Efficient extraction of metric measurements for planar scene under 2D homography with the help of planar circles

Extraction of metric properties from perspective view is a challenging task in many machine vision applications. Most conventional approaches typically first recover the perspective transformation parameters up to a similarity transform and make measurements in the resulting rectified image. In this paper, a new approach is proposed to allow quick and reliable Euclidean measures to be made directly from a perspective view without explicitly recovering the world plane. Unlike previous planar rectification strategies, our approach makes use of planar circles to help identify the image of the absolute conic, which makes it capable of performing effective rectification under many difficult cases that are unable to be treated with other rectification approaches. This is made possible by solving the images of the circular points in closed-form from the vanishing line and the image of one arbitrary planar circle and by exploiting the invariant relationship between the circular points and the absolute conic under projective transformation. Subsequently, planar Euclidean measures can be made directly from the image plane. The practical advantages and the efficiency of this method are demonstrated by experiments on both synthetic and real scenes.     

Euclidean Upgrading from Segment Lengths

We address the problem of the recovery of Euclidean structure of a projectively distorted n-dimensional space from the knowledge of the, possibly diverse, lengths of a set of segments. This problem is relevant, in particular, for Euclidean reconstruction with uncalibrated cameras, extending previously known results in the affine setting. The key concept is the Quadric of Segments (QoS), defined in a higher-dimensional space by the set of segments of a fixed length, from which Euclidean structure can be obtained in closed form. We have intended to make a thorough study of the properties of the QoS, including the determination of the minimum number of segments of arbitrary length that determine it and its relationship with the standard geometric objects associated to the Euclidean structure of space. Explicit formulas are given to obtain the dual absolute quadric and the absolute quadratic complex from the QoS. Experiments with real and synthetic images evaluate the performance of the techniques.     

三视校正的理论及鲁棒性算法

主要讨论两方面的工作.首先,对三视校正问题进行理论分析,给出了校正后图像的基本矩阵与其约束条件之间的关系,讨论了三视校正过程中的6个自由参数的几何含义.这些结果为处理校正过程中带来的图像射影畸变提供了理论根据.其次,在RANSAC(random sampling consensus)框架下,提出了一种鲁棒的三视校正算法.与传统的校正算法不同,该算法不再只依赖于基本矩阵,而是直接利用了原始匹配点的信息.这种基于点的方法有两个优点:一方面,由于噪声的干扰,基本矩阵往往估计得不够准确;另一方面,由于基本矩阵的评价准则与校正结果的评价准则不同,即使从好的基本矩阵出发,也未必能获得好的校正结果.大量的模拟和真实图像实验表明,该算法具有很强的抗噪声及抗错误匹配的能力,能够获得令人满意的校正效果.     

QR码图像的矫正与定位方法研究

QR二维条码作为一种可高速、全方位识别的二维条码，已经在各行各业中得到了广泛的应用。本文针对QR条码图像的识别过程中可能遇到的图像倾斜、几何失真等问题进行了研究，提出了通过双线性变换矫正变形的条码图像，然后使用QR条码符号特性对图像进行旋转并定向。实验证明，本文的方法简单有效，可以用于提高QR条码的正确识别率。     

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.     

An improved algorithm for two-image camera self-calibration and Euclidean structure recovery using absolute quadric

We present an improved algorithm for two-image camera self-calibration and Euclidean structure recovery, where the effective focal lengths of both cameras are assumed to be the only unknown intrinsic parameters. By using the absolute quadric, it is shown that the effective focal lengths can be computed linearly from two perspective images without imposing scene or motion constraints. Moreover, a quadratic equation derived from the absolute quadric is proposed for solving the parameters of the plane at infinity from two images, which upgrades a projective reconstruction to a Euclidean reconstruction.     

一种无需基础矩阵的鲁棒性极线校正算法

立体视觉校正也称为极线校正,它的目的是使得立体图像的对应极线平行于水平方向,消除垂直方向上的视差,从而使得在立体匹配过程中可以更为快速准确地寻找对应点.在传统的投影校正算法的基础上提出了一种鲁棒性校正算法,直接通过原始匹配点计算投影变换矩阵,利用遗传算法良好的全局搜索能力和Levenberg-Marquardt算法稳定快速的局部搜索功能进行分步优化计算,同时本算法采用了随机抽样一致算法（RANSAC）鲁棒估计思想,避免了由于对应点噪声引起的误差.此外,还针对两个平行放置的摄像机之间具有较小运动的情况,提出了一种鲁棒的优化函数.实验结果说明,该算法是一种有效的极线校正方法.     

