拓扑空间关系描述理论研究现状与发展

空间关系研究是空间信息科学的基础,而拓扑空间关系是空间关系的重点与难点,其描述理论一直是研究的热点。该文就这一理论做一综述,阐述“交互模型”(即“区域连接演算”)的基本原理,并介绍其在空间信息科学界基本的理论问题,即该描述理论对应的数学模型包括拓扑学和代数两方面;揭示“交叉模型”(即“九交模型”)所用的拓扑学思想,并叙述其历史发展过程。对连接这两种模型的Mereotopology理论,阐述其概念与基本原理,指出拓扑空间关系描述理论是一个各模型有严密逻辑关联的统一体,以求对现有描述理论做出改进。     

时空拓扑关系描述及其推理研究

空间目标处于一定的时间与空间中,时态拓扑关系和空间拓扑关系经常交织在一起,形成时空拓扑关系,因此有必要在统一框架下研究时空拓扑关系.基于Allen对时态拓扑关系和Egenhofer对空间拓扑关系的研究,对时态拓扑关系和空间拓扑关系分别采用3×3的矩阵进行描述,将时空拓扑关系表示为3×6的矩阵,并描述了简单面/面之间的104种时空拓扑关系.在研究时态拓扑关系推理和空间拓扑关系推理的基础上,提出了一种时空拓扑关系推理方法.该文提出的时空拓扑关系描述和推理方法对于拓展时空拓扑关系的研究具有重要意义.     

复杂体目标之间三维拓扑关系描述模型

三维空间拓扑关系是空间关系研究领域的重要问题。该文分析了三维空间拓扑关系的研究进展和存在的问题,以点集拓扑理论为基础,提出用于描述复杂体目标之间三维拓扑关系的点邻域模型,以15种点邻域结构涵盖三维空间中两个体目标之间任意一点的归属关系,基于点邻域结构设计了描述体目标之间三维拓扑关系的编码。典型三维拓扑关系实例的比较分析表明,对于9IM模型所能区分的三维拓扑关系,点邻域模型均可区分;对于一些复杂的9IM模型无法区分的三维拓扑关系,点邻域模型仍然给出了唯一的描述结果。因此,点邻域模型区分出的复杂体目标之间拓扑关系的种类更多,对三维拓扑关系的描述更加精确。     

基于粗糙模型的模糊地理对象空间拓扑关系研究

在粗糙集的基本概念上,基于上、下近似集定义了二维离散空间中的粗糙区域和粗糙模型,用粗糙模型描述二维离散空间中的模糊地理对象,并给出了粗糙区域的3种类型:确定—确定类型、确定—模糊类型、模糊—模糊类型。在离散空间的空间连接计算理论RCC-D-5的基础上,定义了模糊地理对象拓扑关系之间的拓扑约束关系,并依据概念临近推演和拓扑约束关系,研究得出二维离散空间中简单模糊地理对象之间的73种全拓扑关系,并基于4×4相交包含矩阵进行了描述,使得复杂的拓扑关系在计算机中描述和表达成为可能。     

模糊区域拓扑关系模型

拓扑关系是地理信息系统中空间要素之间最基本也是最重要的关系之一，是进行绝大多数空间查询和分析的基础。非模糊空间要素之间的拓扑关系在一般拓扑学等理论的基础上已有相关的模型和描述，并在实践中得到广泛的应用，如何建立模糊空间要素这间的拓扑关系是建立模糊要素地理信息系统的基础。该文在模糊扑扑学的基础上提出了模糊区域的定义，建立了用于分析模糊区域之间拓扑关系的理论和模型，提出了4*4-intersection模型拓扑关系矩阵，并分析了不同拓扑关系矩阵对于非模糊区域之间、模糊区域之间建立拓扑关系的区别和联系，最后采和不同公式对模糊区域之间的关系进行了系统的描述。     

栅格空间中三维地学实体拓扑关系表达的K6N9-I模型

论述栅格空间中三维地学实体拓扑空间关系研究的理论基础和现实意义,基于数字拓扑理论定义了栅格实体的6邻域内部I6、6邻域边界B6和k阶6邻域E6k,并以此分别替换9-I模型中实体的内部I、边界B和外部E,形成一种适用于栅格空间三维实体拓扑关系描述和分析的新9-I模型,即k阶6邻9-I模型(K6N9-I)。以基于规则六面体表达的地学实体为研究对象,通过扩展关系数据库SQL形成空间关系查询语言,实现了栅格空间中三维地学实体拓扑关系的定性表示和定量计算。以若干地学实体为例进行了初步实验,表明该模型实用方便,且在复杂地学实体的度量、方位等空间关系研究方面亦有较好的应用前景。     

多尺度地理空间点群目标相似关系的计算研究

研究多尺度地理空间点群目标相似关系的计算问题.基于4类点群信息,将点群目标包含的信息重新分成统计信息、专题信息、拓扑信息、几何信息和度量信息,这5类信息是影响点群相似性程度的主要因子.根据这5类信息描述参数的特点,给出了各个因子的相似度计算公式,建立了多尺度地理空间点群目标相似关系的计算模型,并通过算例验证了该模型的可行性与有效性,为地图综合质量的评价提供了一种新方法.     

