多重表达中空间拓扑关系等价性研究
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摘要
空间数据的多重表达就是用不同的空间数据来表达相同的空间场景或者同一种空间现象。这些空间数据或者在详细程度上不同,或者在数据表达模型上有所区别(如矢量模型和栅格模型),或者在描述的时态方面有所差异。多重表达的空间数据在空间关系、语义和几何方面可能存在不一致性,因此必须对这些不一致性进行评价和修正。
空间关系一般是指由空间目标的空间位置和空间形态引起的一类关系,是空间表达和分析的重要内容。在所有的空间关系中,空间拓扑关系被认为是表示最好信息的空间关系,在拓扑关系与其它空间关系之间存在冲突的情况下,拓扑关系必须占支配地位。因此,在多尺度空间信息表达的情况下保持空间拓扑关系的等价性就显得十分重要,需要对空间拓扑关系的等价性进行评价。对于空间拓扑关系的研究,目前大多集中于拓扑关系的形式化描述及分类方面,而在多重表达拓扑关系等价性方面的专门研究较少。并且大多数只是从理论层面进行探讨,实用性不强,因此必须发展具有可操作性的评价规则和模型。
本文概述了拓扑空间和拓扑关系的有关概念以及空间拓扑关系的表达模型和推理方法;详细介绍了拓扑关系的组合推理式描述方法:给出了栅格空间中不同类型空间目标之间拓扑关系类型;描述和判别了不确定空间目标之间拓扑关系;讨论了不同表达空间中以及空间抽象过程中存在的三种类型的拓扑关系等价性;提出了空间拓扑关系的抽象方法;建立了空间场景中空间拓扑关系的等价性评价模型。具体研究工作如下:
概述了拓扑空间和拓扑关系的有关概念以及空间拓扑关系的表达模型和推理方法。拓扑空间和拓扑关系的有关概念和性质是空间拓扑关系的数学基础,因此文章首先对其进行了简单介绍。空间拓扑关系的描述模型主要有基于点集拓扑的交集模型和基于逻辑演算的RCC模型。交集模型又分为4-交集模型和9-交集模型,它们都是形式化的描述模型,具有简洁和完备的特点。但是,4-交集模型和9-交集模型还不具有对拓扑关系进行完全区分的能力,因此人们对交集模型进行了扩展,得到了交集模型的不同扩展形式,包括维数扩展模型、边界交集成分描述模型、基于Voronoi图的模型、结合度量的描述模型、包含空洞区域的拓扑关系描述模型以及栅格空间中的交集模型。除此之外,常用的描述模型还有二维字符串模型、MBR模型和三维模型等。不确定空间目标之间拓扑关系模型主要有卵黄模型和宽边界区域9-交集模型。空间拓扑关系推理是定性空间推理的重要研究内容,对于空间信息的获取有重要的意义。这里简要介绍了空间拓扑关系推理的研究进展,包括空间拓扑关系的邻近推理、空间拓扑关系组合表推理以及空间拓扑关系的逻辑推理等方法。
介绍了拓扑关系的组合推理式描述方法。组合推理式描述方法主要用来描述矢量空间中空间目标之间的拓扑关系,其基本思想就是将空间目标分解为基本的图形单元,考察这些基本图形单元之间的拓扑关系,以此为基本拓扑关系进行不同层次的组合推理,得到不同类型空间目标之间的拓扑关系。根据这种组合推理方法,可以得到57种(或者21)种面-面拓扑关系、97种线-面拓扑关系以及56种线-线拓扑关系。相对于交集模型,这种描述方法更加符合人们认知习惯,并且便于对拓扑关系进行详细描述。
给出了栅格空间中不同类型空间目标之间拓扑关系类型。在计算机图形输出过程中,空间数据的可视化需要以栅格的形式实现,因此必须对栅格数据表达的空间目标之间的拓扑关系进行判别。这里仍然将栅格区域以及栅格线分解为内部、边界和外部,使用9-交集模型来判别它们的拓扑关系。根据9-交集模型,可以得到16种栅格面-面拓扑关系、30种栅格线-面拓扑关系、51种栅格线-线拓扑关系、5种栅格点-面拓扑关系、4种栅格点-线拓扑关系以及3种栅格点-点拓扑关系。
When different spatial data are used to represent the same spatial scene or spatial phenomenon, it is called multiple representations of spatial data. There are some differences among these spatial data, such as level of details, representation model (e.g. vector model and raster model) and temporal representation. There likely are some inconsistencies among spatial relationships, spatial semantics and geometric configuration of spatial objects in multiple representations of spatial data, which must be evaluated and corrected.Spatial relations are those relations derived from spatial locations and configurations of spatial objects, they are important research contents of spatial representation and analysis. Among all spatial relations, spatial topological relation is considered as the spatial relation that could represent best spatial information. When topological relation conflicts with other relations, it should be dominant. Therefore, it is important to keep topological relation equivalency in multiple scales spatial data, and we must evaluate equivalency of spatial topological relation. At present, researches on spatial topological relation focus mainly on formal representation and topological relation classification, very few special researches on equivalency of topological relations in multiple representations were made. Most of literature about topological equivalency discussed the problem only in theoretical level, therefore, some practicable and operable evaluating rules and model must be developed.In the dissertation, some concepts of topological space and topological relation are introduced, and representation models and reasoning methods of spatial topological relation are summarized. Combinatorial reasoning representation method of topological relation is introduced in detail, topological relations between different types of spatial objects in raster space are given, and topological relations between uncertain spatial objects are represented and distinguished. Three types of equivalencies of topological relations, which exist in different representation space and process of spatial abstraction, are discussed. Abstraction methods of topological relations are presented, and equivalency evaluation model of topological relations in spatial scene are established. The main research contents of the dissertation are follows:some concepts of topological space and topological relation are introduced, and representation models and reasoning methods of spatial topological relation are summarized. Relevant concepts and characters of topology space and topological relation are mathematics base of spatial topological relation, so they are introduced simply at first in this dissertation. There are two main models used to represent spatial topological relation, i.e. intersection model based on point-set topology and RCC (region connect calculus) model based on logical calculus. Intersection model include 4-intersection model and 9-interscetion model, both of them are formal models with concision and completeness. However, 4-intersection model and 9-interscetion model have not abilities to distinguish topological relations completely, thus they have been developed and some extended models have been gotten, including dimension extend model, boundary-
