Fuzzy topological relations between fuzzy spatial objects

Fuzziness is an internal property of spatial objects.How to model fuzziness of a spatial object is a main task of next generation GIS.This paper proposes basic fuzzy spatial object types based on fuzzy topology.These object types are the natural extension of current nonfuzzy spatial object types.A fuzzy cell complex structure is defined for modeling fuzzy regions,lines and points.Furthermore,fuzzy topological relations between these fuzzy spatial objects are formalized based on the 9intersection approach.This model can be implemented for GIS applications due to its scientific theory basis.     

Extended model of topological relations between spatial objects in geographic information systems

This paper presents an extended model for describing topological relations between two sets (objects) in geographic information systems (GIS). First, based on the definition of the topological relations between two objects, we uncover a sequence of topological relations between two convex sets.Second, an extended model for topological relations between two sets is proposed based on the new definition. The topological relations between two convex sets are expressed as a sequence of 4 × 4 matrices, which are the topological properties of A^o ∩ B^o, A^o\B, B^o\A, ∂A ∩ ∂B. The model is also extended for handling the properties of the topological relations between two non-convex sets, where the factor of first fundamental group is added to A ∪ B to handle these complex relations.The results show that the number of topological relations between the two sets is not as simple as finite but infinite and can be approximated by a sequence of matrices.     

移动目标空间拓扑关系的度量描述

针对传统9交模型对移动目标空间拓扑关系表达及量化描述的不足,基于格网化思想,提出了度量参数量化描述的方法。首先对移动目标和参考目标进行格网化,划分为固定大小的格网阵列;然后利用9交模型确定空间目标间拓扑关系的形式化描述;最后引入内部分量、边界分量、外部分量3种度量参数对移动目标空间拓扑关系进行度量化描述。试验证明,该方法计算简单、直观,能更加有效地度量移动目标间的拓扑关系。     

Definitions of natural-language spatial relations: Combining topology and directions

Because SQL for querying data from spatial databases is ineffective, the query based on natural or visual language becomes an attractive research field gradually. However, how to define and represent natural languages related to spatial data are still gigantic problems. Because existing models of direction relations can't describe by use of some common concepts. First of all, detailed direction relations are proposed to describe the directions related to the interior of spatial objects, such as “east part of a region”, “east boundary of a region”, and so on. Secondly, by integrating the detailed directions with exterior direction relations and topological relations, several NLSRs are defined, such as “a road goes across the east part of a lake”, “a river goes along the east boundary of a province”, etc. Finally, based on the NLSRs abovementioned, a natural spatial query language (NSQL) is formed to retrieve data from spatial databases.     

Definitions of Natural-Language Spatial Relations： Combining Topology and Directions

Introduction Inmanyapplications(CADandgeographical informationsystem,GIS),dataaremanagedby spatialdatabases,whichstorepoint,line,region objectsandspatialrelationsbetweenthem.Spa tialrelations(topologicalrelations,directionre lationsandapproximatedistancer…     

Dealing with spatial relations for spatial objects with randomness in GIS

To design retrieval algorithm of spatial relations for spatial objects with randomness in GIS, this paper builds up the membership functions based on set theory idea, used for determination of topological spatial relations between random objects, such as between point and point, point and line or polygon, which provides theoretical basis for retrieving spatial relations between certain and random objects. Finally, this paper interprets detailed methods and steps of realizing them by means of some simple examples under the GIS's environment.     

DEALING WITH SPATIAL RELATIONS FOR SPATIAL OBJECTS WITH RANDOMNESS IN GIS

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An Approach to Reasoning Topological Relations Between Areal Objects Under Randomness

This paper describes the geometric and statistical properties of areal object under randomness. In order to describe formally such a uncertain topological relation, a new formal model (i. e. 4ID model) is proposed. On the basis of this, the effects of positional uncertainty on topological relations between areal objects are investigated in detail. Some possibility functions for the determination of relations are constructed based on the assumption that randomness of point location complies with a normal distribution, and the concept of uncertain sets of topological relations under randomness is introduced.     

拓扑关系和方向关系的统一表达模型

统一表达空间关系中的拓扑关系和方向关系是非常有必要的。本文首先对已有的方向模型进行分析和比较,提出了一种方向模型,即采用锥形的方法将空间参照对象的内部、边界和外部分别划分出9个方向区域,描述空间目标对象与这些方向区域的交集的情况,然后结合这种方向模型和九交模型,进而提出了一种能统一表达拓扑关系和方向关系的形式化模型。     

Quantitative relations between spatial similarity degree and map scale change of individual linear objects in multi-scale map spaces

Quantitative relations between spatial similarity degree and map scale change in multi-scale map spaces play important roles in map generalization and construction of spatial data infrastructure. Nevertheless, no achievements have been made regarding this issue. To fill the gap, this paper firstly proposes a model for calculating spatial similarity degrees between an individual linear object at one scale and its generalized counterpart at the other scale. Then psychological experiments are designed to validate the new model, taking four different individual linear objects at five different scales as test samples. The experiments have shown that spatial similarity degrees calculated by the new model can be accepted by a majority of the subjects. After this, it constructs a formula that can calculate spatial similarity degree using map scale change (and vice versa) for individual linear objects in multi-scale map spaces by the curve fitting method using the point data from the psychological experiments. Both the formula and the model can calculate quantitative relations between spatial similarity degree and map scale change of individual linear objects in multi-scale map spaces, which facilitates automation of map generalization algorithms for linear features.     