基于等宽ε-带的三维线-线对象不确定性拓扑关系描述与判别方法

三维空间下不确定性对象拓扑关系是研究三维GIS中不确定性问题的基础。该文将二维平面直线不确定性的思想引入到三维空间,基于二维平面ε-带自旋转构建三维拓展包络体,表达不确定性三维线对象的置信区域。在对不确定性三维线对象进行描述的基础上,对不确定性线-线对象各部分之间的交集程度提出了一种定量化分析方法;通过对交集程度的度量,将三维空间下不确定性线-线拓扑关系用这些度量组成的空间向量表达;结合9I模型确定的参考空间关系向量理论,逐一考察度量化空间关系向量与参考空间关系向量之间的相关度,提出三维空间下不确定性线-线对象之间拓扑关系的描述模型,通过定量化分析方法对其空间拓扑关系进行判别。实验结果表明,该方法具备一定的可行性,可为不确定性问题的探讨提供科学依据。     

基于凸凹理论的三维地质体空间关系模型研究

目前的三维地质体空间关系模型表达能力较弱,限制了其在空间分析、查询等方面的应用。三维模型的应用与发展迫切需要一种新的底层分解与理论建模解决此类问题。该文基于凸凹理论重新对地质体进行结构定义与空间关系建模,提出了内凸体、外凸体、内缘体、外缘体等构造,并在此基础上建立了三维地质体R7×7空间关系模型,将地质体间空间关系表达能力理论上扩充至249种,实际能够表达40余种空间关系;给出了包容、镶嵌、部分镶嵌等关系的定义并对其进行了模型表达;针对不同应用,给出了R7×7模型的变换模型R(5×5 3×3)等。为能够表达地质体交集的边界长度、交面面积、地质体体积、外缘体体积、镶嵌体积等地质空间重要关系,基于凸凹理论建立了地质体度量关系模型,是矿区地质体拓扑关系查询、空间分析推理等应用的基础模型。给出了模型与地质体模糊理论的相契性分析,二者模型能够相辅相成,相互借鉴使用。     

空间关系的动态性和模糊性描述

完备和形式化的空间关系语义描述方法一直是GIS理论研究的重点,空间关系的动态性和模糊性决定了描述方法的复杂性。该文提出一种空间关系动态性和模糊性的描述方法,该方法顾及0维、1维、2维空间目标,在空间关系语义描述中,引入计算语言学的“施动”和“受动”概念,将语义的产生归因于“施动者”空间目标对“受动者”空间目标的作用,将空间目标间空间关系的语义空间分解为分割度、覆盖度、接近度和环绕度,并给出这些量度系数的表达方法和计算方法。其有助于空间关系语义的形式化描述。     

A scale-explicit model for checking directional consistency in multi-resolution spatial data

Multi-resolution spatial data always contain the inconsistencies of topological, directional, and metric relations due to measurement methods, data acquisition approaches, and map generalization algorithms. Therefore, checking these inconsistencies is critical for maintaining the integrity of multi-resolution or multi-source spatial data. To date, research has focused on the topological consistency, while the directional consistency at different resolutions has been largely overlooked. In this study we developed computation methods to derive the direction relations between coarse spatial objects from the relations between detailed objects. Then, the consistency of direction relations at different resolutions can be evaluated by checking whether the derived relations are compatible with the relations computed from the coarse objects in multi-resolution spatial data. The methods in this study modeled explicitly the scale effects of direction relations induced by the map generalization operator – merging, thus they are efficient for evaluating consistency. The directional consistency is an essential complement to topological and object-based consistencies.     

Integrative representation and inference of qualitative locations about points,lines, and polygons

Qualitative knowledge representation of spatial locations and relations is popular in many text-based media, for example, postings on social networks, news reports, and encyclopedia, as representing qualitative spatial locations is indispensable to infer spatial knowledge from them. However, an integrative model capable of handling direction-based locations of various spatial objects is missing. This study presents an integrative representation and inference framework about direction-based qualitative locations for points, lines, and polygons. In the framework, direction partitions of different types of reference objects are first unified to create a partition consisting of cells, segments, and corners. They serve as a frame of reference to locate spatial objects (e.g., points, lines, and polygons). Qualitative relations are then defined to relate spatial objects to the elements in a cell partition, and to form the model of qualitative locations. Last, based on the integrative representation, location-based reasoning mechanism is presented to derive topological relations between objects from their locations, such as point–point, line–line, point–line, point–polygon, line–polygon, and polygon–polygon relations. The presented model can locate any type of spatial objects in a frame of reference composed of points, lines, and polygons, and derive topological relations between any pairs of objects from the locations in a unified method.     

