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。     

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...     

一种新的几何约束结构及其射影不变量

几何不变量,特别是射影不变量,是基于单视点灰度图像识别三维物体的一条有效途径．但理论研究表明,只有特定的几何约束结构,才具有射影不变量．所以,研究并发现这种几何约束结构就具有十分重要的意义．该文提出了一种新的由相邻3平面上5条直线组成的几何约束结构及其所具有的射影不变量．该结构较Sugimoto提出的几何约束结构简单,可从结构同样复杂的物体中获得更多的几何不变量,有利于提高物体识别的稳定性;同时,由于该结构大量存在于由多面体组合而构成的人造物体及地面建筑物中,因此它非常适合这类物体的识别．实验验证了文中提出的几何约束结构具有不随物体成像视点改变的射影不变量．     

Minimal Decomposition of Model-Based Invariants

Model-based invariants are relations between model parameters and image measurements, which are independent of the imaging parameters. Such relations are true for all images of the model. Here we describe an algorithm which, given L independent model-based polynomial invariants describing some shape, will provide a linear re-parameterization of the invariants. This re-parameterization has the properties that: (i) it includes the minimal number of terms, and (ii) the shape terms are the same in all the model-based invariants. This final representation has 2 main applications: (1) it gives new representations of shape in terms of hyperplanes, which are convenient for object recognition; (2) it allows the design of new linear shape from motion algorithms. In addition, we use this representation to identify object classes that have universal invariants.     

Omnidirectional Robot Vision Using Conformal Geometric Computing

In this paper, we show how to use the conformal geometric algebra (CGA) as a framework to model the different catadioptric systems using the unified model (UM). This framework is well suited since it can not only represent points, lines and planes, but also point pairs, circles and spheres (geometric objects needed in the UM). We define our model using the great expressive capabilities of the CGA in a more general and simpler way, which allows an easier implementation in more complex applications. On the other hand, we also show how to recover the projective invariants from a catadioptric image using the inverse projection of the UM. Finally, we present applications in navigation and object recognition. Carlos Alberto López-Franco is a doctoral student at CINVESTAV, GEOVIS Laboratory, Unidad Guadalajara, México. He received in 2003 the M.S. degree in Computer Science from CINVESTAV, Unidad Guadalajara. His scientific interests are in the fields of computer vision, robotics and the applications of geometric algebra for mobile robots. Eduardo Jose Bayro-Corrochano gained his Ph.D. in Cognitive Computer Science in 1993 from the University of Wales at Cardiff. From 1995 to 1999 he has been Researcher and Lecturer at the Institute for Computer Science, Christian Albrechts University, Kiel, Germany, working on applications of geometric Clifford algebra to cognitive systems. At present is a full professor at CINVESTAV Unidad Guadalajara, México, Department of Electrical Engineering and Computer Science. His current research interest focuses on geometric methods for artificial perception and action systems. It includes geometric neural networks, visually guided robotics, color image processing, Lie bivector algebras for early vision and robot maneuvering. He developed the quaternion wavelet transform for quaternion multi-resolution analysis using the phase concept. He is associate editor of Robotics and Journal of Advanced Robotic Systems and member of the editorial board of Journal of Pattern Recognition, Journal of Mathematical Imaging and Vision, Iberoamerican Journal of Computer and Systems and Journal Of Theoretical And Numerical Approximation. He is editor and author of the following books: Geometric Computing for Perception Action Systems, E. Bayro-Corrochano, Springer Verlag, 2001; Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano and G. Sobczyk (Eds.), Birkahauser 2001; Handbook of Geometric Computing for Pattern Recognition, Computer Vision, Neurocomputing and Robotics, E. Bayro-Corrochano, Springer Verlag, 2005. He has published over 120 refereed journal, book chapters and conference papers.     

