基于小波惟一描述子的多边形逼近方法

提出了一种基于小波惟一描述子的多边形逼近方法。对提取的多边形采用小波描述子,通过比较原始多边形和逼近多边形之间小波惟一描述子偏差的大小,选择一个最佳的逼近结果,以得到一个顶点数递减的近似多边形序列。与现有方法比较,本文方法既考虑了轮廓的整体信息,又考虑了轮廓的局部信息,因而具有更好的鲁棒性。将该方法与面积法及勒让德矩方法进行了比较,实验结果表明,采用该方法得到的逼近结果具有更好的效果及可靠性。     

一种基于面积误差的多边形逼近算法

多边形逼近是提取曲线特征点和简化数据加快图形运算的一个重要方法。文中提出了一种基于面积误差的多边形逼近算法。算法可以在指定的面积误差门限范围内,满足用户对逼近效果的要求。同时这种算法稍加改造可满足指定逼近结果中多边形顶点数目的要求。实验证明这种算法逼近效果好,可以控制面积误差。     

一种基于面积误差的多边形逼近算法

多边形逼近是提取曲线特征点和简化数据加快图形运算的一个重要方法.文中提出了一种基于面积误差的多边形逼近算法.算法可以在指定的面积误差门限范围内,满足用户对逼近效果的要求.同时这种算法稍加改造可满足指定逼近结果中多边形顶点数目的要求.实验证明这种算法逼近效果好,可以控制面积误差.     

一种楔波近似快速算法

为了降低多边形区域上矩计算的复杂度和减少楔波近似的运算时间，提出了一种楔波近似快速新算法。采用任意局部退化模型代替局部恒定退化模型，对比实验结果表明：新算法与现有文献的算法相比，运算速度提高了3个数量级；适用于不同参数的模型，灵活性得到较大提高。     

实现逼近细分模式的统一分解架构

多边形是计算机图形学的一个普遍的建模原语,为渲染多边形而量身度制的图形硬件也已经成为现实。然而,在实现高度分片逼近光滑曲面时,使用多边形建模存在很多问题。这是因为这样的逼近往往含有数十万的多边形,使得设计者难以自由地控制形状。细分则是解决这个难题的新技术,细分曲面的生成也正被广泛地应用于计算机图形研究和几何建模应用,并将成为下一代几何建模原语。本文研究了使用具有分解因子的统一架构生成以逼近模式为例的多边形网格细分曲面建模,并且实现了基于四边形／三角形混合网格的细分。     

基于轮廓匹配算法的非标准件在线检测系统研究

随着机器视觉在标准件检测中的应用,基于机器视觉的非标准件检测研究受到越来越多的关注。对符合非标准件在线检测要求的视觉检测方法进行了研究。利用视觉系统,采集非标准件的图像。通过轮廓提取算法,提取工件的轮廓和相应的计算机辅助设计(CAD)模型的轮廓。计算工件轮廓和相应CAD模型轮廓的图形不变矩。比较图像不变矩的近似程度并判断该工件是否符合造型要求。在验证试验中,随机选取19件冲压模具镶块进行了检测方法的检验并在各工件间进行交叉验证。试验结果表明,检测正确率为100%、平均检测用时为1.4 s/件。以CAD图形为基准进行检测,无需事先收集工件的图像。基于图形不变矩进行相似度匹配,对检测环境要求低,硬件的可配置性强。由于只匹配轮廓信息,检测效率高,能满足非标准件在线检测的多样化应用需求。     

基于归一化投影直方图不变矩的图像特征提取

提出归一化投影直方图和在平移缩放变换下保持不变的归一化投影直方图不变矩概念,由此构造归一化投影直方图不变矩,用于提取图像特征。实验结果证明,与经典不变矩理论相比,该方法能有效反映图像的结构特征,识别细微差异和区分相似图形的能力更强,应用于图像识别时具有较好的鲁棒性。     

基于Legendre正交矩的区域填充方法

提出一种基于Ｌｅｇｅｎｄｒｅ正交矩的区域填充方法。该方法不仅可以达到很好的填充效果,而且能够起到平滑多边形边角的目的,因而对三维医学图像处理和重建具有重要意义。文章首先介绍Ｌｅｇｅｎｄｒｅ正交矩及其逆变换,接着给出Ｌｅｇｅｎｄｒｅ正交矩的快速计算方法,然后描述用Ｌｅｇｅｎｄｒｅ正交矩填充区域的基本原理及方法,最后给出该方法的计算机实验结果,以说明它的有效性。     

Bezier矩及其在人体姿态识别中的应用

首次提出了Bezier矩的定义,并用于人体姿态的识别。该矩具有较好的数学表达形式,充分反映了形状特性。文中给出了Bezier矩的推导,并给出试验结果以及改进的hu不变矩的试验比较结果,试验证明Bezier矩方法优于改进的hu不变矩方法。     

一个适合于特征计算的多边形逼近算法

逼近是加快图形特征计算的一个重要方法．本文提出了一个具有确定性的高效的多边形逼近算法，算法设置了一容错系数以满足用户对逼近的不同要求．算法稍加修改后可以处理开端曲线．作者在人体三围特征识别和语音频谱分析时应用了该算法，速度快、效果好．     

Moment-based methods for polygonal approximation of digitized curves

Object shape representation plays an important role in the area of image processing, pattern recognition and computer vision. In the past two decades, many algorithms have been suggested for creating approximated polygons. In this study, two new polygonal approximation methods based on the geometric moments and the orthogonal moments defined in terms of Legendre polynomials are proposed. The difference between the moments defined by the initial contour and those of the approximated polygon is taken as the objective function. Each algorithm provides various polygonal approximation results with different number of line segments for different application situations. For a given error bound, we can determine the optimal polygon with a minimum number of line segments. The procedures are applied to some digital curves and better results are obtained in comparison with some known methods.     

