基于类似形原理从单幅透视图识别平面立体

根据透视不变性提出了5个描述多边形形状的拓扑特征和几何特征,以这些特征作为约束条件给出透视投影下类似形的定义。根据类似形的定义提出了识别多边形是类似形的新方法。据此提出了基于类似形原理从单幅透视投影线图识别平面立体的新方法。新定义的类似形能将平面立体中的表面分类。匹配过程限制在类似形内进行,大大减少了搜索范围。用拓扑结构对类似形进行定性分析,对噪音不敏感,用几何特征进行定量分析,则能反应平面立体形状的细微差别。该识别方法不仅能识别不同形状的平面立体目标,而且还可以区分形状相同但大小、比例不同的平面立体目标。实验结果表明该方法是有效的。     

基于类似形的轴测图识别

给出了一种基于多面体的面的类似性来识别多面体线图的新方法.根据仿射不变性提出了在仿射投影下多边形的类似形定义,以区别于各种具有不同特征的面,并将线图中的面分类.匹配过程限制在类似形内进行,从而大大减少了搜索范围.由于新定义的类似形结合了面的拓扑特征和几何特征,因而该算法能够反应多面体形状的细微差别并且对噪音不敏感.不仅能识别不同形状的目标,而且还可以把形状相同但大小、比例不同的目标区分开来.实验结果表明该方法是有效的.     

基于几何约束识别简单平面立体

已有的识别方法对于简单平面立体的识别均不能凑效。依据投影几何中的距离约束和角度约束,给出了三边形和平行四边形的识别方法;提出用属性关系图（ARG）表示平面立体和线图,该描述方法是一种结合表面特征和几何特征的方法。提出一种从单幅线图识别简单平面立体的新方法,该方法在匹配待识别线图与模型结点之前,先用拓扑信息进行候选模型的筛选,大大提高了识别的效率。结合几何特征和拓扑特征表示ARG中的每个结点,不仅能识别不同形状的目标,而且能把拓扑结构相同,但各部分大小、比例不相同的目标区分开。实验结果表明该识别方法是有效的,能够用于识别形状为简单平面立体的工业部件等。     

利用单个透视投影识别空间多边形

本文提出一种利用单个透视投影识别空间多边形的方法.空间多边形的识别依据于在透视投影下的基本不变量:交比.提出了使用交比描绘多边形的形状.该描绘子的基本特点具有在透视投影下观点不变性质,因此这种方法可直接应用到机器人视觉技术中.     

运载火箭控制系统的BIT设计与实现

根据拓扑性质知觉原理,视觉原语是从整体到局部,拓扑感知优先。根据此仿生原理,建立感知目标物的形状拓扑信息的数学模型。首先提取物体三维轮廓信息;将空间图形轮廓降维映射到二维投影平面中进行处理;建立提取空间图形拓扑特征的数学模型。将轮廓拓扑空间同胚映射到(Hausdorf或度量空间或)二维投影平面,保持了拓扑不变性,因此便于分析出拓扑特征,可继续应用拓扑映射原理,分析点集拓扑。最终,拓扑特征与知识库模型相匹配,识别出物体。     

基于形态图表示的三维物体识别算法

基于形态图表示的三维物体识别的基本思路是：首先建立待识别物体的模型库，找出模型集中所有模型物体的形态图和特征视图，并提取以它们的拓扑结构信息和几何信息；其次对物体真实图像作轮廓提取和0边界跟踪，得到二维图像的线架图，同时提取出它的拓扑结构信息和几何信息；最后将物体图像的拓扑结构信息和几何信息与模型库中模型物体的拓扑结构信息和几何信息匹配，从而达到识别的目的。文中提出了在生成线图链码时提取其拓扑结构信息和几何信息的方法，由拓扑结构信息和几何信息构造特征矩阵的方法，以及识别过程中特征矩阵的匹配算法。     

保内部相似性的平面形状混合算法

为了在计算机动画中可以得到较好的图形过渡效果,提出了一保持平面多边形内部相似性的形状混合算法,从而有效地避免了中间多边形发生局部萎缩或者膨胀的现象.此方法从源和目标多边形的同构三角剖分出发,对同构三角网格每一个夹角处表示边角关系的几何量线性插值得到相对应的中间几何量,通过这些中间几何量以及它们与顶点坐标之间的关系来建立线性方程组,给定初始条件后用现成的程序库快速求解来得到中间三角网格(其边界即为中间多边形).还通过引入特征多边形来保持混合多边形的全局视觉特征.该算法计算量小、运行效率高,对形状复杂的多边形仍然可以得到满意的结果,适合于实际应用中实时的要求.     

一种建筑物多边形合并、化简与优化的自动方案

介绍了一种城市地图中基于建筑物矩形几何特征的多边形全自动综合算法。采用Delaunay三角网探测多边形之间的拓扑邻近关系，根据视觉邻近关系聚合多边形。采用基于分割栅格多次扫描的方法对建筑物多边形进行化简以及形状优化。     

基于切平面中值坐标的Laplacian网格变形算法

网格模型变形往往需要保持局部几何细节,Laplacian网格变形算法能够较好地保持局部几何细节特征,但细节特征描述子-Laplacian坐标的计算欠缺精确性.从平面多边形中值坐标的角度出发,对Laplacian坐标进行重新定义,将顶点的一阶邻域投影到顶点处切平面上,根据顶点相对投影点的中值坐标构建的Laplacian坐标能够精确地描述模型的局部几何细节特征,实验验证能够获得较好的编辑效果.     