Synthesizing Novel Views from Unregistered 2-D Images

Synthesizing the image of a 3-D scene as it would be captured by a camera from an arbitrary viewpoint is a central problem in Computer Graphics. Given a complete 3-D model, it is possible to render the scene from any viewpoint. The construction of models is a tedious task. Here, we propose to bypass the model construction phase altogether, and to generate images of a 3-D scene from any novel viewpoint from prestored images. Unlike methods presented so far, we propose to completely avoid inferring and reasoning in 3-D by using projective invariants. These invariants are derived from corresponding points in the prestored images. The correspondences between features are established off-line in a semi-automated way. It is then possible to generate wireframe animation in real time on a standard computing platform. Well understood texture mapping methods can be applied to the wireframes to realistically render new images from the prestored ones. The method proposed here should allow the integration of computer generated and real imagery for applications such as walkthroughs in realistic virtual environments. We illustrate our approach on synthetic and real indoor and outdoor images.     

基于空间透视不变量的摄象机标定方法

本文给出了一种以空间不变量的数据来计算摄象机外部参数的方法．空间透视不变量是指在几何变换中如投影或改变观察点时保持不变的形状描述．由于它可以得到一个相对于外界来讲独立的物体景物的特征描述，故可以很广泛的应用到计算机视觉等方面．摄象机标定是确定摄象机摄取的２Ｄ图象信息及其３Ｄ实际景物的信息之间的变换关系，它包括内部参数和外部参数两个部分．内部参数表征的是摄象机的内部特征和光学特征参数，包括图象中心（Ｃｘ，Ｃｙ）坐标、图象尺度因子Ｓｘ、有效的焦距长度ｆ和透镜的畸变失真系数Ｋ；外部参数表示的是摄象机的位置和方向在世界坐标中的坐标参数，它包括平移矩阵Ｔ和旋转矩阵Ｒ３×３，一般情况下可以写成一个扩展矩阵［ＲＴ］３×４．本文基于空间透视不变量的计算数据，给出了一种标定摄象机外部参数的方法，实验结果表明该方法具有很强的鲁棒性．     

一种由未定标图象估计三维射影不变量的新算法

本文提出了一种由未定标图象估计三维射不变量的新算法。实验结果表明了本算法的有效性。     

计算射影与排列不变量的新方法

给出了一种表示和计算离散有限点集的射影与排列不变量的简单有效方法.该不变量在计算机视觉、模式识别中有重要应用.首先导出了射影直线上4个点的基于一种对称函数的射影与排列不变量,该不变量等于这4个点的某个原始交比值,具有计算量低,不丢失分辨力等优点.然后根据这个简单的对称函数,结合基本的多项式对称函数,推导出了平面上5个点的两个函数无关的射影与排列不变量,以及空间中6个点的3个函数无关的射影与排列不变量.     

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．     

Viewpoint invariant characteristics of articulated objects

The aim of this paper is to investigate whether it is possible to construct invariants for articulated objects—these are objects that are composed of different rigid parts which are allowed to perform a restricted motion with respect to each other—which use only partial information from each component. To this end, the transformation group describing the deformations of the image of an articulated object due to relative motions of the components, and/or changes in the position of the camera, is identified. It turns out that for a planar articulated object with two rigid components that are allowed to move within the object plane, this transformation group is (anti-isomorphic to) the semi-direct product of the group one would obtain if the object was rigid, and its smallest normal subgroup containing the transformations due to the relative motions of the components. Depending on the projection model, different answers to the question above evoke. For instance, when using perspective projection no other invariants exist than those obtained by considering each part separately as a rigid object, whereas in the pseudo-orthographic case simpler invariants (using only partial information from each component) do exist. Examples of such invariants are given.Postdoctoral Research Fellow of the Belgian National Fund for Scientific Research (N.F.W.O.).     

Model-Based Recognition of 3D Curves From One View

It is well known that there are no geometric invariants of a projection from 3D to 2D. However, given some modeling assumptions about the 3D object, such invariants can be found. The modeling assumptions should be sufficiently strong to enable us to find such invariants, but not stronger than necessary. In this paper we find such modeling assumptions for general 3D curves under affine projection. We show, for example, that if one of the two affine curvatures is known along the 3D curve, the other can be found from the curve's 2D image. We can also derive the point correspondence between the curve and its image. We also deal with point sets and direction vectors.     

