Degeneracy from Twisted Cubic Under Two Views

Fundamental matrix, drawing geometric relationship between two images, plays an important role in 3-dimensional computer vision. Degenerate configurations of the space points and the two camera optical centers affect stability of computation for fundamental matrix. In order to robustly estimate fundamental matrix, it is necessary to study these degenerate configurations. We analyze all the possible degenerate configurations caused by twisted cubic and give the corresponding degenerate rank for each case. Relationships with general degeneracies, the previous ruled quadric degeneracy and the homography degeneracy, are also reported.     

Octree Representation and Its Applications in CAD

In this paper,a survey of octree representation and its applications in CAD is presented.The octree representation may be categorized as pure octree representation and polytree(or extended octree),and the latter is actually a boundary representation decomposed by octree.Linear octree which is a variant of regular octree representation has the advantage of saving memory space.The mapping between Cartesian coordinates and node addresses in linear octree is discussed.Then,algorithms for converting a boundary representation of 3D object into an octree are investiged and major approaches for transforming an octree encoded object are presented.After that,some of the applications of octree representation in CAD are listed,in particular,the applications in solid modeling,in accelerating ray tracing and in generating meshes for FEM.     

基于三维网格物体的鲁棒性盲水印方案

提出了一种基于3D网格物体的鲁棒性盲水印方案。先将3D物体模型转换到仿射不变空间，然后把顶点坐标转换到球面坐标，利用球面坐标来嵌入水印。由于在仿射不变空间下，3D物体模型不受平移、旋转和比例变换的影响，故该水印方案对于此类变化具有很强的鲁棒性。试验结果也证明了这一点，且该水印具有良好的不可见性。     

Least-squares-based fitting of paraboloids

A technique for reconstructing a class of quadric surfaces from 3D data is presented. The technique is driven by a linear least-squares-based fitting mechanism. Previously, such fitting was restricted to recovery of central quadrics; here, extension of that basic mechanism to allow recovery of one commonly-occurring class of non-central quadric, the elliptic paraboloids, is described. The extension uses an indirect solution approach that involves introducing a variable to the basic mechanism that is a function of a quadric surface invariant. Results from fitting real and synthetic data are also exhibited.     

Algebraic Specification of a 3D-Modeler Based on Hypermaps

We present the algebraic specification of a prototype interactive geometric modeler for 3D objects, whose topologies are represented by 3-dimensional generalized maps. After a reminder of some topological models, particularly maps and extensions, we begin with the more general frame of n-dimensional hypermaps. We specify algebraically a hierarchy of operations on hypermaps and generalized maps, which are embedded in a 3-dimensional Euclidean space. We make precise the modeling area and give the main functionalities of the modeler. We detail high-level operations on 3D objects, and some technical features of this software. Some constructions are explained using pictures. We show that hypermaps and algebraic specification constitute an efficient formal frame for developing large pieces of software in the area of boundary representation.     

Object representation and recognition in shape spaces

In this paper, we describe a shape space based approach for invariant object representation and recognition. In this approach, an object and all its similarity transformed versions are identified with a single point in a high-dimensional manifold called the shape space. Object recognition is achieved by measuring the geodesic distance between an observed object and a model in the shape space. This approach produced promising results in 2D object recognition experiments: it is invariant to similarity transformations and is relatively insensitive to noise and occlusion. Potentially, it can also be used for 3D object recognition.     

A robust method to recognize critical configuration for camera calibration

When space points and camera optical center lie on a twisted cubic, no matter how many pairs there are used from the space points to their image points, camera parameters cannot be determined uniquely. This configuration is critical for camera calibration. We set up invariant relationship between six space points and their image points for the critical configuration. Then based on the relationship, an algorithm to recognize the critical configuration of at least six pairs of space and image points is proposed by using a constructed criterion function, where no any explicit computation on camera projective matrix or optical center is needed. Experiments show the efficiency of the proposed method.     

