Identical Projective Geometric Properties of Central Catadioptric Line Images and Sphere Images with Applications to Calibration

Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. Lines and spheres in space are all projected into conics in the central catadioptric image planes, and such conics are called line images and sphere images, respectively. We discovered that there exists an imaginary conic in the central catadioptric image planes, defined as the modified image of the absolute conic (MIAC), and by utilizing the MIAC, the novel identical projective geometric properties of line images and sphere images may be exploited: Each line image or each sphere image is double-contact with the MIAC, which is an analogy of the discovery in pinhole camera that the image of the absolute conic (IAC) is double-contact with sphere images. Note that the IAC also exists in the central catadioptric image plane, but it does not have the double-contact properties with line images or sphere images. This is the main reason to propose the MIAC. From these geometric properties with the MIAC, two linear calibration methods for central catadioptric cameras using sphere images as well as using line images are proposed in the same framework. Note that there are many linear approaches to central catadioptric camera calibration using line images. It seems that to use the properties that line images are tangent to the MIAC only leads to an alternative geometric construction for calibration. However, for sphere images, there are only some nonlinear calibration methods in literature. Therefore, to propose linear methods for sphere images may be the main contribution of this paper. Our new algorithms have been tested in extensive experiments with respect to noise sensitivity.     

Range identification for nonlinear parameterizable paracatadioptric systems

In this paper, a new range identification technique for a calibrated paracatadioptric system mounted on a moving platform is developed to recover the range information and the three-dimensional (3D) Euclidean coordinates of a static object feature. The position of the moving platform is assumed to be measurable. To identify the unknown range, first, a function of the projected pixel coordinates is related to the unknown 3D Euclidean coordinates of an object feature. This function is nonlinearly parameterized (i.e., the unknown parameters appear nonlinearly in the parameterized model). An adaptive estimator based on a min-max algorithm is then designed to estimate the unknown 3D Euclidean coordinates of an object feature relative to a fixed reference frame which facilitates the identification of range. A Lyapunov-type stability analysis is used to show that the developed estimator provides an estimation of the unknown parameters within a desired precision. Numerical simulation results are presented to illustrate the effectiveness of the proposed range estimation technique.     

Weaving patterns of lines and line segments in space

Aweaving W is a simple arrangement of lines (or line segments) in the plane together with a binary relation specifying which line is above the other. A system of lines (or line segments) in 3-space is called arealization ofW, if its projection into the plane isW and the above-below relations between the lines respect the specifications. Two weavings are equivalent if the underlying arrangements of lines are combinatorially equivalent and the above-below relations are the same. An equivalence class of weavings is said to be aweaving pattern. A weaving pattern isrealizable if at least one element of the equivalence class has a three-dimensional realization. A weaving (pattern)W is calledperfect if, along each line (line segment) ofW, the lines intersecting it are alternately above and below. We prove that (i) a perfect weaving pattern ofn lines is realizable if and only ifn 3, (ii) a perfect m byn weaving pattern of line segments (in a grid-like fashion) is realizable if and only if min(m, n) 3, (iii) ifn is sufficiently large, then almost all weaving patterns ofn lines are nonrealizable.Jànos Pach has been supported in part by Hungarian NFSR Grant 1812, NSF Grant CCR-8901484, and the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), a National Science Foundation Science and Technology Center, under NSF Grant STC88-09648. Richard Pollack has been supported in part by NSA Grant MDA904-89-H-2030, NSF Grants DMS-85-01947 and CCR-8901484, and DIMACS. Emo Welzl has been supported in part by the ESPRIT II Basic Research Actions Program of the EC under Contract No. 3075 (project ALCOM) and DIMACS.     

Designing parallel assembly lines

In this paper, alternative assembly line design strategies for a single product are discussed. The problem occurs when the production volume is substantially high and there are more operators needed than the number of assembly operations. The objective is to determine the number of assembly lines with minimum total manpower. It is allowed to have multiple assembly lines with identical configuration. A 3-phase methodology is proposed; 1) assembly line balancing, 2) determining parallel stations, 3) determining parallel lines. Later, the proposed procedure is illustrated with a numerical example.     

Differential geometry properties of lines of curvature of parametric surfaces and their visualization

We present algorithms for computing the differential geometry properties of lines of curvature of parametric surfaces. We derive a unit tangent vector, curvature vector, binormal vector, torsion, and algorithms to evaluate their higher-order derivatives of lines of curvature of parametric surfaces. Among these quantities, it is shown that the curvature and its first derivative of the lines of curvature lend a hand for the formation of curved plates in shipbuilding. We also visualize the twist of lines of curvature, which enables us to observe how much the osculating plane of the line of curvature turns about the tangent vector.     