boundary intersection components representation model, Voronoi-based 9-interscetion model, metric combined model, topological relation between regions with holes representation model and intersection model in raster space. Except these models above, there are some other models such as 2-D string model, MBR (minimum bound rectangle) model and 3-dimensional model. Representation models of topological relations between uncertain spatial objects mainly include egg-yolk model and 9-interscetion models of regions with wide boundaries. Spatial topological relation reasoning is important content of qualitative spatial reasoning. It is significant to gain spatial information. Research developments of spatial topological relation reasoning are introduced briefly, mainly referring to neighborhood reasoning, combinatorial table reasoning and logic reasoning of spatial topological relations.? Combinational reasoning representation method of topological relation is introduced in detail. The method is mainly used to represent topological relation between spatial objects in vector space. The basic idea of this method is to divide spatial objects into elementary figure cells, and examine topological relations between these elementary figure cells. By combinational reasoning in different level based on these relations, topological relation between different types spatial objects can be gained. By this method, 57 (or 21) topological relations between regions, 97 topological relations between line and region, and 56 topological relations between lines are distinguished. Compared with intersection model, combinational reasoning representation method is better to accord with human cognitive habits, and more convenient to represent topological relations.?Topological relations between different types of spatial objects in raster space are given. In the process of map output by computer, the visualization of spatial data needs to realize in form of raster data, so topological relations between spatial objects in raster space must be represented. In this dissertation, each raster region and raster line should be divided into inner, boundary and exterior in order to use 9-intersection model to describe topological relations. In terms of 9-intersection model, 16 topological relations between raster regions, 30 topological relations between raster line and raster regions, 51 topological relations between raster lines, 5 topological relations between raster point and raster region, 4 topological relations between raster point and raster line and 3 topological relations between raster points have been induced.? Topological relations between uncertain spatial objects are represented and distinguished. Because of notional or semantic fuzziness and imprecise measurements, many data in spatial databases are imprecise, topological relations between uncertain spatial objects must be represented and distinguished. In order to do it, uncertain spatial objects must be described in detail. Here we use fuzzy region, epsilon band and fuzzy point to represent indeterminate spatial objects respectively. Then, fuzzy region and epsilon band are divided into inner, boundary and exterior regions, and intersection degree of these different parts of two objects should be calculated. At last, the relation vectors corresponding topological relations distinguished by 4-intersection and 9-intersection models are regarded as reference relation vectors, the correlative degree between quantitative relation vectors composed of the intersection degrees and reference relation vectors are calculated, topological relations between uncertain spatial objects are distinguished through comparing with all of these correlative degrees.