Generating high-quality discrete LOD meshes for 3D computer games in linear time

The real-time interactive 3D multimedia applications such as 3D computer games and virtual reality (VR) have become prominent multimedia applications in recent years. In these applications, both visual fidelity and degree of interactivity are usually crucial to the success or failure of employment. Although the visual fidelity can be increased using more polygons for representing an object, it takes a higher rendering cost and adversely affects the rendering efficiency. To balance between the visual quality and the rendering efficiency, a set of level-of-detail (LOD) meshes has to be generated in advance. In this paper, we propose a highly efficient polygonal mesh simplification algorithm that is capable of generating a set of high-quality discrete LOD meshes in linear run time. The new algorithm adopts memoryless vertex quadric computation, and suggests the use of constant size replacement selection min-heap, pipelined simplification, two-stage optimization, and a new hole-filling scheme, which enable it to generate very high-quality LOD meshes using relatively small amount of main memory space in linear runtime.     

斜对称面检测在二次曲面体中的应用

对称是三维重建中的一个十分重要的约束条件,真实的对称在全局观察视角下变成了斜对称。斜对称检测可以大大降低三维重建的复杂度。本文提出了二次曲面体的斜对称面检测方法,该方法首先将SUGIMOTO等提出的斜对称检测方法扩展到任意二次曲线,然后将二次曲面体进行面域提取,对提取的各个面域运用前面的斜对称检测方法进行斜对称轴检测,从所有检测到的对称轴中提取出对称面多边形的边界,采用极左邻边搜索法构造对称面多边形即斜对称面同实体的相交面。由于算法对于物体的摆放位置没有要求,因而扩展了实体的覆盖域。     

曲面实体造型中曲线和曲面交点的求解

求交是曲面实体造型系统中影响拼合算法效率和稳定性的重要因素，而求交算法又是和曲面的几何表示密切相关的。ＮＵＲＢＳ虽然能统一表示所有曲面，但却给二次曲面的求交带来了不必要的复杂性。二次曲面经常在机械零件的设计中被用来描述轴、孔、槽等几何特征，因此它们的求交算法应具有高精度、高效率和高稳定性。为此，对一种实用的二次曲面表示方法——几何法进行了深入研究后，给出了构成二次曲面轮廓的几种二次曲线和空间四次曲线与二次曲面交点的求法。     

Representing planetary terrains into a virtual reality environment for space exploration

3D terrain representation has been widely exploited in a number of applications to depict terrestrial surface simulations. Nevertheless, it could also be successfully employed by aerospace industry to represent planetary soils, such as the Lunar and the Martian ones. In this paper, we are discussing the results of an application developed at Thales Alenia Space—Italy and aiming at building a detailed 3D model of such terrains for space exploration purposes.     

Local observability of invariant dynamics on compact Lie groups with square integrable output map functions

In this work, we give a sufficient algebraic condition for the local observability problem of invariant control systems on compact Lie groups such that the output map is not differentiable. In particular, the usual techniques involving Lie derivatives do not work. Our approach comes from the representation theory. We use the regular representation to construct a bilinear system on the Hilbert space of the square integrable function defined on the group to a finite-dimensional vector space. If this bilinear system is observable, then we prove that the invariant control system is locally observable.     

A Zero-Crossing-Based Optimal Three-Dimensional Edge Detector

Three-dimensional (3D) image processing and interpretation is very important in many medical and industrial applications. Detection of 3D boundaries is an essential step in most of the 3D image analysis tasks. In this paper a new computational approach to 3D edge detection is proposed. Optimality criteria such as signal-to-noise ratio, localization, and spurious response for zero-crossing-based, rotationally invariant 3D step edge detectors are derived. An optimal 3D step edge detector is obtained by optimizing a penalty function which combines all the three criteria. The closed form solution to the optimization problem yields the optimal detector. The detector is the Laplacian of a rotationally invariant function, which has a finite spatial support. The behavior of the proposed detector is theoretically analyzed and compared to that of the 3D Laplacian of Gaussian detector. Experimental results with some synthetic and real images are presented.     