Structure recovery with multiple cameras from scaled orthographicand perspective views

This paper presents a novel framework for Euclidean structure recovery utilizing a scaled orthographic view and perspective views simultaneously. A scaled orthographic view is introduced in order to automatically obtain camera parameters such as camera positions, orientation, and focal length. Scaled orthographic properties enable all camera parameters to be calculated implicitly and perspective properties enable a Euclidean structure to be recovered. The method can recover a Euclidean structure with at least seven point correspondences across a scaled orthographic view and perspective views. Experimental results for both computed and natural images verify that the method recovers structure with sufficient accuracy to demonstrate potential utility. The proposed method can be applied to an interface for 3D modeling, recognition and tracking     

基于未标定图像的三维重建算法

提出一种基于多幅未标定图像的三维重建算法。在标记点匹配的基础上进行射影重建,通过施加度量约束将射影重建升级为欧氏重建,即利用未标定的透视图像恢复相机的内、外部参数以及标记点的三维空间坐标,实现场景的三维重建。标记点易于进行点对精确匹配,较手动拾取匹配提高了效率。实验结果表明,利用该算法能够大幅减小再投影误差。     

Optimal Binary Morphological Bandpass Filters Induced by Granulometric Spectral Representation

Euclidean granulometries are used to decompose a binary image into a disjoint union based on interaction between image shape and the structuring elements generating the granulometry. Each subset of the resulting granulometric spectral bands composing the union defines a filter by passing precisely the bands in the subset. Given an observed image and an ideal image to be estimated, an optimal filter must minimize the expected symmetric-difference error between the ideal image and filtered observed image. For the signal-union-noise model, and for both discrete and Euclidean images, given a granulometry, a procedure is developed for finding a filter that optimally passes bands of the observed noisy image. The key is characterization of an optimal filter in the Euclidean case. Optimization is achieved by decomposing the mean functions of the signal and noise size distributions into singular and differentiable parts, deriving an error representation based on the decomposition, and describingoptimality in terms of generalized derivatives for the singular parts and ordinary derivatives for the differentiable parts. Owing to the way in which spectral bands are optimally passed, there are strong analogies with the Wiener filter.     

引入欧氏距离的各向异性扩散相干斑抑制

目的 相干斑噪声严重影响SAR影像解译。抑制相干斑同时,获取较好的边缘保持效果始终是相干斑抑制的重点。针对该问题,提出一种引入欧氏距离的各向异性扩散（EDAD）相干斑抑制方法。方法 EDAD算法以P-M模型与SRAD算法为基础,利用邻近像素间区域欧氏距离代替原有边缘检测算子,自适应区分同质区与异质区,有效构造各向异性扩散系数,完成相干斑抑制。结果 运用EDAD算法与现存各向异性扩散算法对截取的两景TanDEM-X影像进行试验研究并比较各类算法的评估参数。EDAD算法的等效视数分别为3.996与5.859,均高于其他算法,体现优越的相干斑抑制能力;EDAD算法相干斑抑制前后比值影像的均值分别为0.999与1.001,方差分别为0.270与0.269,较其他算法均更接近理想值1与0.273,展现更优边缘保持与相干斑抑制能力。结论 本文算法可有效提高边缘检测能力,获取更优相干斑抑制效果。经验证,对分布较散的弱相干斑区域与分布较集中的强相干斑区域均有较好适用性。     

航片二次几何校正的应用研究

应用ERDAS软件对高分辨率航片进行二次几何校正的研究,从中找出适合各种航片再校正的可行性方法,尤其是对地图采点模式校正方法的科学性、准确性、实用性进行了重点研究,从而获得了一种常规方法无法校正的新校正模式,即综合采点模式。而且,这项技术也完全适用于TM和SPOT等卫星图像的二次几何校正,并且提高了校正精度和速度,是一种比较实用的二次几何校正模型。     

On the Euclidean distance of images

We present a new Euclidean distance for images, which we call image Euclidean distance (IMED). Unlike the traditional Euclidean distance, IMED takes into account the spatial relationships of pixels. Therefore, it is robust to small perturbation of images. We argue that IMED is the only intuitively reasonable Euclidean distance for images. IMED is then applied to image recognition. The key advantage of this distance measure is that it can be embedded in most image classification techniques such as SVM, LDA, and PCA. The embedding is rather efficient by involving a transformation referred to as standardizing transform (ST). We show that ST is a transform domain smoothing. Using the face recognition technology (FERET) database and two state-of-the-art face identification algorithms, we demonstrate a consistent performance improvement of the algorithms embedded with the new metric over their original versions.     

Multiple motion scene reconstruction with uncalibrated cameras

In this paper, we describe a reconstruction method for multiple motion scenes, which are scenes containing multiple moving objects, from uncalibrated views. Assuming that the objects are moving with constant velocities, the method recovers the scene structure, the trajectories of the moving objects, the camera motion, and the camera intrinsic parameters (except skews) simultaneously. We focus on the case where the cameras have unknown and varying focal lengths while the other intrinsic parameters are known. The number of the moving objects is automatically detected without prior motion segmentation. The method is based on a unified geometrical representation of the static scene and the moving objects. It first performs a projective reconstruction using a bilinear factorization algorithm and, then, converts the projective solution to a Euclidean one by enforcing metric constraints. Experimental results on synthetic and real images are presented.     

