随时间演化的不确定区域间拓扑关系判定

不确定性处理是时空数据库技术研究的新领域,现有研究成果集中在时空不确定性的表示模型方面,缺乏不确定性对象间时空关系特别是拓扑关系的分析.提出了利用3维拓扑分析模型来分析2维运动对象的时空关系,针对随时间演化的2维不确定性区域,将Egg/Yolk模型中的RCC（region connection calculus）区域扩充至3维,得到46种联合完备且互不相交的基本拓扑关系,根据各基本拓扑关系的时空特性,将46种基本关系归类为21类不确定性时空关系.     

模糊栅格区域的层次拓扑关系模型

空间区域拓扑关系建模是空间推理和地理信息系统(GIS)等领域的一个主要研究内容,近年来模糊空间区域建模及其拓扑关系分析显现出越来越重要的作用．根据栅格数据模型下模糊区域的特征和实际应用领域中拓扑关系分析的特点,提出了一种模糊栅格区域的层次拓扑关系模型,该模型利用3个谓词的真值来分析栅格区域间的拓扑关系,将分明栅格区域作为特例统一处理,能够根据谓词的多种真值实现模糊栅格区域在多个层次上的拓扑关系分析．该模型表达能力强、易于实现,并且在实际应用中得到了令人满意的结果．     

空间区域拓扑关系分析方法综述

空间关系形式化模型的发展是空间推理、地理信息系统(geographic information systems,简称GIS)、计算机视觉等领域中的一个非常重要的主题,近年来受到相关领域研究者的极大关注,特别是在空间区域间拓扑关系模型的研究方面取得了很大进展.介绍了区域间拓扑关系形式化分析的主要研究内容、研究方法和研究进展,并探讨了目前存在的问题和今后的发展方向.     

Spatial data methods and vague regions: A rough set approach

Uncertainty management has been considered essential for real world applications, and spatial data and geographic information systems in particular require some means for managing uncertainty and vagueness. Rough sets have been shown to be an effective tool for data mining and uncertainty management in databases. The 9-intersection, region connection calculus (RCC) and egg–yolk methods have proven useful for modeling topological relations in spatial data. In this paper, we apply rough set definitions for topological relationships based on the 9-intersection, RCC and egg–yolk models for objects with broad boundaries. We show that rough sets can be used to express and improve on topological relationships and concepts defined with these models.     

地理信息系统中空间对象间拓扑关系的推理

首先讨论了地理信息系统中空间对象的空间数据模型,然后定性地分析了空间对象点与点、点与线和点与区域之间的拓扑关系,并给出了空间对象拓扑关系的推理算法.最后,将模糊技术与空间对象之间的拓扑关系的推理算法结合起来,使其可以方便地处理地理信息系统中的模糊性和不确定性.     

空间对象及其拓扑关系

论文首先讨论了传统的地理信息系统中空间对象的空间数据模型,提出了面向对象的层次矢量数据模型。然后定性地分析了空间对象点与点、点与线和点与区域之间的拓扑关系,并给出了一种形式化表达空间对象成分拓扑关系的模型。最后,将这种模型与空间对象之间的拓扑关系结合起来,使其可以方便地处理地理信息系统中的对象间的拓扑关系。     

一种模糊区域的拓扑关系模型

空间区域拓扑关系建模是空间推理、地理信息系统(GIS)和计算机视觉等领域一个非常重要的主题，模糊区域的拓扑关系建模正日益受到相关领域研究者的重视，在分析现有模型的基础上，提出了一种模糊区域的拓扑关系模型，该模型利用模糊集来表示模糊区域，通过三个谓词的真值来判断区域间的拓扑关系，将分明区域作为特例统一处理，根据谓词的多种真值能够实现多层次上的拓扑关系分析．     

一种基于Hadoop的高效空间拓扑关系判定方法

互联网数据规模增长迅速,作为判定位置相关性的空间分析方法在互联网数据分析中得到广泛应用,空间拓扑关系判定是空间分析算法的重要基础。考虑到互联网数据的海量规模,采用传统方法的空间拓扑关系判定已远超出当前系统的处理能力。文中以分层法和二分查找法为基础提出了一种判定海量地理坐标与给定区域空间拓扑关系的高效判定算法,并结合Hadoop/Hive平台对算法进行优化。实验结果表明该方法可高效实现对海量空间数据的拓扑关系判定,并在算法精度上具有与ESRI传统算法相媲美的结果。     