? Three types of equivalencies of topological relations, which exist in different representation space and process of spatial abstraction, are discussed. Spatial data can be represented by different data models, and can be transformed each other, so the equivalence of topological relation among different representation spaces must be studied. Because of this, the problem about equivalency among vector space, raster space and map space is discussed. Topological relation equivalency in the course of spatial abstraction is the basis of equivalency evaluation of topological relations in multiple scale representations. The equivalency can be discussed in two sides. The first equivalency is that keeps in the course of spatial abstractions in gradual changes, which does not change holistic structure of spatial objects but simplifies details of topological relation. The second equivalency is that keeps among corresponding topological relations when dimension of spatial objects changes. For example, if two regions are abstracted into a linear object and a point, corresponding topological relations should be equivalent.?Abstraction methods of topological relations are presented. Abstraction of spatial topoiogical relation includes semantic abstraction and figure abstraction. According to conception neighborhood graph and main feature of spatial topological relation, topological relations between regions, line and region and lines could be represented by elementary relation predicates, so the corresponding between topological relations and predicates here. In order to abstract spatial topological relations, the metric features of topological relation must be represented in details. In this dissertation, all local topological relations between spatial objects are represented by component sequence, and the importance of pertinent components is counted by length of components, area of component correlative regions and exterior correlative regions. According to importance of components and shape feature, spatial topological relations are abstracted by deletion, amalgamation and collapse operations. Using simplification methods of Delaunay Triangulation Networks and observing visualization feature of point objects, simplification method for point group, which can keep equivalency between topological relations, is presented. Based on basic principle of graph theory, abstraction method of linear objects group is discussed. Abstraction methods of area objects are discussed and reasoning rules of relation matrix simplification are given.?Equivalency evaluation model of topological relations in spatial scene are established. Every spatial scene is composed of different types of spatial objects, the number and configuration of these spatial objects could have much distinction, but topological relation between them must keep equivalent in multiple representations. The content of multiple representation is very widely, however, only equivalency of topological relations in multiple scales representations is studied here, i.e., equivalency evaluation of topological relations in spatial abstraction. In this dissertation, conceptions about equivalency of topological relations in spatial scene are debated. By analyzing residential area and correlative spatial objects, spatial topological relations between these factors that make up of spatial scene are determined. Combining with some rules about spatial relations manipulation in cartographic generalization, equivalency calculation models, which are used to calculate equivalency of topological relations between different types of spatial objects or objects groups in spatial abstraction are given. Based on this, a synthetic model, which can be used to calculated topological relation equivalency in spatial scenes has been built. At last,
the applied field of these evaluation models and abstraction method is discussed, and an example of application of the models is given.This dissertation aims to discuss abstraction rules of spatial topological relations, build up equivalency evaluation models of topological relations in the process of spatial abstraction, which could provide theoretical basis for equivalency maintenance of spatial topological relations in cartographic automated generalization. The work should be keep up in the future. We hope more researchers would pay attention to this field, and more outstanding achievements would be made out.
