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。     

利用场模型拓扑表达GIS中的地理目标

该文阐述为了实现在GIS中描述自然界里带有模糊不确定性的地理目标 ,扩充GIS的模糊查询功能 ,首先基于集合论思想探讨了确定性地理目标的代数解析表达与其拓扑表达 ,指出了确定性点、线、面之间拓扑表达的构成机理 ;然后 ,基于场模型建立了模糊地理目标的空间表达 ,分析了模糊地理目标的位置不确定性 ,进而建立了模糊地理目标的拓扑表达模型 ,即点集拓扑内部、边界和外部。分析表明 ,公认的Egenhofer模型是该文模型在地理目标不带有误差或不确定性情况下的特例。最后 ,与Clementini(1996 )提出的模型做了比较分析 ,表明了该文模型的合理性。     

Boolean matrix operators for computing binary topological relations between complex regions

Complex regions are composed of a finite number of simple regions, and are always defined by hierarchical representation methods. This article focuses on a unified method for computing n-intersection-based binary topological relations between complex regions based on hierarchical characteristics, using known topological relations between simple regions. The hierarchical representation of complex regions is defined as the recursive process of region decomposition using a context-free grammar. To distinguish multiple components of a region and whether the interior of a hole is a part of the inner exterior or the outer exterior, three region operators are proposed to describe the configuration of a region represented as a formal expression. Then, three corresponding 25-intersection (25I) based Boolean matrix operators are proposed to compute topological relations based on the relationships between decomposed regions. Herein, the invalid conditions of the operators are verified in detail, and the invalidities can be eliminated by either applying our definition of complex regions or with the inclusion of additional information. The proposed 25I-based operators, as shown in our cases, can be used as a ‘bridge’ to link different n-intersection models, and as a useful computation tool for analyzing topological relations between regions with specific configurations.     

Multidimensional-unified topological relations computation: a hierarchical geometric algebra-based approach

This article presents a geometric algebra-based model for topological relation computation. This computational model is composed of three major components: the Grassmann structure preserving hierarchical multivector-tree representation (MVTree), multidimensional unified operators for intersection relation computation, and the judgement rules for assembling the intersections into topological relations. With this model, the intersection relations between the different dimensional objects (nodes at different levels) are computed using the Tree Meet operator. The meet operation between two arbitrary objects is accomplished by transforming the computation into the meet product between each pair of MVTree nodes, which produces a series of intersection relations in the form of MVTree. This intersection tree is then processed through a set of judgement rules to determine the topological relations between two objects in the hierarchy. Case studies of topological relations between two triangles in 3D space are employed to illustrate the model. The results show that with the new model, the topological relations can be computed in a simple way without referring to dimension. This dimensionless way of computing topological relations from geographic data is significant given the increased dimensionality of geographic information in the digital era.     

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.     

A complete classification of spatial relations using the Voronoi-based nine-intersection model

In this article we show that the Voronoi-based nine-intersection (V9I) model proposed by Chen et al. (2001, A Voronoi-based 9-intersection model for spatial relations. International Journal of Geographical Information Science, 15 (3), 201–220) is more expressive than what has been believed before. Given any two spatial entities A and B, the V9I relation between A and B is represented as a 3 × 3 Boolean matrix. For each pair of types of spatial entities that is, points, lines, and regions, we first show that most Boolean matrices do not represent a V9I relation by using topological constraints and the definition of Voronoi regions. Then, we provide illustrations for all the remaining matrices. This guarantees that our method is sound and complete. In particular, we show that there are 18 V9I relations between two areas with connected interior, while there are only nine four-intersection relations. Our investigations also show that, unlike many other spatial relation models, V9I relations are context or shape sensitive. That is, the existence of other entities or the shape of the entities may affect the validity of certain relations.     