多尺度表达中空间拓扑关系等价性评价模型

本文主要讨论不同尺度下地理目标之间拓扑关系的等价性问题。根据人类认知习惯,得出从大比例尺地理空间中拓扑关系抽象为小比例尺空间中拓扑关系应当遵循的基本规则,并利用模糊函数将这些规则定量化;在此基础上,得到评价地理空间场景中多个空间目标之间拓扑关系在不同尺度下是否等价的综合评价模型。该模型可以用于检验和维护空间数据质量、为地图自动综合提供空间关系处理和评价方法的参考。     

A study of supervised classification accuracy in fuzzy topological methods

The multiple classifier system (MCS) is an effective automatic classification method, useful in connection with remote sensing analysis techniques. Combining MSC with induced fuzzy topology enables a decomposition of image classes. This fuzzy topological MCS then provides a new and improved approach to classification. The basic classification methods discussed in this paper include maximum likelihood classification (MLC), minimum distance classification (MIND) and Mahalanobis distance classification (MAH).     

在空间抽象中线状目标间拓扑关系的等价转换

拓扑关系在抽象过程中的等价转换是维护多尺度空间关系一致性的基础。本文以空间拓扑关系组合推理所描述的线状目标之间的拓扑关系为例,采用成分抽象的等价转换方法,研究了线之间拓扑关系等价转换的原则,并绘出了相应的等价转换图。     

Topological relations between spherical spatial regions with holes

ABSTRACT

There is growing interest in globally modelling the entire planet. Although topological relations between spherical simple regions and topological relations between regions with holes in the plane have been investigated, few studies have focused on the topological relations between spherical spatial regions with holes. The 16-intersection model (16IM) is proposed to describe the topological relations between spatial regions with holes. A total of 25 negative conditions are proposed to eliminate the impossible topological relations between spherical spatial regions with holes. The results show that (1) 3 disjoint relations, 3 meet relations, 66 overlap relations, 7 cover relations, 3 contain relations, 1 equal relation, 7 coveredBy relations, 3 inside relations, 1 attach relation, 52 entwined relations, and 28 embrace relations can be distinguished by the 16IM and that (2) the formalisms of attach, entwined, and embrace relations between the spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on the simplified 16IM are different, whereas the formalisms of other types of relations between spherical spatial regions without holes based on the 9IM and that between the spherical spatial regions with holes based on a simplified 16IM are the same.     

基于面状要素拓扑关系的数据匹配技术研究

数据匹配技术是空间数据集成与融合中的关键技术。本文根据9交模型中的面状拓扑关系的描述,对面积叠置率进行了几何度量上的定义,提出了基于面积迭置率的数据匹配思路,实现了面状要素一对一、多对一、多对多的数据匹配。最后,以面状目标为研究对象,以城市居民地的大比例尺数据为例,对基于面积迭置率的面状要素数据匹配算法进行了试验与分析。     

3D GIS中空间对象的存储与快速查询

空间对象的存储和快速查询是三维地理信息系统研究的基本问题。本文采用面向对象的方法将三维空间对象抽象为点、线、面、体四类,点对象用一个坐标点(x,y,z)来表示,线对象用一组首尾相接的线段表示,面对象与体对象用三角网表示,然后采用SQL Server 2005来组织存储数据。为了提高空间数据库的检索速度,作者编程实现了线性八叉树空间索引,应用程序采用目前比较流行的ADO.net技术来访问数据库。     

三个目标间空间方位关系表达模型及其GIS应用

空间方位是一类重要的空间关系,它不同于目前研究较多的方向关系。空间方位关系描述的是三个目标间的空间关系,它的理论基础是基于射影几何中的三点共线不变性。本文首先阐述了空间方位的基本定义、表达基础以及它与拓扑关系、方向关系的区别。然后,重点回顾了6种较为有代表性的方位关系描述模型,指出了这些模型的适用性,并对这些模型进行了比较分析。最后,简要地分析了空间方位关系在GIS中的应用前景以及有待进一步研究的若干问题。     

基于OpenMP的矢量空间数据并行拓扑算法设计与实现

高性能并行GIS逐渐成为GIS发展的新方向。矢量数据的复杂性使得一些并行GIS算法难以实现,从而无法满足并行GIS的发展要求。文中针对GIS算法中的拓扑算法,借助OpenMP编程模型,通过消除并行拓扑处理过程中的数据依赖,在单机多核的环境下设计并实现了矢量空间数据并行拓扑算法。通过实验对比串行拓扑算法和并行拓扑算法的处理时间和结果,验证了并行拓扑算法的正确性,同时证明并行拓扑算法能够在一定程度上提升拓扑处理的效率。