Measuring linearity of open planar curve segments

In this paper we define a new linearity measure for open planar curve segments. We start with the integral of the squared distances between all the pairs of points belonging to the measured curve segment, and show that, for curves of a fixed length, such an integral reaches its maximum for straight line segments. We exploit this nice property to define a new linearity measure for open curve segments. The new measure ranges over the interval (0, 1], and produces the value 1 if and only if the measured open line is a straight line segment. The new linearity measure is invariant with respect to translations, rotations and scaling transformations. Furthermore, it can be efficiently and simply computed using line moments. Several experimental results are provided in order to illustrate the behaviour of the new measure.     

Triangulating input-constrained planar point sets

We present a linear-time algorithm for computing a triangulation of n points in 2D whose positions are constrained to n disjoint disks of uniform size, after O(nlogn) preprocessing applied to these disks. Our algorithm can be extended to any collection of convex sets of bounded areas and aspect ratios, assuming no point lies in more than some constant number of sets (bounded depth of overlap), and each set contains only a constant number of query points.     

Monochromatic geometric k-factors for bicolored point sets with auxiliary points

Given a bicolored point set S, it is not always possible to construct a monochromatic geometric planar k-factor of S. We consider the problem of finding such a k-factor of S by using auxiliary points. Two types are considered: white points whose position is fixed, and Steiner points which have no fixed position. Our approach provides algorithms for constructing those k-factors, and gives bounds on the number of auxiliary points needed to draw a monochromatic geometric planar k-factor of S.     

On the approximation of convex hulls of finite grid point sets

The outer or inner approximation of the convex hull of a grid point set may be used to speed up the feature extraction process in a shape analysis system. Some properties of these approximations are given.     

A new extension of fuzzy sets using rough sets: R-fuzzy sets

This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some examples are provided.     

多阈值提取平面点云边界点的方法

针对基于切片技术的点云数据重建算法需要提取切片内点云边界点,及现有算法效率低、提取效果不好等问题,提出一种多阈值提取平面点云边界点的算法。通过选取判断点的k个近邻点,计算相邻两点与判断点连线间夹角,由于边界点必存在最大夹角,通过判断最大夹角是否超过设定阈值,从而快速提取边界点。通过对阈值设值分析,不同点云数据的边界提取实验及几种方法间比较,该方法不受点云形状影响,均能较好提取边界点,且优于其他3种算法。结果表明该方法在保证原始点云特征信息的前提下,可较好提取边界点,提高后续点云重建速度与效率。     

油品倾点的测量方法

介绍了根据斯托克斯定律 ,采用自由落体式粘度检测方法 ,分析油品倾点的测量原理、电路和分析过程     

基于深度信念网络的异常点集间的匹配算法

在存在异常值、噪声或缺失点的情况下,损坏的点集中很难区分异常点与正常点,并且点集之间的匹配关系也会受到这些异常点的影响。基于正常点之间存在某种联系以及正常点与异常点之间存在差异的先验知识,提出将点集间匹配关系的估计问题模型化为机器学习的过程。首先,考虑到两个正常点集之间的误差特征,提出了一种基于深度信念网络（DBN）的学习方法来训练具有正常点集的网络;然后,使用训练好的DBN测试损坏的点集,根据设置的误差阈值在网络输出端就可以识别异常值和不匹配的点。对存在噪声和缺失点的2D、3D点集所做的匹配实验中,利用模型预测样本的结果定量评估了点集间的匹配性能,其中匹配的精确率可以达到94%以上。实验结果表明,所提算法可以很好地检测点集中的噪声,即使在数据缺失的情况下,该算法也可以识别几乎所有的匹配点。     

Surface processing methods for point sets using finite elements

We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs on point surfaces. This discretization is based on the local assembly of PDE-specific mass and stiffness matrices, using a local point coupling computation. Point couplings are computed using a local tangent plane construction and a local Delaunay triangulation of point neighborhoods. The definition of tangent planes relies on moment-based computation with proven scaling and stability properties. Once local stiffness matrices are obtained, we are able to easily assemble global matrices and efficiently solve the corresponding linear systems by standard iterative solvers. We demonstrate our framework by several types of PDE-based surface processing applications, such as segmentation, texture synthesis, bump mapping, and geometric fairing.     

一种Vague集向Fuzzy集转化的新方法

基于Vague集理论及投票模型下的解释,介绍了Vague集向Fuzzy集转化的一些方法,并指出了这些方法的不足,在此基础上提出了一种新的转化方法,并证明了该方法的有效性,实例表明该方法比已有的方法更合理。     

软直觉模糊集

直觉模糊集是在模糊集上增加了一个新的属性参数：非隶属度函数,成为描述“非此非彼”的“模糊概念”的工具。为了提高决策的精确性,将软集与直觉模糊集相结合,构造了一种新的数学模型,即直觉模糊软集,对其性质进行了一些讨论。     

一种Vague集转化为Fuzzy集的方法

已存在的Vague集向Fuzzy集转化的多种模型都存在着一定缺陷。论文从另一种角度探讨了Vague集到Fuzzy集的转化,它把模糊隶属度看成是参数k的函数,这样在计算模糊隶属度时,只需给定满足条件的参数k即可;另一方面,在进行模糊信息处理时,会遇到一些不确定因素,如果所得到的模糊隶属度与实际结果有些偏差,可根据参数k的数学性质有目的地调整k,而不必去重新建立方法模型,因此,此方法比已存在方法灵活,适用;文章也对已有的转化方法与所提模型进行了比较,说明了所提模型的正确性及有效性。     