Change detection for 3D vector data: a CGA-based Delaunay–TIN intersection approach

In this paper, conformal geometric algebra (CGA) is introduced to construct a Delaunay–Triangulated Irregular Network (DTIN) intersection for change detection with 3D vector data. A multivector-based representation model is first constructed to unify the representation and organization of the multidimensional objects of DTIN. The intersection relations between DTINs are obtained using the meet operator with a sphere-tree index. The change of area/volume between objects at different times can then be extracted by topological reconstruction. This method has been tested with the Antarctica ice change simulation data. The characteristics and efficiency of our method are compared with those of the Möller method as well as those from the Guigue–Devillers method. The comparison shows that this new method produces five times less redundant segments for DTIN intersection. The computational complexity of the new method is comparable to Möller’s and that of Guigue–Devillers methods. In addition, our method can be easily implemented in a parallel computation environment as shown in our case study. The new method not only realizes the unified expression of multidimensional objects with DTIN but also achieves the unification of geometry and topology in change detection. Our method can also serve as an effective candidate method for universal vector data change detection.     

Areas of fuzzy geographical entities

Fuzzy Geographical Entities (FGEs) refer in this paper to geographical entities with fuzzy spatial extent. The use of FGEs in geographical information systems requires the existence of operators capable of processing them. In this paper, our contribution to that field focuses on the computation of areas. Two methods are considered, one crisp due to Rosenfeld (1984 Rosenfeld, A. 1984. The diameter of a fuzzy set. Fuzzy Sets and Systems, 13: 241–246. [Crossref], [Web of Science ®] , [Google Scholar]), which has limited applicability, and the other fuzzy, which is a new approach. The new fuzzy area operator gives more information about the possible values of the area and enables the fuzziness in the spatial extent of the entity to be propagated to the area. Crisp and fuzzy areas have different meanings, and the use of one or the other depends not only on the purpose of the computation but also on the semantics of the membership functions. When the FGEs are represented by normal fuzzy sets, the fuzzy area operator generates fuzzy numbers, and therefore arithmetic operations can be performed with them using fuzzy arithmetic. However, we show that care must be taken with the use of the fuzzy arithmetic operators because, in some situations, the usual operators should not be applied. Properties of the Rosenfeld and fuzzy area operators are analysed, establishing a parallel with properties of the areas of crisp sets.     

Asymmetric fuzzy relation analysis method for ranking geoscience variables

A fuzzy relation analysis method is used to derive weights for qualitative variables based on their partial order relations. Two asymmetric measure indexes (incidence coefficient and probability difference) are proposed to measure the asymmetric associations between geoscience variables from which the partial order relations can be constructed. The fuzzy relation analysis method can be implemented in combination with the asymmetric measure indexes leading to new methods for pattern overlay and data integration in mineral potential prediction. Two types of models are proposed and illustrated by two artificial examples: one for predicting targets for undiscovered deposits, and the other for estimating the mineral resource potential of the targets.     

数字拓扑研究现状及其在GIS中的应用

数字拓扑主要研究栅格空间中离散几何对象的拓扑性质,这些性质在GIS空间分析和栅格数据处理中非常重要。该文从图论、混合拓扑和公理型3方面对数字拓扑的研究现状进行了分类和综述,并讨论数字拓扑在GIS领域的应用,指出三维数字拓扑和球面数字拓扑是数字拓扑在GIS中的两个发展趋势和研究热点。     

越南政治地理的脆弱性

政治地理的脆弱性是一个国家自然地理基础、社会文化历史、国内关系和国际关系的综合函数,直接关系到一个国家的国家安全。本文引入生态学关于脆弱性的概念,从内部和外部双重视角分析越南政治地理的脆弱性特征,同时分析梳理越南与世界大国、周边邻国特别是同中国的关系,并从区域热点问题入手,以期对中国周边地缘战略研究提供分析视角。     

Error propagation in a fuzzy logic multi-criteria evaluation for petroleum exploration