Evaluating structural and topological consistency of complex regions with broad boundaries in multi-resolution spatial databases

Multi-resolution or multi-scale spatial databases store and manage multiple representations of spatial objects in the same area, so consistency among multiple representations of the same objects should be evaluated and maintained. Although many approaches have been proposed to check inconsistencies in multi-resolution databases, there is still a lack of effective approaches working for complex objects, especially for regions with broad boundaries which is a general model for representing various types of uncertainties. This paper presents approaches for evaluating structural and topological consistency among multiple representations of complex regions with broad boundaries (CBBRs) based on map generalization operators: merging, dropping, and hybrid of these two. For evaluation of structural consistency, all possible multiple representations of a CBBR are generated automatically and organized into a structured neighborhood graph, and then correspondences and equivalences among the multiple representations are defined to determine whether two representations at different levels of detail are structurally consistent. For evaluation of topological consistency, the topological relations between all pairs of regions in two CBBRs are considered, and their variation with change of spatial scale is analyzed. Since the approaches in this paper are built on a hiearchical representation of CBBRs with arbitrarily complex structure, they will also work well for evaluating consistency among multiple representations of complex objects.     

OCL for formal modelling of topological constraints involving regions with broad boundaries

Integrity constraints can control topological relations of objects in spatial databases. These constraints can be modelled using formal languages such as the spatial extension of the Object Constraint Language (Spatial OCL). This language allows the expression of topological integrity constraints involving crisp spatial objects but it does not support constraints involving spatial objects with vague shapes (e.g. forest stand, pollution zone, valley or lake). In this paper, we propose an extension of Spatial OCL based on (1) a geometric model for objects with vague shapes, and (2) an adverbial approach for modelling topological constraints involving regions with broad boundaries. This new language provides an easiness in the formal modelling of these complex constraints. Our approach has been implemented in a code generator. A case study is also presented in the paper in the field of agriculture spreading activities. AOCL _OVS takes account of the shape vagueness of spread parcel and improve spatial reasoning about them.     

利用简化9交模型进行三维拓扑分析

针对点、线、面和体等简单空间对象提出新的否定规则，对9交模型进行了简化．利用简化后的9交模型，仅需分析4组相交关系即可得出实际拓扑关系．在此基础上构建了拓扑关系推导表，可进一步分析复合空间对象之间的拓扑关系，并以线与体之间拓扑关系为例讨论了算法实现．与已有的算法相比，该算法能分析更为复杂的空间对象之间的拓扑关系．     

A fuzzy sets theoretic approach to approximate spatial reasoning

Relational composition-based reasoning has become the most prevalent method for qualitative reasoning since Allen's 1983 work on temporal intervals. Underlying this reasoning technique is the concept of a jointly exhaustive and pairwise disjoint set of relations. Systems of relations such as RCC5 and RCC8 were originally developed for ideal regions, not subject to imperfections such as vagueness or fuzziness which are found in many applications in geographic analysis and image understanding. This paper, however, presents a general method for classifying binary topological relations involving fuzzy regions using the RCC5 or the RCC8 theory. Our approach is based on fuzzy set theory and the theory of consonant random set. Some complete classifications of topological relations between fuzzy regions are also given. Furthermore, two composition operators on spatial relations between fuzzy regions are introduced in this paper. These composition operators provide reasonable relational composition-based reasoning engine for spatial reasoning involving fuzzy regions.     

Modeling and computing ternary projective relations between regions

Current spatial database systems offer limited querying capabilities beyond binary topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane into separate zones that are obtained from projective properties of two reference objects: then, by considering the empty/nonempty intersections of a primary object with these zones, the model is able to distinguish between 34 different projective relations. Then, the paper proposes original algorithms for computing the relations under the assumption that regions of the plane are stored as vector polygons in a spatial database. These algorithms run in optimal O(nlogn) time.     