Nonsplitting Macro Patches for Implicit Cubic Spline Surfaces

Macro patches are important for generating quadric or cubic implicit spline surfaces from the input of a polyhedron. All existing macro patches split the triangular facets of the polyhedron; this paper presents cubic nonsplitting macro patches (NMP) that do not split these facets. The NMP's are based on a necessary and sufficient condition for nonsplitting constructions of implicit cubic spline surfaces. This condition can be satisfied for most practical applications, so the NMP's lead to an efficient and powerful spline surface scheme using implicit cubics. The free parameters in an NMP are set using a new technique for excluding topological anomalies such as extraneous sheets, splits, unwanted holes, self-intersections, and unwanted handles. Each cubic patch obtained by this technique best approximates, in a least-squares sense, a quadric patch from a single algebraic component of a monotone polynomial derived from the input data.     

基于八叉树结构的三维体素模型检索

随着VR/AR技术发展以及三维模型的广泛应用,实现三维检索具有越来越重要的现实意义.基于模型的检索较好地保留了模型的空间信息和几何特征,其不仅包含模型的表面信息而且还包含模型的内部属性.但是,基于模型的检索往往存在着高存储、高计算的问题.为了解决该问题,本文研究了三维模型预处理及三维模型表示的方法,提出了一种基于八叉树结构的三维体素模型检索方法,即将模型进行体素化处理后提取模型的粗粒度特征和细粒度特征,将两种特征进行融合用八叉树形式表达特征,输入到卷积神经网络中进行训练,最终通过特征的欧氏距离度量实现模型的检索.运用八叉树特征表示法,可以有效地节省体素化存储过程的空间占用量,而且也能保留原始三维网格模型的细节信息.同时考虑到计算性能,本文还在模型体素化的过程中做出一定的改进,通过仅对模型外表面进行体素化,实现了对体素化过程以及数据存储和卷积神经网络训练的优化,大大降低了时间开销.实验中将三维体素模型特征存储在八叉树结构中作为卷积神经网络的输入,结合SOFTMAX代价函数,通过大量的模型训练数据,对该卷积神经网络模型进行训练.与其他同类算法对比,证明了该算法在三维模型检索中的优越性.     

The twisted cubic curve: a computer-aided geometric design approach

The twisted cubic curve has the attraction of combining both commonly used curve definitions, the conic section and the parametric cubic, in a single form. A definition of the twisted cubic is developed in terms of geometric ‘handles’ convenient for CAD and independent of parametrization, analogous to a well-known definition of conics. Conditions for the occurrence of asymptotes are investigated and shown to be considerably more complex than those for conics. Several more controllable subsets of the general curve are described. The paper concludes that use of the full generality of the twisted cubic is in most cases unjustified.     

一种非定标图像高精度三维重建算法

由非定标图像重建三维场景有着广泛的应用。给出了一种非定标多视图像三维重建算法。该算法主要基于因子分解和光束法平差技术。首先用因子分解方法得到射影空间下相机投影矩阵和物点坐标,以旋转矩阵的正交性以及对偶绝对二次曲面秩为3为约束,将射影空间升级到欧式空间,最后用光束法平差进行优化。该方法可同时获得相机的内外参数、畸变系数和场景的三维坐标。仿真实验表明,在1000 mm×1000 mm×400mm的范围内,当像点检测误差在0-1pixel和0-2pixel内,所重建三维点的误差分别为0.1530 mm和0.6712 mm。在500 mm×500 m×200 mm下,真实实验重构三维点的误差在0.3 mm以内。所提出的算法稳定可靠,可对实际工程进行指导。     

二维形状的透视不变性认别

在计算机视觉中,二维形状的识别有着十分重要的意义.为了实现二维形状的透视投影 不变性识别,本文推导出了一种共面二次曲线对的透视投影不变量,提出了一种基于椭圆的平 面曲线的透视不变性表示方法,并且给出了用该不变量和不变性表示方法实现二维形状识别 的算法.实验结果证实了该算法的有效性.     

Solid reconstruction using recognition of quadric surfaces from orthographic views

The reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthographic views, and quadric surface features (QSFs) are defined by special basic patterns of LRG as well as aggregation rules. By hint-based pattern matching in the LRGs of three orthographic views in an order of priority, the corresponding QSFs are recognized, and the geometry and topology of quadric surfaces are recovered simultaneously. This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. Several examples are provided.