地理空间关系确定性描述与集成推理

地理要素的空间关系在GIS空间数据建模、空间分析、地图自动综合等方面起着重要作用,研究如何快速判断要素间空间关系是否发生变化,从而有效维护空间关系具有重要的科学意义。对目前有关地理空间关系确定性描述及其集成推理的研究成果进行综合分析与分类,分析其适应性与特点,并就该研究方向存在和需要解决的问题进行分析。     

A Euler number-based topological computation model for land parcel database updating

Intersection relations are important topological considerations in database update processes. The differentiation and identification of non-empty intersection relations between new updates and existing objects is one of the first steps in the automatic incremental update process for a land parcel database. The basic non-empty intersection relations are meet, overlap, cover, equal and inside, but these basic relationships cannot reflect the complex and detailed non-empty relations between a new update and the existing objects. It is therefore necessary to refine the basic non-empty topological relations to support and trigger the relevant update operations. Such relations have been refined by several researchers using topological invariants (e.g., dimension, type and sequence) to represent the intersection components. However, the intersection components often include only points and lines, and the refined types of 2-dimensional intersection components that occur between land parcels have not been defined. This study examines the refinement of non-empty relations among 2-dimensional land parcels and proposes a computation model. In this model, an entire spatial object is directly used as the operand, and two set operations (i.e., intersection (∩) and difference (\)) are applied to form the basic topological computation model. The Euler number is introduced to refine the relations with a single 2-dimensional intersection (i.e., cover, inside and overlap) and to distinguish the refined types of 2-dimensional intersection components for the relations with multiple intersections. In this study, the cover and overlap relations with single intersections between regions are refined into seven cases, and nine basic types of 2-dimensional intersection components are distinguished. A composite computation model is formed with both Euler number values and dimensional differences. In this model, the topological relations with single intersections are differentiated by the value of the dimension and the Euler number of the resulting set of the whole-object intersection and differences, whereas the relations with multiple intersections are discriminated by the value of the resulting set at a coarse level and are further differentiated by the type and sequence of the whole-object intersection component in a hierarchical manner. Based on the refined topological relations, an improved method for automatic and incremental updating of the land parcel database is presented. The effectiveness of the models and algorithms was verified by the incremental update of a land cover database. The results of this study represent a new avenue for automatic spatial data handling in incremental update processes.     

Modeling the scale dependences of topological relations between lines and regions induced by reduction of attributes

The scale dependences of topological relations are caused by the changes of spatial objects at different scales, which are induced by the reduction of attributes. Generally, the detailed partitions and multi-scale attributes are stored in spatial databases, while the coarse partitions are not. Consequently, the detailed topological relations can be computed and regarded as known information, while the coarse relations stay unknown. However, many applications (e.g., multi-scale spatial data query) need to deal with the topological relations at multiple scales. In this study new methods are proposed to model and derive the scale dependences of topological relations between lines and multi-scale region partitions. The scale dependences of topological relations are modeled and used to derive the relations between lines and coarse partitions from the relations about the detailed partitions. The derivation can be performed in two steps. At the first step, the topological dependences between a line and two meeting, covered and contained regions are computed and stored into composition tables, respectively. At the second step, a graph is used to represent the neighboring relations among the regions in a detailed partition. The scale dependences and detailed relations are then used to derive topological relations at the coarse level. Our methods can also be extended to handle the scale dependences of relations about disconnected regions, or the combinations of connected and disconnected regions. Because our methods use the scale dependences to derive relations at the coarse level, rather than generating coarse partition and computing the relations with geometric information, they are more efficient to support scale-dependent applications.     

多尺度地图空间相似关系基本问题研究

基于多尺度地图数据库建设中地图自动综合的终止判断条件,引出多尺度地图空间相似关系问题。基于集合论给出空间相似关系的定义,论述空间相似关系的5个性质,即反身性、对称性、非传递性、多尺度自相似性与尺度依赖性;并从图形相似和属性相似的角度论述多尺度地图空间相似关系的分类体系。该成果是研究地图自动综合和地图空间相似查询等的基础。     

国内外区域空间相互作用研究进展

区域空间相互作用是区域科学、经济地理学关注的重点。文章对国内外空间相互作用的相关理论、研究内容及测度模型进行梳理。从研究内容来看,区域联系特征及区域空间结构的关注较多,而针对区域间地缘经济关系的研究还有待深化,尤其是在测度方面需要更为深入的探讨,质性方法在研究中的分量也需要强化。经典的引力模型在实践应用中不断调整和深化,而对于城市流模型和地缘经济关系模型的支撑理论较为薄弱,模型应用过程中呈现出新技术、新方法运用的趋势。传统的研究还集中于地理意义上的区域空间及城市组织,针对虚拟空间中的信息技术流动和技术创新等因素的影响应作出积极回应。随着全球城市网络的显现,借助各种属性数据探索垂直层面的联系将是一个重要方向,不同尺度下的城市与区域间的网络结构、功能和关系研究将成为关注的重点。