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.     

Solving the recognition problem for six lines using the Dixon resultant

The “Six-line Problem” arises in computer vision and in the automated analysis of images. Given a three-dimensional (3D) object, one extracts geometric features (for example six lines) and then, via techniques from algebraic geometry and geometric invariant theory, produces a set of 3D invariants that represents that feature set. Suppose that later an object is encountered in an image (for example, a photograph taken by a camera modeled by standard perspective projection, i.e. a “pinhole” camera), and suppose further that six lines are extracted from the object appearing in the image. The problem is to decide if the object in the image is the original 3D object. To answer this question two-dimensional (2D) invariants are computed from the lines in the image. One can show that conditions for geometric consistency between the 3D object features and the 2D image features can be expressed as a set of polynomial equations in the combined set of two- and three-dimensional invariants. The object in the image is geometrically consistent with the original object if the set of equations has a solution. One well known method to attack such sets of equations is with resultants. Unfortunately, the size and complexity of this problem made it appear overwhelming until recently. This paper will describe a solution obtained using our own variant of the Cayley–Dixon–Kapur–Saxena–Yang resultant. There is reason to believe that the resultant technique we employ here may solve other complex polynomial systems.     

Self-calibration from one circular motion sequence and two images

This paper describes a new method for self-calibration of camera with constant internal parameters under circular motion, using one sequence and two images captured with different camera orientations. Unlike the previous method, in which three circular motion sequences are needed with known motion, the new method computes the rotation angles and the projective reconstructions of the sequence and the images with circular constraint enforced, which is called a circular projective reconstruction, using a factorization-based method. It is then shown that the images of the circular points of each circular projective reconstruction can be readily obtained. Subsequently, the image of the absolute conic and the calibration matrix of the camera can be determined. Experiments on both synthetic and real image sequence are given, showing the accuracy and robustness of the new algorithm.     

Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment

This paper outlines a new geometric parameterization of 2D curves where parameterization is in terms of geometric invariants and parameters that determine intrinsic coordinate systems. This new approach handles two fundamental problems: single-computation alignment, and recognition of 2D shapes under Euclidean or affine transformations. The approach is model-based: every shape is first fitted by a quartic represented by a fourth degree 2D polynomial. Based on the decomposition of this equation into three covariant conics, we are able, in both the Euclidean and the affine cases, to define a unique intrinsic coordinate system for non-singular bounded quartics that incorporates usable alignment information contained in the polynomial representation, a complete set of geometric invariants, and thus an associated canonical form for a quartic. This representation permits shape recognition based on 11 Euclidean invariants, or 8 affine invariants. This is illustrated in experiments with real data sets.     

基于射影变换模型的图像特征点集配准

图像配准是计算机视觉中目标识别的一种基本方法,其目的是在待识别图像中寻找与模型图像的最佳匹配。该文讨论以特征点表示的图像间的配准问题,利用矩阵分解理论推导出射影变换下特征点集配准的闭合公式,给出变换参数估计的算法,并用模拟数据和图像角点检测的真实数据加以验证。实验表明该方法精确、稳定、受噪声影响小。     

摄像机内参数自标定——理论与算法

讨论如何通过摄像机的旋转运动标定其内参数.当摄像机绕其坐标轴旋转时,运用 代数方法给出了计算内参数的公式.该公式在2D投影变换接近理论值P时是非常实用的. 在摄像机绕未知轴旋转时,根据相应的2D投影变换,运用矩阵特征向量理论给出了内参数的 通解公式.通过摄像机绕两个不同未知轴的旋转,摄像机内参数能被唯一地确定.这些结果为 摄像机自标定算法提供了理论基础,同时也给出了实用性算法.模拟实验和真实图像实验的 结果表明本文所给的算法具有一定实用价值.