Corisco: Robust edgel-based orientation estimation for generic camera models

The estimation of camera orientation from image lines using the anthropic environment restriction is a well-known problem, but traditional methods to solve it depend on line extraction, a relatively complex procedure that is also incompatible with distorted images. We propose Corisco, a monocular orientation estimation method based on edgels instead of lines. Edgels are points sampled from image edges with their tangential directions, extracted in Corisco using a grid mask. The estimation aligns the measured edgel directions with the predicted directions calculated from the orientation, using a known camera model. Corisco uses the M-estimation technique to define an objective function that is optimized by two algorithms in sequence: RANSAC, which gives robustness and flexibility to Corisco, and FilterSQP, which performs a continuous optimization to refine the initial estimate, using closed formulas for the function derivatives. Corisco is the first edgel-based method able to analyze images with any camera model, and it also allows for a compromise between speed and accuracy, so that its performance can be tuned according to the application requirements. Our experiments demonstrate the effectiveness of Corisco with various camera models, and its performance surpasses similar edgel-based methods. The accuracy displayed a mean error below 2° for execution times above 8 s in a conventional computer, and above 3° for less than 2 s.     

结构光视觉传感器现场标定几何法研究

与基于交比不变性求解特征点坐标来标定激光平面的方法不同,本文提出了一种可适用于未知环境的线结构光三维视觉传感器现场标定的新方法,该方法只需简单几何知识,就可直接利用几何方法实现快速标定。通过拍摄一个与线结构光相交并以不同姿态随机自由移动的平面靶标的图像(至少三幅),就可同时实现三维视觉传感器CCD和激光平面的快速标定。该方法方便,快捷,简单,可实现自动化,标定精度高。实验结果证明了该方法的方便和有效性。     

A new algorithm to extract the lines and edges through orthogonal projections

The present paper provides a generalization to the approach proposed by Frei and Chen to masks of any even dimension for line and edge detection in digital images. In the work presented in ICCS2004 we proposed the generalization to masks of odd dimension. We are completed with masks of even dimension and therefore the decomposition of Euclidean space in direct sum of the three subspaces: edge, line and uniform. We propose in this paper, first, a new algorithm based on the use of the norm projection vector as the best guarantee against the angle of projection since its use is independent of the chosen convolution masks. This will reduce the computational time of operations. Second, we designed the multiplicative factor of the standard deviation, f, allows us to modify the threshold value to decide which candidate pixel is an edge or line. Because the calculation of the average of all standard deviations implies a high computational time, we propose a new logarithmic model that acts automatically depending only on the size of the image and the size of the mask used. It is completed with the application of the designed algorithm to the synthetic and real image.     

Fitting straight lines to point patterns

In many types of point patterns, linear features are of greatest interest. A very general algorithm is presented here which determines non-overlapping clusters of points which have large linearity. Given a set of points, the algorithm successively merges pairs of clusters or of points, encompassing in the merging criterion both contiguity and linearity. The algorithm is a generalization of the widely-used Ward's minimum variance hierarchical clustering method. The application of this algorithm is illustrated using examples from the literature in biometrics and in character recognition.     

基于立体折反射全向成像的柱面全景深度估算

针对立体视觉原理的新型立体折反射全向成像系统结构设计和面向立体柱面全景像对的局域灰度相关对应点快速匹配算法,从捕获的全向市体影像中提取有效深度信息,用于辅助全向视频分析处理中的对象检测和跟踪.采用单相机和两个不同参数的抛物面型反射镜构造了一种共轴结构的折反射全向立体成像装置,捕获的存在一定视差的原始全向立体像对被投影展开为立体柱面全景像对,而后通过特定对应点匹配算法提取稠密的深度信息.对应点匹配算法采用局部区域灰度相关的算了,并充分利用了双向匹配和柱面全景的外极线约束来提高匹配的速度和准确度.仿真实验有效恢复了场景深度信息,证明了整套装置结构设计及深度估计方法的有效性.     

Extracting lines of curvature from noisy point clouds

We present a robust framework for extracting lines of curvature from point clouds. First, we show a novel approach to denoising the input point cloud using robust statistical estimates of surface normal and curvature which automatically rejects outliers and corrects points by energy minimization. Then the lines of curvature are constructed on the point cloud with controllable density. Our approach is applicable to surfaces of arbitrary genus, with or without boundaries, and is statistically robust to noise and outliers while preserving sharp surface features. We show our approach to be effective over a range of synthetic and real-world input datasets with varying amounts of noise and outliers. The extraction of curvature information can benefit many applications in CAD, computer vision and graphics for point cloud shape analysis, recognition and segmentation. Here, we show the possibility of using the lines of curvature for feature-preserving mesh construction directly from noisy point clouds.     