Polygonal extrusion

A sweeping operation called polygonal extrusion is defined to improve the modeling power of CSG-based modeling. It is assumed that a 2D cross-sectional polygon (sweeping polygon) moves in space while its containing plane is kept orthogonal to the tangent direction of the trajectory curve, a planar polygonal chain having no self-intersections. The objective of the paper is to compute the boundary of the swept volume of the sweeping polygon as a set of polygons (or triangles). The most significant challenge to accomplishing this objective is the problem of trimming the swept volume. To solve the trimming problem, 2D-curve offsetting methods are employed. Two algorithms are presented for polygonal extrusion that are based on different offsetting methods, the Voronoi diagram and PWID offset. The proposed algorithms have been implemented and tested with various examples. Published online: 28 January 2003     

An efficient evolutionary algorithm for accurate polygonal approximation

An optimization problem for polygonal approximation of 2-D shapes is investigated in this paper. The optimization problem for a digital contour of N points with the approximating polygon of K vertices has a search space of C(N, K) instances, i.e., the number of ways of choosing K vertices out of N points. A genetic-algorithm-based method has been proposed for determining the optimal polygons of digital curves, and its performance is better than that of several existing methods for the polygonal approximation problems. This paper proposes an efficient evolutionary algorithm (EEA) with a novel orthogonal array crossover for obtaining the optimal solution to the polygonal approximation problem. It is shown empirically that the proposed EEA outperforms the existing genetic-algorithm-based method under the same cost conditions in terms of the quality of the best solution, average solution, variance of solutions, and the convergence speed, especially in solving large polygonal approximation problems.     

遗传算法在曲线多边形近似中的应用

在平面数字曲线的多边形近似中,为克服顶点的检测只依靠部区域,缺 乏全局信息的弱点,文中把多边形近似问题作了寻找在满足一定的近似误差下使顶点数最少,或者使顶点数和近似误差都尽可能少的最优化问题来处理。     

GEOMPACK — a software package for the generation of meshes using geometric algorithms

We describe the mathematical software package GEOMPACK, which contains standard Fortran 77 routines for the generation of two-dimensional triangular and three-dimensional tetrahedral finite element meshes using efficient geometric algorithms. This package results from our research into mesh generation and geometric algorithms. It contains routines for constructing two- and three-dimensional Delaunay triangulations, decomposing a general polygonal region into simple or convex polygons, constructing the visibility polygon of a simple polygon from a viewpoint, and other geometric algorithms, from which our mesh generation method is built and others can be implemented. Our method generates meshes in polygonal or polyhedral regions specified by their boundary representation and possible interfaces between subregions.     

Geometric algorithm for dominant point extraction from shape contour

In this paper we propose a new algorithm for extracting dominant points from the real contour of a digital shape. A polygonal approximation of the shape can be obtained by the set of dominant points. In the proposed algorithm, in the first step before searching for dominant points, the real contour is made sparse using a geometric concept, named convex deficiency tree. This helps to select a set of candidate points from real contour. In comparison with break points (which are initial points in many algorithms), the set of candidate points is more heuristic and the ratio of them to the all points of the contour is lower. In the second step of the proposed algorithm, the less informative candidate points are removed in an iterative manner. After removing one candidate point, its adjacent positions are searched to find more stable position for its neighbors. The comparative result of the proposed algorithm with others shows its efficiency. The algorithm finds an effective polygonal approximation for digital shapes especially for the real contours, which makes the method more practical.     

A dissimilarity function for geospatial polygons

Similarity plays an important role in many data mining tasks and information retrieval processes. Most of the supervised, semi-supervised, and unsupervised learning algorithms depend on using a dissimilarity function that measures the pair-wise similarity between the objects within the dataset. However, traditionally most of the similarity functions fail to adequately treat all the spatial attributes of the geospatial polygons due to the incomplete quantitative representation of structural and topological information contained within the polygonal datasets. In this paper, we propose a new dissimilarity function known as the polygonal dissimilarity function (PDF) that comprehensively integrates both the spatial and the non-spatial attributes of a polygon to specifically consider the density, distribution, and topological relationships that exist within the polygonal datasets. We represent a polygon as a set of intrinsic spatial attributes, extrinsic spatial attributes, and non-spatial attributes. Using this representation of the polygons, PDF is defined as a weighted function of the distance between two polygons in the different attribute spaces. In order to evaluate our dissimilarity function, we compare and contrast it with other distance functions proposed in the literature that work with both spatial and non-spatial attributes. In addition, we specifically investigate the effectiveness of our dissimilarity function in a clustering application using a partitional clustering technique (e.g. \(k\) -medoids) using two characteristically different sets of data: (a) Irregular geometric shapes determined by natural processes, i.e., watersheds and (b) semi-regular geometric shapes determined by human experts, i.e., counties.     

Gradient algorithms for polygonal approximation of convex contours

The subjects of this paper are descent algorithms to optimally approximate a strictly convex contour with a polygon. This classic geometric problem is relevant in interpolation theory and data compression, and has potential applications in robotic sensor networks. We design gradient descent laws for intuitive performance metrics such as the area of the inner, outer, and “outer minus inner” approximating polygons. The algorithms position the polygon vertices based on simple feedback ideas and on limited nearest-neighbor interaction.