基于形态和约束结构的几何哈希法

几何哈希法,作为一种有效的模型搜索算法,在物体识别中有着重要的应用。现有的几何哈希法仅适合于仿射变换下的二维景物识别,论文提出了适合透视投影变换下三维物体识别的几何哈希方法。该方法利用物体的三维形态和物体中具有射影不变量的几何约束结构来构造哈希表。一方面,几何约束结构提供了物体模型的索引功能;另一方面,物体的三维形态提供了物体成像位姿的有关信息,使后续的匹配验证得以简化。实验中使用人造物体对该方法进行了验证,实验表明该方法正确有效。     

一种消除图像射影失真的实用方法

本文介绍一种实用的消除图像射影失真的方法.首先,从射影几何的角度出发,介绍了2D射影矩阵,给出求解该矩阵的求精算法;其次,在已知2D射影矩阵的情况下,介绍了消除射影失真,恢复物体真实几何形状的方法;最后,利用上述方法对真实图像进行了恢复实验.这种方法不需要事先标定摄像机,经实验表明,处理简单,效果理想 ,实用性强,可以应用于测量、公安等各个领域.     

一种消除图像射影失真的实用方法

本文介绍一种实用的消除图像射影失真的方法。首先,从射影几何的角度出发,介绍了2D射影矩阵,给出求解该矩阵的求精算法;其次,在已知2D射影矩阵的情况下,介绍了消除射影失真,恢复物体真实几何形状的方法;最后,利用上述方法对真实图像进行了恢复实验。这种方法不需要事先标定摄像机,经实验表明,处理简单,效果理想,实用性强,可以应用于测量、公安等各个领域。     

利用2D射影变换求解空间复杂结构的3D不变量

3D不变量作为不随姿态、视点等成像条件变化而变化的特征参量，可以广泛应用于计算机视觉的多重领域．通过分析2D射影变换矩阵求解的多种可能性，由单纯基于点集对应的思路扩展到利用点集、线集、点、线组合等其它方法，从而拓宽了建立两射影平面对应关系的应用条件．由此提出了一种基于多种点线组合构造虚元素的方法，结合实元素和虚元素可以巧妙提取空间复杂结构下的多种3D不变量，以用于目标识别和描述当中．实验结果验证了方法的有效性。     

图像中射影不变量在目标识别中的应用*

研究了利用灰度图像进行目标识别的方法。根据射影变换的定义,导出了两组射影不变量,然后给出了利用哈希表进行模型数据存储和查找的识别算法。最后用实验验证了这两组不变量的不变性和可区分性。     

一种平面物体射影不变性识别方法

提出一种基于方向可变滤波器的平面物体射影不变性识别方法。该方法首先利用方向可变滤波器检测出平面物体的边缘方向特征,从单幅图像中提取平面物体在射影变化下的不变特征,建立经典框架,然后用填充经典框架图像的矩识别物体。该方法是图像局部识别方法,允许景物中有部分的遮挡物存在。     

基于外点检测与校正的填充射影分解算法

针对三维重构中存在的数据缺失和遮挡问题,提出可处理缺失数据的填充射影分解算法,利用子空间约束与对极几何约束进行矩阵拟合并填充缺失数据,通过奇异值分解得到射影运动与结构参数。为克服该算法对噪声和外点的敏感性,结合RANSAC算法和三角形法对其进行外点检测与校正。实验结果表明,加入外点校正后的算法可提高射影重构的鲁棒性,降低误差,具有较高的实用价值。     

计算机二维绘图系统的射影几何表征

文章给出了一种在传统的计算机二维绘图系统增加射影几何方法的途径。该方法基于位于以视点为中心的单位球表面上的点与图像面上的点之间的投影变换。简要介绍了射影几何基础以及用它来处理视图的基本方法,用实例初步演示了该系统的某些优点和准三维功能。     

基于空间六点不变量的道路立体目标识别方法

城市道路中常设置具有3D效果的平面路障或标志物,其具有高度的立体性和真实性,导致行人和辅助驾驶系统误判而造成严重事故,因此需要对道路立体目标进行识别,以获得真实路面情况.常见的射影不变量如交比是基于共面五点计算的,存在局限性,论文提出一种基于空间点元素的几何不变量计算方法,把空间元素的共点和共线用具有物理意义的量来表示...     