空间关系一般是指由空间目标的空间位置和空间形态引起的一类关系,是空间表达和分析的重要内容。在所有的空间关系中,空间拓扑关系被认为是表示最好信息的空间关系,在拓扑关系与其它空间关系之间存在冲突的情况下,拓扑关系必须占支配地位。因此,在多尺度空间信息表达的情况下保持空间拓扑关系的等价性就显得十分重要,需要对空间拓扑关系的等价性进行评价。对于空间拓扑关系的研究,目前大多集中于拓扑关系的形式化描述及分类方面,而在多重表达拓扑关系等价性方面的专门研究较少。并且大多数只是从理论层面进行探讨,实用性不强,因此必须发展具有可操作性的评价规则和模型。
本文概述了拓扑空间和拓扑关系的有关概念以及空间拓扑关系的表达模型和推理方法;详细介绍了拓扑关系的组合推理式描述方法:给出了栅格空间中不同类型空间目标之间拓扑关系类型;描述和判别了不确定空间目标之间拓扑关系;讨论了不同表达空间中以及空间抽象过程中存在的三种类型的拓扑关系等价性;提出了空间拓扑关系的抽象方法;建立了空间场景中空间拓扑关系的等价性评价模型。具体研究工作如下:
概述了拓扑空间和拓扑关系的有关概念以及空间拓扑关系的表达模型和推理方法。拓扑空间和拓扑关系的有关概念和性质是空间拓扑关系的数学基础,因此文章首先对其进行了简单介绍。空间拓扑关系的描述模型主要有基于点集拓扑的交集模型和基于逻辑演算的RCC模型。交集模型又分为4-交集模型和9-交集模型,它们都是形式化的描述模型,具有简洁和完备的特点。但是,4-交集模型和9-交集模型还不具有对拓扑关系进行完全区分的能力,因此人们对交集模型进行了扩展,得到了交集模型的不同扩展形式,包括维数扩展模型、边界交集成分描述模型、基于Voronoi图的模型、结合度量的描述模型、包含空洞区域的拓扑关系描述模型以及栅格空间中的交集模型。除此之外,常用的描述模型还有二维字符串模型、MBR模型和三维模型等。不确定空间目标之间拓扑关系模型主要有卵黄模型和宽边界区域9-交集模型。空间拓扑关系推理是定性空间推理的重要研究内容,对于空间信息的获取有重要的意义。这里简要介绍了空间拓扑关系推理的研究进展,包括空间拓扑关系的邻近推理、空间拓扑关系组合表推理以及空间拓扑关系的逻辑推理等方法。
介绍了拓扑关系的组合推理式描述方法。组合推理式描述方法主要用来描述矢量空间中空间目标之间的拓扑关系,其基本思想就是将空间目标分解为基本的图形单元,考察这些基本图形单元之间的拓扑关系,以此为基本拓扑关系进行不同层次的组合推理,得到不同类型空间目标之间的拓扑关系。根据这种组合推理方法,可以得到57种(或者21)种面-面拓扑关系、97种线-面拓扑关系以及56种线-线拓扑关系。相对于交集模型,这种描述方法更加符合人们认知习惯,并且便于对拓扑关系进行详细描述。
给出了栅格空间中不同类型空间目标之间拓扑关系类型。在计算机图形输出过程中,空间数据的可视化需要以栅格的形式实现,因此必须对栅格数据表达的空间目标之间的拓扑关系进行判别。这里仍然将栅格区域以及栅格线分解为内部、边界和外部,使用9-交集模型来判别它们的拓扑关系。根据9-交集模型,可以得到16种栅格面-面拓扑关系、30种栅格线-面拓扑关系、51种栅格线-线拓扑关系、5种栅格点-面拓扑关系、4种栅格点-线拓扑关系以及3种栅格点-点拓扑关系。
When different spatial data are used to represent the same spatial scene or spatial phenomenon, it is called multiple representations of spatial data. There are some differences among these spatial data, such as level of details, representation model (e.g. vector model and raster model) and temporal representation. There likely are some inconsistencies among spatial relationships, spatial semantics and geometric configuration of spatial objects in multiple representations of spatial data, which must be evaluated and corrected.Spatial relations are those relations derived from spatial locations and configurations of spatial objects, they are important research contents of spatial representation and analysis. Among all spatial relations, spatial topological relation is considered as the spatial relation that could represent best spatial information. When topological relation conflicts with other relations, it should be dominant. Therefore, it is important to keep topological relation equivalency in multiple scales spatial data, and we must evaluate equivalency of spatial topological relation. At present, researches on spatial topological relation focus mainly on formal representation and topological relation classification, very few special researches on equivalency of topological relations in multiple representations were made. Most of literature about topological equivalency discussed the problem only in theoretical level, therefore, some practicable and operable evaluating rules and model must be developed.In the dissertation, some concepts of topological space and topological relation are introduced, and representation models and reasoning methods of spatial topological relation are summarized. Combinatorial reasoning representation method of topological relation is introduced in detail, topological relations between different types of spatial objects in raster space are given, and topological relations between uncertain spatial objects are represented and distinguished. Three types of equivalencies of topological relations, which exist in different representation space and process of spatial abstraction, are discussed. Abstraction methods of topological relations are presented, and equivalency evaluation model of topological relations in spatial scene are established. The main research contents of the dissertation are follows:some concepts of topological space and topological relation are introduced, and representation models and reasoning methods of spatial topological relation are summarized. Relevant concepts and characters of topology space and topological relation are mathematics base of spatial topological relation, so they are introduced simply at first in this dissertation. There are two main models used to represent spatial topological relation, i.e. intersection model based on point-set topology and RCC (region connect calculus) model based on logical calculus. Intersection model include 4-intersection model and 9-interscetion model, both of them are formal models with concision and completeness. However, 4-intersection model and 9-interscetion model have not abilities to distinguish topological relations completely, thus they have been developed and some extended models have been gotten, including dimension extend model, boundary-
