Quantitative fuzzy topological relations of spatial objects by induced fuzzy topology

This paper presents a study on the modeling of fuzzy topological relations between uncertain objects in Geographic Information Systems (GIS). Based on the recently developed concept of computational fuzzy topological space, topological relations between simple fuzzy spatial objects are modeled. The fuzzy spatial objects here cover simple fuzzy region, simple fuzzy line segment and fuzzy point. To compute the topological relations between the simple spatial objects, intersection concepts and integration methods are applied and a computational 9-intersection model are proposed and developed. There are different types of intersection, and we have proposed different integration methods for computation in different cases. For example, surface integration method is applied to the case of the fuzzy region-to-fuzzy region relation, while the line integration method is used in the case of fuzzy line segment-to-fuzzy line segment relation. Moreover, this study has discovered that there are (a) sixteen topological relations between simple fuzzy region to line segment; (b) forty-six topological relations between simple fuzzy line segments; (c) three topological relations between simple fuzzy region to fuzzy point; and (d) three topological relations between simple fuzzy line segment to fuzzy point.     

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。     

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。     

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.     

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。     

居民地与道路之间拓扑关系一致性的模糊评价

在地图制图综合中必须保持不同尺度同一区域地图要素之间拓扑关系的一致性,但目前有关的一致性评价方面的研究较少,本文讨论了不同比例尺地图中居民地与道路之间拓扑关系一致性的模糊评价问题。从制图规则和视觉限制的角度,分析了多尺度地图表达中居民地与道路之间的应该保持拓扑关系的一致性的几项规则;基于模糊数学理论提出了制图综合中拓扑关系的一致性评价模型,并通过一个简单实例证明了该方法的可行性。     

基于9-Intersection模型的模糊空间对象间的拓扑关系研究

本文将从地理认知的角度上分析并选择一个适合于在GIS中应用9-Intersection模型的模糊空间对象的边界定义,并构建一个能够采用9-Intersection模型精确判断模糊空间对象之间拓扑关系的模糊拓扑空间(CITfts),并进行相应的证明,最后建立简单模糊区域,采用empty/no-empty算子给出模糊空间对象之间的拓扑关系的表达形式。     

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。     

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.     

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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一种单线与多面要素间的拓扑关系描述方法

本文将线要素与多面要素的拓扑关系分解为简单面要素与其相关线组之间的局部拓扑关系;并将局部拓扑关系细化为线面基本拓扑关系,用度量关系对线面基本拓扑关系进行描述,提出了一种描述单线与多面要素之间拓扑关系的方法,可应用于线与多面要素数据库的建立、数据存储和查询。实验证明了其有效性。     

模糊对象粗糙表达及其空间关系研究

空间数据的模糊性是当前GIS领域研究的难点之一。现有的GIS数据模型基本上还不具备对模糊性进行描述、处理和分析的功能 ,使得GIS对数据的处理容易造成信息损失。把粗糙集和模糊集对空间数据的模糊性和不确定性处理的优势结合起来表达模糊对象 ,即利用粗糙集处理由于知识的粒度性所造成的模糊性和不精确性 ;利用模糊集处理模糊对象原始数据所具有的不确定性 ,从而扩展了空间数据模型对模糊数据的表达能力 ,并详细研究了模糊面与模糊面以及模糊线与模糊面之间的拓扑关系     

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…     

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.     

MODELING FUZZY GEOGRAPHIC OBJECTS WITHIN FUZZY FIELDS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｅｐｒｅｓｅｎｔａｔｉｏｎｏｆｓｐａｔｉａｌｏｂｊｅｃｔｓｉｓｏｎｅｏｆｔｈｅｋｅｙｉｓｓｕｅｓｉｎｃｕｒｒｅｎｔｒｅｓｅａｒｃｈｏｎｔｈｅｓｐａｔｉａｌｄａｔａｂａｓｅｔｈｅｏｒｙｏｆＧＩＳ (ＢｕｒｒｏｕｇｈａｎｄＭｃＤｏｎｎｅｌｌ,1 998) .Ｓｐａｔｉａｌｏｂｊｅｃｔｓｉｎｎａｔｕｒｅａｒｅｃｌａｓｓｉｆｉｅｄａｓｔｗｏｋｉｎｄｓ:ｏｂｊｅｃｔｓｗｉｔｈｄｉｓｔｉｎｃｔｉｖｅｂｏｕｎｄａｒｉｅｓａｎｄｏｂ ｊｅｃｔｓｗｉｔｈｔｒａｎｓｉｔｉｏｎａｌｏｒｆｕｚｚｙ…     

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。     

基于建筑平面图的室内空间拓扑模型自动生成算法

针对以建筑平面图为数据源构建室内导航模型时,建筑平面图缺少拓扑信息,尤其是缺少对房间、走廊等多边形对象拓扑描述的问题,本文提出了一种自动化构建室内空间拓扑模型的算法.该算法首先根据CAD建筑平面图的基本特征,将墙线抽象为弧段,门窗抽象为点,房间抽象为多边形;然后从起始墙线出发,将该墙线顺时针或逆时针遇到的第一条墙线作为...