基于几何不变量的图像特征识别

图像的特征识别是图像处理和识别中的一个重要问题，几何不变量作为特征的特征值在很多领域已经得到了广泛的应用。实际中，普遍采用在仿射变换及射影变换下保持不变的仿射、射影不变量作为特征值。本文根据具体图像的特点，利用4类仿射和射影不变量构成特征的特征值空间，依据4步识别策略来识别图像中的特征点，从而完成识别任务。实验表明，这4类不变量能够较好地识别出实际图像中的特征。     

A Geometric Approach for the Theory and Applications of 3D Projective Invariants

A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing position. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes in the observation parameters. The study of such geometric invariance is a field of active research. This paper presents the theory and computation of projective invariants formed from points and lines using the geometric algebra framework. This work shows that geometric algebra is a very elegant language for expressing projective invariants using n views. The paper compares projective invariants involving two and three cameras using simulated and real images. Illustrations of the application of such projective invariants in visual guided grasping, camera self-localization and reconstruction of shape and motion complement the experimental part.     

Model-Based Object Recognition Using Geometric Invariants of Points and Lines

In this paper, we derive new geometric invariants for structured 3D points and lines from single image under projective transform, and we propose a novel model-based 3D object recognition algorithm using them. Based on the matrix representation of the transformation between space features (points and lines) and the corresponding projected image features, new geometric invariants are derived via the determinant ratio technique. First, an invariant for six points on two adjacent planes is derived, which is shown to be equivalent to Zhu's result [1], but in simpler formulation. Then, two new geometric invariants for structured lines are investigated: one for five lines on two adjacent planes and the other for six lines on four planes. By using the derived invariants, a novel 3D object recognition algorithm is developed, in which a hashing technique with thresholds and multiple invariants for a model are employed to overcome the over-invariant and false alarm problems. Simulation results on real images show that the derived invariants remain stable even in a noisy environment, and the proposed 3D object recognition algorithm is quite robust and accurate.     

Planar shape representation and matching under projective transformation

This paper introduces a new representation for planar objects which is invariant to projective transformation. Proposed representation relies on a new shape basis which we refer to as the conic basis. The conic basis takes conic-section coefficients as its dimensions and represents the object as a convex combination of conic-sections. Pairs of conic-sections in this new basis and their projective invariants provides the proposed view invariant representation. We hypothesize that two projectively transformed versions of an object result in the same representation. We show that our hypothesis provides promising recognition performance when we use the nearest neighbor rule to match projectively deformed objects.     

一种基于投影不变量的目标交接改进方法

在多摄像机视频监控系统中,图像之间的视点对应以及目标的交接是重要的研究内容。不需要标定摄像机的参数,该文提出了一种利用尺度不变特征变换（SIFT：scale-invariant features transform）及融合颜色信息的投影不变量实现目标交接的方法。利用SIFT方法自动生成图像间匹配的特征点对,并由此生成视野分界线,然后利用融合颜色信息的投影不变量方法完成对多摄像机之间目标身份的确认。     

Model-based recognition of 3D objects from single images

In this work, we treat major problems of object recognition which have received relatively little attention lately. Among them are the loss of depth information in the projection from a 3D object to a single 2D image, and the complexity of finding feature correspondences between images. We use geometric invariants to reduce the complexity of these problems. There are no geometric invariants of a projection from 3D to 2D. However, given certain modeling assumptions about the 3D object, such invariants can be found. The modeling assumptions can be either a particular model or a generic assumption about a class of models. Here, we use such assumptions for single-view recognition. We find algebraic relations between the invariants of a 3D model and those of its 2D image under general projective projection. These relations can be described geometrically as invariant models in a 3D invariant space, illuminated by invariant “light rays,” and projected onto an invariant version of the given image. We apply the method to real images     

一种基于投影不变量的目标跟踪方法

提出了一种基于平面投影不变量的目标跟踪算法．算法从图像中提取直线边缘计算投影不变量，用于对目标建模并跟踪．为提取直线边缘，使用改进的序列细化算法将边缘细化为单像素宽，而后用一种快速曲率估计方法估算边缘点的曲率，并保留估算值很小（约等于零）的点拟合直线．在所得直线族中按照邻近规则或者窗口规则挑选直线计算投影不变量．图像处理实验给出了用文中提出的图像预处理算法获得的直线边缘效果，并通过使用所得直线计算不变量的值衡量了所得不变量的稳定性和视角不变性．跟踪实验检验了跟踪算法的鲁棒性和实用性．     

Projective invariants of co-moments of 2D images

Functions of moments of 2D images that are invariant under some changes are important in image analysis and pattern recognition. One of the most basic changes to a 2D image is geometric change. Two images of the same plane taken from different viewpoints are related by a projective transformation. Unfortunately, it is well known that geometric moment invariants for projective transformations do not exist in general. Yet if we generalize the standard definition of the geometric moments and utilize some additional information from the images, certain type of projective invariants of 2D images can be derived. This paper first defines co-moment as a moment-like function of image that contains two reference points. Then a set of functions of co-moments that is invariant under general projective transformations is derived. The invariants are simple and in explicit form. Experimental results validated the mathematical derivations.