基于Grassmann流形的仿射不变形状识别

传统的Kendall形状空间理论仅适用于相似变换, 然而成像过程中目标发生的几何变形在更多情形时应该用仿射变换来刻画. 基于Grassmann流形理论, 本文分析了仿射不变形状空间的非线性几何结构, 提出了基于Grassmann流形的仿射不变形状识别算法. 算法首先对训练集中的每类形状分别计算形状均值和方差, 进而在形状均值附近的切空间构建多变量正态分布; 最后,根据测试形状的观测和先验形状模型求解测试形状的最大似然类, 对形状进行贝叶斯分类. MPEG 7形状数据库的实验结果表明, 与传统Kendall形状分析中的基于Procrustean度量识别算法相比, 本文识别算法具有明显优势; 真实场景中的目标识别结果进一步表明, 本文算法对仿射变形有更好的适应能力, 在复杂场景下能以较高的后验概率辨识出目标类别.     

Shape averaging and its applications to industrial design

A computer-assisted technique called shape averaging is presented. Shape averaging produces an abstraction of the typical representation from a set of shapes. Since the averaging is assumed to preserve the characteristics of the original shapes, the result is useful in predicting trends in form or extracting stereotypes from a group of related shapes. The technique can be used to create new forms by blending global features of existing unrelated shapes. The syntactic averaging of shapes consisting of 2-D planar polygons or of 3-D objects represented by planar contours is examined. An algorithm is presented to determine the correspondence between polygons defined by arbitrary numbers of vertices. Algorithms to extract the mean, the median, and the mode from the shapes are also introduced. Potential applications of shape averaging in design are illustrated     

Translation separability of sets of polygons

We consider the problem of separating a set of polygons by a sequence of translations (one such collision-free translation motion for each polygon). If all translations are performed in a common direction the separability problem so obtained has been referred to as the uni-directional separability problem; for different translation directions, the more general multi-directional separability problem arises. The class of such separability problems has been studied previously and arises e.g. in computer graphics and robotics. Existing solutions to the uni-directional problem typically assume the objects to have a certain predetermined shape (e.g., rectangular or convex objects), or to have a direction of separation already available. Here we show how to compute all directions of unidirectional separability for sets of arbitrary simple polygons.The problem of determining whether a set of polygons is multi-directionally separable had been posed by G.T. Toussaint. Here we present an algorithm for solving this problem which, in addition to detecting whether or not the given set is multidirectionally separable, also provides an ordering in which to separate the polygons. In case that the entire set is not multi-directionally separable, the algorithm will find the largest separable subset.Research supported by NSERC under grant No. A9173 and A0392, respectively     

一种面向扩展空间对象的密度聚类算法

提出一个面向扩展空间对象的基于密度的空间聚类算法,对点、线和多边形等扩展空间对象进行聚类。在该算法中,通过空间对象的缓冲区统一计算各对象在其附近空间的密度值,并根据参数区分两类不同的空间聚类应用场景,从而实现对空间对象的分类。实验表明,算法能够较好实现对空间对象分类。     

An intuitive polygon morphing

We present a new algorithm for morphing simple polygons that is inspired by growing forms in nature. While previous algorithms require user-assisted definition of complicated correspondences between the morphing objects, our algorithm defines the correspondence by overlapping the input polygons. Once the morphing of one object into another is defined, very little or no user interaction is necessary to achieve intuitive results. Our algorithm is suitable namely for growth-like morphing. We present the basic algorithm and its three variations. One of them is suitable mainly for convex polygons, the other two are for more complex polygons, such as curved or spiral polygonal forms.     

Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications

The clustering algorithm DBSCAN relies on a density-based notion of clusters and is designed to discover clusters of arbitrary shape as well as to distinguish noise. In this paper, we generalize this algorithm in two important directions. The generalized algorithm—called GDBSCAN—can cluster point objects as well as spatially extended objects according to both, their spatial and their nonspatial attributes. In addition, four applications using 2D points (astronomy), 3D points (biology), 5D points (earth science) and 2D polygons (geography) are presented, demonstrating the applicability of GDBSCAN to real-world problems.     

Interactive real-time motion blur

Motion blurring of fast-moving objects is highly desirable for virtual environments and 3D user interfaces. However, all currently known algorithms for generating motion blur are too slow for inclusion in interactive 3D applications. We introduce a new motion-blur algorithm that works in three dimensions on a per object basis. The algorithm operates in real time even for complex objects consisting of several thousand polygons. While it only approximates true motion blur, the generated results are smooth and visually consistent. We achieve this performance break-through by taking advantage of hardware-assisted rendering of semitransparent polygons, a feature commonly available in today's workstations.     

Relaxation algorithm for shape matching of two-dimensional objects

This paper describes a relaxation algorithm without a parameter for shape matching of partially occluded two-dimensional objects. This technique is based on a relaxation labelling process of Rosenfeld et al. for reducing or eliminating the ambiguity. The shapes are represented by polygonal approximation. The proposed relaxation method is used to find acceptable line segment pairs of polygons.     

Detecting conjugate-point pairs for map alignment between two polygon datasets

When the same objects in different datasets have different positions and shapes, map alignment is necessary to minimise these geometric inconsistencies for successful map integration. In this paper, we propose a method to detect conjugate-point pairs for aligning two polygon datasets by matching the contours of corresponding polygons. This method comprises three processes, including identification of the corresponding polygon pairs, shape approximation with virtual corner-vertices and detection of conjugate-point pairs with our modified vertex-attributed-string-matching (VASM) algorithm. We applied this method to two distinct spatial datasets; a cadastral map and a topographical map of the same urban area. Then, the performance of our method was assessed visually and statistically. Both evaluations showed satisfactory results.