本矩阵的鲁棒估计算法

通过分析基本矩阵的鲁棒估计方法的特点,提出了三点改进：在RANSAC（RANdom SAmpling Consensus）方法中采用了极小化再投影误差判别数据点的类别;给出再投影误差的一阶近似算法;由求出的基本矩阵和局内点数据采用LM算法对结果过一步求精,给出更好的基本矩阵估计值,使得再投影误差进一步减小,避免结果趋于局部极值。合成数据和真实图像实验均证明了该方法的有效性和可靠性。     

Nonlinear estimation of the fundamental matrix with minimal parameters

The purpose of this paper is to give a very simple method for nonlinearly estimating the fundamental matrix using the minimum number of seven parameters. Instead of minimally parameterizing it, we rather update what we call its orthonormal representation, which is based on its singular value decomposition. We show how this method can be used for efficient bundle adjustment of point features seen in two views. Experiments on simulated and real data show that this implementation performs better than others in terms of computational cost, i.e., convergence is faster, although methods based on minimal parameters are more likely to fall into local minima than methods based on redundant parameters.     

Estimating the fundamental matrix based on least absolute deviation

The epipolar geometry is the intrinsic projective geometry between two views, and the algebraic representation of it is the fundamental matrix. Estimating the fundamental matrix requires solving an over-determined equation. Many classical approaches assume that the error values of the over-determined equation obey a Gaussian distribution. However, the performances of these approaches may decrease significantly when the noise is large and heterogeneous. This paper proposes a novel technique for estimating the fundamental matrix based on least absolute deviation (LAD), which is also known as the L₁ method. Then a linear iterative algorithm is presented. The experimental results on some indoor and outdoor scenes show that the proposed algorithm yields the accurate and robust estimates of the fundamental matrix when the noise is non-Gaussian.     

改进的RANSAC方法在基础矩阵中的应用

为提高求解精度,提出一种基于改进的随机抽样一致性（RANSAC）算法的基础矩阵求解方法。采用加权策略,将局内点占全部匹配点的比例作为权重函数的自变量;利用本质矩阵和基础矩阵的关系,鉴于本质矩阵两个非零奇异值应该相等这个特性,利用加权因子和本质矩阵的奇异值构造目标函数,这两点改进意味着目标函数中有两个约束条件的限制;利用matlab遗传算法工具箱来求解目标函数的最小值,可以得到准确的基础矩阵。模版图像实验和场景图像实验验证了该算法的有效性。     

Estimating the fundamental matrix via constrained least-squares: aconvex approach

In this paper, a new method for the estimation of the fundamental matrix from point correspondences in stereo vision is presented. The minimization of the algebraic error is performed while taking explicitly into account the rank-two constraint on the fundamental matrix. It is shown how this nonconvex optimization problem can be solved avoiding local minima by using recently developed convexification techniques. The obtained estimate of the fundamental matrix turns out to be more accurate than the one provided by the linear criterion, where the rank constraint of the matrix is imposed after its computation by setting the smallest singular value to zero. This suggests that the proposed estimate can be used to initialize nonlinear criteria, such as the distance to epipolar lines and the gradient criterion, in order to obtain a more accurate estimate of the fundamental matrix     

改进的变步长行加权仿射投影算法

针对带衰减因子的变步长仿射投影算法(VS-APA-FF)中加权投影矩阵容易产生病态化的问题,文献[8]提出了正则化的VS-APA-FF(vs-APA-FF-REGU)算法,但加权投影矩阵的运算量仍然较大,为此提出改进的行加权变步长仿射投影算法(VS-APA-RW)对加权投影矩阵的计算进行简化.该算法采用间歇更新的变步长策略,有效降低了的整体运算量.最后通过有色输入下的信道盲辨识表明了算法的性能.     