Applications of a direct algorithm for the rectification of uncalibrated images

An algorithm for the rectification of uncalibrated images is presented and applied to a variety of cases. The algorithm generates the rectifying transformations directly from the geometrical relationship between the images, using any three correspondences in the images to define a reference plane. A small set of correspondences is used to calculate an initial rectification. Additional correspondences are introduced semi-automatically, by correlating regions of the rectified images. Since the rectified images of surfaces in the reference plane have no relative distortion, features can be matched very accurately by correlation, allowing small changes in disparity to be detected. In the 3-d reconstruction of an architectural scene, differences in depth are resolved to about 0.001 of the distance from camera to subject.     

Image Manifolds which are Isometric to Euclidean Space

Recently, the Isomap procedure [10] was proposed as a new way to recover a low-dimensional parametrization of data lying on a low-dimensional submanifold in high-dimensional space. The method assumes that the submanifold, viewed as a Riemannian submanifold of the ambient high-dimensional space, is isometric to a convex subset of Euclidean space. This naturally raises the question: what datasets can reasonably be modeled by this condition? In this paper, we consider a special kind of image data: families of images generated by articulation of one or several objects in a scene—for example, images of a black disk on a white background with center placed at a range of locations. The collection of all images in such an articulation family, as the parameters of the articulation vary, makes up an articulation manifold, a submanifold of L ². We study the properties of such articulation manifolds, in particular, their lack of differentiability when the images have edges. Under these conditions, we show that there exists a natural renormalization of geodesic distance which yields a well-defined metric. We exhibit a list of articulation models where the corresponding manifold equipped with this new metric is indeed isometric to a convex subset of Euclidean space. Examples include translations of a symmetric object, rotations of a closed set, articulations of a horizon, and expressions of a cartoon face. The theoretical predictions from our study are borne out by empirical experiments with published Isomap code. We also note that in the case where several components of the image articulate independently, isometry may fail; for example, with several disks in an image avoiding contact, the underlying Riemannian manifold is locally isometric to an open, connected, but not convex subset of Euclidean space. Such a situation matches the assumptions of our recently-proposed Hessian Eigenmaps procedure, but not the original Isomap procedure.     

基于Gabor滤波器的遥感图像纹理查询方法

介绍了一种基于Gabor纹理特征的遥感图像检索方法。利用Gabor滤波器对图像进行多分辨率分解，提出了一种改进的基于滤波图像及图像能量的纹理特征提取方法，利用尺度、方向、纹理结构构成特征向量，使用归一化欧氏距离进行了相似性判断。该方法计算过程简单、快速，提高了方向判别的可靠性。仿真实验和实际运用验证了该算法的有效性。     

Omnidirectional Image Stabilization for Visual Object Recognition

In this paper, we present a pipeline for camera pose and trajectory estimation, and image stabilization and rectification for dense as well as wide baseline omnidirectional images. The proposed pipeline transforms a set of images taken by a single hand-held camera to a set of stabilized and rectified images augmented by the computed camera 3D trajectory and a reconstruction of feature points facilitating visual object recognition. The paper generalizes previous works on camera trajectory estimation done on perspective images to omnidirectional images and introduces a new technique for omnidirectional image rectification that is suited for recognizing people and cars in images. The performance of the pipeline is demonstrated on real image sequences acquired in urban as well as natural environments.     

Some Results on Minimal Euclidean Reconstruction from Four Points

Methods for reconstruction and camera estimation from miminal data are often used to boot-strap robust (RANSAC and LMS) and optimal (bundle adjustment) structure and motion estimates. Minimal methods are known for projective reconstruction from two or more uncalibrated images, and for “5 point” relative orientation and Euclidean reconstruction from two calibrated parameters, but we know of no efficient minimal method for three or more calibrated cameras except the uniqueness proof by Holt and Netravali. We reformulate the problem of Euclidean reconstruction from minimal data of four points in three or more calibrated images, and develop a random rational simulation method to show some new results on this problem. In addition to an alternative proof of the uniqueness of the solutions in general cases, we further show that unknown coplanar configurations are not singular, but the true solution is a double root. The solution from a known coplanar configuration is also generally unique. Some especially symmetric point-camera configurations lead to multiple solutions, but only symmetry of points or the cameras gives a unique solution.     

Extracting Group Transformations from Image Moments

Image distortion induced by the relative motion between an observer and the scene is an important cue for recovering the motion and the structure of the scene. It is known that the distortion in images can be described by transformation groups, such as Euclidean, affine, and projective groups. In this paper, we investigate how the moments of image curves are changed by group transformations, and we derive a relationship between the change in image moments and the invariant vector fields of the transformation groups. The results are used to formalize a method for extracting invariant vector fields of affine transformations from changes in the moments of orientation of curve segments in images. The method is applied to a realtime robot visual navigation task.