An optimal speed-up parallel algorithm for triangulating simplicial point sets in space

Previous research on developing parallel triangulation algorithms concentrated on triangulating planar point sets.O(log³ n) running time algorithms usingO(n) processors have been developed in Refs. 1 and 2. Atallah and Goodrich⁽³⁾ presented a data structure that can be viewed as a parallel analogue of the sequential plane-sweeping paradigm, which can be used to triangulate a planar point set inO(logn loglogn) time usingO(n) processors. Recently Merks⁽⁴⁾ described an algorithm for triangulating point sets which runs inO(logn) time usingO(n) processors, and is thus optimal. In this paper we develop a parallel algorithm for triangulating simplicial point sets in arbitrary dimensions based on the idea of the sequential algorithm presented in Ref. 5. The algorithm runs inO(log² n) time usingO(n/logn) processors. The algorithm hasO(n logn) as the product of the running time and the number of processors; i.e., an optimal speed-up.     

Level sets and the representation theorem for intuitionistic fuzzy sets

We discuss the concept of a level set of a fuzzy set and the related ideas of the representation theorem and Zadeh’s extension principle. We then describe the extension of these ideas to the case of interval valued fuzzy sets (IVFS). We then recall the formal equivalence between IVFS and intuitionistic fuzzy sets (IFS). This equivalence allows us to naturally extend the concepts of level sets, representation theorem and extension principle from the domain of IVFS to the domain of IFS. What is important to note here is that in the case of these non-standard fuzzy sets, interval valued and intuitionistic, the number of distinct level sets can be greater then the number of distinct membership grades of the fuzzy set being represented. This is a result of the fact that the distinct level sets are generated by the power set of the membership grades. In particular, the minimum of each subset of membership grades provides a level set. In the case of the standard fuzzy sets the minimum of a subset of membership grades results in one of the elements in the subset. In the case of the non-standard fuzzy sets, the membership grades are not linearly ordered and hence taking the minimum of a subset of these can result in a value that was not one of the members of the subset.

Computation of the medial axis of planar domains based on saddle point programming

This paper presents a saddle point programming approach to compute the medial axis (MA). After exploring the saddle point properties of the medial axis transform (MAT), the mathematical programming method is employed to establish the saddle point programming model of the MAT. By using the optimal conditions, i.e., the number and distribution of the tangent points between the boundary and medial axis disk, the one- and two-dimensional saddle point algorithms are developed. In order to determine the branch point, it is better to consider its generating mechanism. Here, we identify the branch point according to the sudden changes of the solutions to the one-dimensional saddle point algorithm. Hence, all the regular and irregular points of MA can be computed by a general algorithm, and it is proved to be efficient and accurate by the numerical examples.     

Soft sets and soft rough sets

In this study, we establish an interesting connection between two mathematical approaches to vagueness: rough sets and soft sets. Soft set theory is utilized, for the first time, to generalize Pawlak’s rough set model. Based on the novel granulation structures called soft approximation spaces, soft rough approximations and soft rough sets are introduced. Basic properties of soft rough approximations are presented and supported by some illustrative examples. We also define new types of soft sets such as full soft sets, intersection complete soft sets and partition soft sets. The notion of soft rough equal relations is proposed and related properties are examined. We also show that Pawlak’s rough set model can be viewed as a special case of the soft rough sets, and these two notions will coincide provided that the underlying soft set in the soft approximation space is a partition soft set. Moreover, an example containing a comparative analysis between rough sets and soft rough sets is given.     

二元截集下的Vague集的分解定理

为了揭示Vague集和经典集之间的联系,在Vague集二元截集的基础上,提出了两个新的Vague集的分解定理。Vague集的分解定理表明Vague集可以由它分解出的截集簇来表示,而这些截集簇都是普通集。最后实例说明了其有效性。     

The three-dimensional fuzzy sets and their cut sets

In this paper, a new kind of L-fuzzy set is introduced which is called the three-dimensional fuzzy set. We first put forward four kinds of cut sets on the three-dimensional fuzzy sets which are defined by the 4-valued fuzzy sets. Then, the definitions of 4-valued order nested sets and 4-valued inverse order nested sets are given. Based on them, the decomposition theorems and representation theorems are obtained. Furthermore, the left interval-valued intuitionistic fuzzy sets and the right interval-valued intuitionistic fuzzy sets are introduced. We show that the lattices constructed by these two special L-fuzzy sets are not equivalent to sublattices of lattice constructed by the interval-valued intuitionistic fuzzy sets. Finally, we show that the three-dimensional fuzzy set is equivalent to the left interval-valued intuitionistic fuzzy set or the right interval-valued intuitionistic fuzzy set.     

犹豫模糊软集

犹豫模糊集是对模糊集的一种推广,它是一类关于域中每个元素所含隶属度的集合,常应用于群决策中,但由于其本身在参数工具上的缺乏使得难于处理不确定数据。为了提高决策的精确性,将软集与犹豫模糊集结合起来,提出犹豫模糊软集的概念,并给出犹豫模糊软集的基本运算法则和性质。