This article applies error propagation in a Monte Carlo simulation for a spatial-based fuzzy logic multi-criteria evaluation (MCE) in order to investigate the output uncertainty created by the input data sets and model structure. Six scenarios for quantifying uncertainty are reviewed. Three scenarios are progressively more complex in defining observational data (attribute uncertainty); while three other scenarios include uncertainty in observational data (position of boundaries between map units), weighting of evidence (fuzzy membership assignment), and evaluating changes in the MCE model (fuzzy logic operators). A case study of petroleum exploration in northern South America is used. Despite the resources and time required, the best estimate of input uncertainty is that based on expert-defined values. Uncertainties for fuzzy membership assignment and boundary transition zones do not affect the results as much as the attribute assignment uncertainty. The MCE fuzzy logic operator uncertainty affects the results the most. Confidence levels of 95% and 60% are evaluated with threshold values of 0.7 and 0.5 and show that accepting more uncertainty in the results increases the total area available for decision-making. Threshold values and confidence levels should be predetermined, although a series of combinations may yield the best decision-making support.     

基于格网索引的GIS矢量数据拓扑重建研究

GIS中对原始矢量数据进行拓扑分析和重建是对其进行存储和使用的前提。引入包括规则格网和四叉树格网在内的索引结构,将全局的矢量拓扑分析转化为单个格网范围内足够少的矢量线段求交过程,减少了运算的复杂度;并用一种重组算法实现将原始矢量数据转化为符合“逢交必断”标准的矢量数据。试验表明,该算法适合海量和高散乱度的矢量数据。     

地理空间意像模式的Voronoi模型

提出用Voronoi空间模型来表达意像模式，Voronoi模型无岐义空间邻近关系，构建能封装对象间空间关系的拓扑网络，使用该模型将各种空间介词映射为不同的拓扑结构，GIS采用该模型，可按自然语言中空间介词描述的定性空间关系查询检索模糊地理信息。     

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.     

Modelling conceptual neighbourhoods of topological line-region relations

Abstract

Based on the 9-intersection for binary topological relations, two models of conceptual neighbourhoods among topological relations between a line and a region are developed. The snapshot model derives the neighbourhoods by comparing pairs of topological relations and selects neighbours based on least noticeable differences, whereas the smooth-transition model develops neighbourhoods based on the knowledge of the deformations that may change a topological relation. The resulting similarity diagrams show some differences, which were compared with the results from tests in which human subjects were asked to organized line-region relations into groups of similar relations. The groupings the subjects made indicate that the smooth-transition model captures more important aspects of the similarity of topological line-region relations than the snapshot model.     

Groundwater vulnerability mapping: A GIS and fuzzy rule based integrated tool

Contamination of groundwater has become a major concern in recent years. Since testing of water quality of all domestic and irrigation wells within large watersheds is not economically feasible, one frequently used monitoring strategy is to develop contamination potential maps of groundwater, and then prioritize those wells located in the potentially highly contaminated areas for testing of contaminants. However, generation of contamination potential maps based on groundwater sensitivity and vulnerability is not an easy task due inherent uncertainty. Therefore, the overall goal of this research is to improve the methodology for the generation of contamination potential maps by using detailed landuse/pesticide and soil structure information in conjunction with selected parameters from the DRASTIC model. The specific objectives of this study are (i) to incorporate GIS, GPS, remote sensing and the fuzzy rule-based model to generate groundwater sensitivity maps, and (ii) compare the results of our new methodologies with the modified DRASTIC Index (DI) and field water quality data. In this study, three different models were developed (viz. DI_fuzz, VI_fuzz and VI_{fuzz_ped}) and were compared to the DI. Once the preliminary fuzzy logic-based (DI_fuzz) was generated using selected parameters from DI, the methodology was further refined through VI_fuzz and VI_{fuzz_ped} models that incorporated landuse/pesticide application and soil structure information, respectively. This study was conducted in Woodruff County of the Mississippi Delta region of Arkansas. Water quality data for 55 wells were used to evaluate the contamination potential maps. The sensitivity map generated by VI_{fuzz_ped} with soil structure showed significantly better coincidence results when compared with the field data.