采用逐层迭代方法的基础矩阵估计

为解决未知环境下运动序列中的基础矩阵估计问题,提出了一种逐层迭代优化的方法。该方法基于最优鲁棒估计方法,加入运动连续性以及多尺度对应的约束条件以减少虚假对应;然后,逐层将高层模型的数据内点添加到下层数据集,以更新数据集并同时估计单应性模型;最终,在底层全局优化并修正模型。实验表明,该方法的几何变换误差的均值不大于2.891821pixel,误差波动范围的方差不大于0.295172pixel,相对于传统方法,当运动序列中场景表面的深度层次较多,深度变化连续时,误差均值及波动方差均有一定程度的降低。     

Performance characterization of fundamental matrix estimation under image degradation

The fundamental matrix represents the epipolar geometry between two images. We describe an algorithm for simultaneously estimating the fundamental matrix and corresponding points automatically from the two images. The performance of this algorithm is then assessed as the images are degraded by JPEG lossy compression. A number of performance measures are proposed and evaluated over image pairs corresponding to different camera motions and scene types.     

Stereo rectification of pushbroom satellite images by robustly estimating the fundamental matrix

ABSTRACT

Stereo rectification is one of the most important steps for stereo matching and subsequently for digital surface model generation from satellite stereo images. This study proposes a new framework to rectify two pushbroom images along the epipolar geometry in order to omit the vertical parallax between two images. Here, we assume the interior and relative parameters between the two pushbroom images are not known and the images can be taken at different dates. Traditional stereo rectification methods of pushbroom images require metadata such as rational polynomial coefficients (RPCs), parameters of physical sensor model or ground control points (GCPs). In this study, we develop an image-based framework for stereo rectification, which works without the need for such data. In the proposed framework, the correspondences are densely extracted by a tilling strategy, and then the fundamental matrix is robustly estimated by two geometric constraints. Both affine and projective fundamental matrices could be used for stereo rectification from pushbroom stereo images. The results on IRS P5, World view III, GeoEye and IKONOS stereo pairs as well as on multi-date stereo images demonstrate that the pushbroom images are rectified with sub-pixel accuracy.     

Linear matrix inequality tests for frequency domain inequalities with affine multipliers

This paper revisits an alternative formulation of the Kalman-Yakubovich-Popov (KYP) Lemma, relating an infinite dimensional Frequency Domain Inequality (FDI) to a pair of finite dimensional Linear Matrix Inequalities (LMI). It is shown that this alternative formulation allows a certain class of the coefficient matrix of the FDI to be frequency dependent without introducing conservatism. The construction provided in the present paper is helpful in other problems where system augmentation is commonly used, such as those involving rational or polynomial multipliers for stability and performance analysis.     

基于各点异性理论的基础矩阵鲁棒估计

针对基础矩阵常用算法对噪声过于敏感、抗干扰能力差等缺点,基于误差与变量相关（Errors-in—Variables,EIV）模型提出1种新的鲁棒性基础矩阵估计算法．该算法采用各点异性回归技术,建立EIV模型,依据数据矢量观测集合最优地估计EIV模型参数和数据矢量真值集合．实验结果表明,在存在较大噪声干扰的条件下,此算法仍能较为准确地估计基础矩阵,具有良好的鲁棒性和较快的运算速度.     

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。     

Robust structure from motion with affine camera via low-rank matrix recovery

We present a novel approach to structure from motion that can deal with missing data and outliers with an affine camera. We model the corruptions as sparse error. Therefore the structure from motion problem is reduced to the problem of recovering a low-rank matrix from corrupted observations. We first decompose the matrix of trajectories of features into low-rank and sparse components by nuclear-norm and l1-norm minimization, and then obtain the motion and structure from the low-rank components by the classical factorization method. Unlike pervious methods, which have some drawbacks such as depending on the initial value selection and being sensitive to the large magnitude errors, our method uses a convex optimization technique that is guaranteed to recover the low-rank matrix from highly corrupted and incomplete observations. Experimental results demonstrate that the proposed approach is more efficient and robust to large-scale outliers.     