一种基于切线的曲线直线拟合的矢量化算法

提出一种在位图矢量化系统中用直线拟合曲线的新算法.算法利用曲线的一系列切线寻找曲线上与切线距离为门限距离的点作为直线拟合的特征点.算法包括两个步骤:尖点提取和直线逼近.第一步将曲线中具有局部曲率极大值的尖点提取出来,并利用尖点将曲线分割为多个曲线片断;第二步利用曲线片断的切线系找出特征点,再分别用直线依次将邻近两特征点相连,即完成拟合过程.经实验表明,算法既能准确提取边界形状的特征关键点,又能有效地实现对曲线的直线拟合.     

Algebraic and geometric invariant of a pair of non-coplanar conics in space

It is easy to construct the geometric invariant of a pair of non-coplanar conics in space. It is the crossratio of the 4 intersection points of the two conics with the common line of the two conic planes. In this paper, the algebraic invariant of a pair of non-coplanar conics is derived from the invariant algebra of a pair of quaternary quadratic forms by using the dual representation of space conics. Then, the relationship between the algebraic invariant and the geometric invariant is established.     

Another test of sensor lines on control panels

In this experiment all panels had four circular displays arranged in a square on a vertical surface and four controls aligned vertically to the right of the displays. Two panels had linkages between controls and displays which earlier research had shown to be compatible, the other two had incompatible linkages. Each of these four panels was tested with and without sensor lines showing the linkages between controls and displays. Ninety-six subjects each made 128 trials on one of the eight panels. A subject's task was to respond as quickly as possible by pushing the correct control to extinguish a light when it appeared in one of the displays. Sensor lines had no effect on performance with the compatible panels but impaired performance on the incompatible panels. The results also confirm again the potency of the compatibility principle: responses were faster and fewer errors were made when using the compatible panels.     

Visually guided ranging from observations of points, lines and curves via an identifier based nonlinear observer

In this paper we consider the problem of estimating the range information of features on an affine plane in by observing its image with the aid of a CCD camera, wherein we assume that the camera is undergoing a known motion. The features considered are points, lines and planar curves located on planar surfaces of static objects. The dynamics of the moving projections of the features on the image plane have been described as a suitable differential equation on an appropriate feature space. This dynamics is used to estimate feature parameters from which the range information is readily available. In this paper the proposed identification has been carried out via a newly introduced identifier based observer. Performance of the observer has been studied via simulation.     

Extraction of lines and regions from grey tone line drawing images

An algorithm is described for extracting lines from grey level digitizations of industrial drawings. The algorithm is robust, noniterative, sequential and includes procedures for differentiating shaded areas from lines. Examples are given for complex regions of a typical mechanical drawing.     

Image-based memory for robot navigation using properties of omnidirectional images

This paper proposes a new technique for vision-based robot navigation. The basic framework is to localise the robot by comparing images taken at its current location with reference images stored in its memory. In this work, the only sensor mounted on the robot is an omnidirectional camera. The Fourier components of the omnidirectional image provide a signature for the views acquired by the robot and can be used to simplify the solution to the robot navigation problem. The proposed system can calculate the robot position with variable accuracy (‘hierarchical localisation’) saving computational time when the robot does not need a precise localisation (e.g. when it is travelling through a clear space). In addition, the system is able to self-organise its visual memory of the environment. The self-organisation of visual memory is essential to realise a fully autonomous robot that is able to navigate in an unexplored environment. Experimental evidence of the robustness of this system is given in unmodified office environments.     

论中国画中的线条魅力

人类有相互沟通的语言方式,同样人与艺术也拥有相应的沟通媒介,中国画艺术的艺术表达媒介便是画中线条,中国画中的线条不仅是艺术表达的方式更是整个艺术作品的灵魂。在古代名画中的线条绘制过程极其灵活,之所以被很多艺术名家所采用就是因为在灵活多变的前提之下的线条魅力能够吸引众人的眼球,向读者传达丰富的艺术内涵。文章就中国画中的线条进行深度解析。     

Determination of 3-D object orientation from projections

A method is presented for determination of the orientation in 3-space of 3-D objects without point correspondence information and without requiring only differential motion between images. Either 2-D projections or 3-D surface coordinate information may be used.     

Correspondence of 2-D projections by bipartite matching

A method is presented to determine the correspondence between 2-D projections of a 3-D scene. The problem is formulated as a maximum cardinality with minimum weight matching of a bipartite graph and is solved by a network flow algorithm.