Multi-level Topological Relations Between Spatial Regions Based Upon Topological Invariants

Topological relations have played important roles in spatial query, analysis and reasoning. In a two-dimensional space (IR²), most existing topological models can distinguish the eight basic topological relations between two spatial regions. Due to the arbitrariness and complexity of topological relations between spatial regions, it is difficult for these models to describe the order property of transformations among the topological relations, which is important for detailed analysis of spatial relations. In order to overcome the insufficiency in existing models, a multi-level modeling approach is employed to describe all the necessary details of region–region relations based upon topological invariants. In this approach, a set of hierarchically topological invariants is defined based upon the boundary–boundary intersection set (BBIS) of two involved regions. These topological invariants are classified into three levels based upon spatial set concept proposed, which include content, dimension and separation number at the set level, the element type at the element level, and the sequence at the integrated level. Corresponding to these hierarchical invariants, multi-level formal models of topological relations between spatial regions are built. A practical example is provided to illustrate the use of the approach presented in this paper.

Mining multiple-level spatial association rules for objects with a broad boundary

Spatial data mining, i.e., mining knowledge from large amounts of spatial data, is a demanding field since huge amounts of spatial data have been collected in various applications, ranging from remote sensing to geographical information systems (GIS), computer cartography, environmental assessment and planning. The collected data far exceeds people's ability to analyze it. Thus, new and efficient methods are needed to discover knowledge from large spatial databases. Most of the spatial data mining methods do not take into account the uncertainty of spatial information. In our work we use objects with broad boundaries, the concept that absorbs all the uncertainty by which spatial data is commonly affected and allows computations in the presence of uncertainty without rough simplifications of the reality. The topological relations between objects with a broad boundary can be organized into a three-level concept hierarchy. We developed and implemented a method for an efficient determination of such topological relations. Based on the hierarchy of topological relations we present a method for mining spatial association rules for objects with uncertainty. The progressive refinement approach is used for the optimization of the mining process.     

Modelling topological spatial relations: Strategies for query processing

This paper investigates the processing of spatial queries with topological constraints, for which current database solutions are inappropriate. Topological relations, such as disjoint, meet, overlap, inside, and contains, have been well defined by the 9-intersection, a comprehensive model for binary topological relations. We focus on two types of queries: (1) “Which objects have a stated topological relation with a given spatial object?” and (2) “What is the topological relation between two given spatial objects?” Such queries are processed at two levels of detail. First, Minimum Bounding Rectangles are used as an approximation of the objects' geometry and as a means of identifying candidates that might satisfy the query. Next, the nine intersections that determine the topological relations between candidate pairs are calculated. We present algorithms for minimizing these computations. Considerable performance can be gained by exploiting the semantics of spatial relations. We also compare the approach for a naive cost model, which assumes that all relations have the same frequency of occurrence, with a refined cost model, which considers the probability of occurrence of the topological relations. The strategies presented here have three key benefits: (1) they are based on a well-defined formalism; (2) they are customizable; and (3) they can take into account important statistical information about the data.     

空间数据库的方向关系模型

方向作为一个定性的空间关系,是空间拓扑关系的一个重要补充。现在的方向关系模型运用十分粗糙的最小包含矩形或概括为单个的点来表示近似方向关系。文章设计的方向关系矩阵模型克服了传统模型的限制,为复杂空间对象提供了更好的方向近似,包括凹面区域和有洞的对象。     

基于弱水印的地理数据拓扑完整性检验方法

拓扑关系是空间关系研究的基础问题,被广泛应用在空间查询和空间推理等方面。为了检测地理数据拓扑关系的完整性,提出了一种基于弱水印的地理数据拓扑完整性检验方法。通过地物之间空间相离距离生成水印信息,并修改其相离距离比值,根据比值进行地物缩放以达到嵌入水印的目的。在水印检测时,根据生成的水印与提取的水印的匹配结果来判定地理数据的拓扑完整性。实验结果表明,本方法可以有效地检测出矢量地理数据的拓扑完整性。     

定性方向关系模型研究进展

空间关系形式化模型的发展是空间推理、地理信息系统(GIS)、机器人导航等领域的一个非常重要的研究内容,近年来受到相关领域研究者的极大重视。空间对象的方向关系模型的研究已经取得了一定的进展。本文介绍了近年来空间对象的方向关系形式化模型的主要研究内容、研究方法和研究进展,对已有的方向关系模型做了比较,并探讨了目前存在的问题和今后的发展方向。