Analysis and design of an affine fuzzy system via bilinear matrix inequality

A novel analysis and design method for affine fuzzy systems is proposed. Both continuous-time and discrete-time cases are considered. The quadratic stability and stabilizability conditions of the affine fuzzy systems are derived and they are represented in the formulation of bilinear matrix inequalities (BMIs). Two diffeomorphic state transformations (one is linear and the other is nonlinear) are introduced to convert the plant into more tractable affine form. The conversion makes the stability and stabilizability problems of the affine fuzzy systems convex and makes the problems solvable directly by the convex linear matrix inequality (LMI) technique. The bias terms of the fuzzy controller are solved simultaneously together with the gains. Finally, the applicability of the suggested method is demonstrated via an example and computer simulation.     

An efficient fundamental matrix estimation method for wide baseline images

Fundamental matrix estimation for wide baseline images is significantly difficult due to the fact that the proportion of inliers in putative correspondences is generally very low. Traditional robust fundamental matrix estimation methods, such as RANSAC, will encounter the problems of computational inefficiency and low accuracy when outlier ratio is high. In this paper, a novel robust estimation method called inlier set sample optimization is proposed to solve these problems. First, a one-class support vector machine-based preselection algorithm is performed to efficiently select a candidate inlier set from putative SIFT correspondences according to distribution consistency of features in location, scale and orientation. Then, the quasi-optimal inlier set is refined iteratively by maximizing a soft decision objective function. Finally, fundamental matrix is estimated with the optimal inlier set. Experimental results show that the proposed method is superior to several state-of-the-art robust methods in speed, accuracy and stability and is applicable to wide baseline images with large differences.     

一种基于改进拟仿射变换的基础矩阵估计方法

以基础矩阵的估计为基础,使用计算机视觉的方法从一组不同角度、不同距离拍摄的同一场景所得的二维序列图像中还原出目标对象的三维空间信息,是实现基于图像的建模、即时定位与地图构建等前沿热点问题的主流解决方案。在基础矩阵估计问题中,准确性和效率是2个主要的衡量指标。准确性不够时,往往需要通过后端优化等方式花费高昂的代价对其进行修正,效率低则会影响系统的实时性。针对该问题,提出一种基于改进拟仿射变换的基础矩阵估计方法。具体来说,在QUATRE算法基础上,首先提出一种基于特定“基因-染色体”模式的种群协作方法。其次,重新定义齐次坐标系所表示的离散解空间中的种群初始化、变异和交叉等操作。此外,还提出一种基于置信度的迭代次数确定方式,用于加速本文方法。实验表明,该方法能有效剔除噪声和误匹配所产生的外点干扰,在准确性和效率方面优于LMedS、RANSAC和MSAC等方法,可有效解决基础矩阵估计问题。     

一种新的高精度的L-M基本矩阵估计算法

分析了基于随机抽样检测思想的现有鲁棒算法在基本矩阵估计中存在的不足,结合LMedS和M估计法各自的优点,提出一种新的高精度的L-M基本矩阵估计算法。利用LMedS思想方法获得内点集,此时内点集通常情况下不包含误匹配,但仍存在位置误差,用Torr-M估计法计算基本矩阵,因为当匹配点只存在位置误差时,用M估计法得到的基本矩阵非常精确。大量的模拟实验和真实图像实验数据表明,在高斯噪声和误匹配存在的情况下,该算法具有更高的鲁棒性和精确度。     

基于单目视频帧的基础矩阵鲁棒估计算法

为从视频图像获得鲁棒的基础矩阵,提出一种适用于视频帧的基础矩阵鲁棒估计算法。利用连续3帧为一组,分别在连续帧间两两匹配,确定最优和较优的2个子样本集,在较优子样本集中随机抽取采样,使用新的预检验方法,获得初始矩阵。并结合匹配点的分数和内点率作为权重因子,加权估算出待优化基础矩阵。由第一帧和第三帧对应于中间帧的两条极线交于同一点,构成约束关系,利用光束平差法对2个待优化基础矩阵同时进行优化。实验表明:该方法在精度和鲁棒性上,相比传统方法均能有明显提升。