boundary intersection components representation model, Voronoi-based 9-interscetion model, metric combined model, topological relation between regions with holes representation model and intersection model in raster space. Except these models above, there are some other models such as 2-D string model, MBR (minimum bound rectangle) model and 3-dimensional model. Representation models of topological relations between uncertain spatial objects mainly include egg-yolk model and 9-interscetion models of regions with wide boundaries. Spatial topological relation reasoning is important content of qualitative spatial reasoning. It is significant to gain spatial information. Research developments of spatial topological relation reasoning are introduced briefly, mainly referring to neighborhood reasoning, combinatorial table reasoning and logic reasoning of spatial topological relations.? Combinational reasoning representation method of topological relation is introduced in detail. The method is mainly used to represent topological relation between spatial objects in vector space. The basic idea of this method is to divide spatial objects into elementary figure cells, and examine topological relations between these elementary figure cells. By combinational reasoning in different level based on these relations, topological relation between different types spatial objects can be gained. By this method, 57 (or 21) topological relations between regions, 97 topological relations between line and region, and 56 topological relations between lines are distinguished. Compared with intersection model, combinational reasoning representation method is better to accord with human cognitive habits, and more convenient to represent topological relations.?Topological relations between different types of spatial objects in raster space are given. In the process of map output by computer, the visualization of spatial data needs to realize in form of raster data, so topological relations between spatial objects in raster space must be represented. In this dissertation, each raster region and raster line should be divided into inner, boundary and exterior in order to use 9-intersection model to describe topological relations. In terms of 9-intersection model, 16 topological relations between raster regions, 30 topological relations between raster line and raster regions, 51 topological relations between raster lines, 5 topological relations between raster point and raster region, 4 topological relations between raster point and raster line and 3 topological relations between raster points have been induced.? Topological relations between uncertain spatial objects are represented and distinguished. Because of notional or semantic fuzziness and imprecise measurements, many data in spatial databases are imprecise, topological relations between uncertain spatial objects must be represented and distinguished. In order to do it, uncertain spatial objects must be described in detail. Here we use fuzzy region, epsilon band and fuzzy point to represent indeterminate spatial objects respectively. Then, fuzzy region and epsilon band are divided into inner, boundary and exterior regions, and intersection degree of these different parts of two objects should be calculated. At last, the relation vectors corresponding topological relations distinguished by 4-intersection and 9-intersection models are regarded as reference relation vectors, the correlative degree between quantitative relation vectors composed of the intersection degrees and reference relation vectors are calculated, topological relations between uncertain spatial objects are distinguished through comparing with all of these correlative degrees.
? Three types of equivalencies of topological relations, which exist in different representation space and process of spatial abstraction, are discussed. Spatial data can be represented by different data models, and can be transformed each other, so the equivalence of topological relation among different representation spaces must be studied. Because of this, the problem about equivalency among vector space, raster space and map space is discussed. Topological relation equivalency in the course of spatial abstraction is the basis of equivalency evaluation of topological relations in multiple scale representations. The equivalency can be discussed in two sides. The first equivalency is that keeps in the course of spatial abstractions in gradual changes, which does not change holistic structure of spatial objects but simplifies details of topological relation. The second equivalency is that keeps among corresponding topological relations when dimension of spatial objects changes. For example, if two regions are abstracted into a linear object and a point, corresponding topological relations should be equivalent.?Abstraction methods of topological relations are presented. Abstraction of spatial topoiogical relation includes semantic abstraction and figure abstraction. According to conception neighborhood graph and main feature of spatial topological relation, topological relations between regions, line and region and lines could be represented by elementary relation predicates, so the corresponding between topological relations and predicates here. In order to abstract spatial topological relations, the metric features of topological relation must be represented in details. In this dissertation, all local topological relations between spatial objects are represented by component sequence, and the importance of pertinent components is counted by length of components, area of component correlative regions and exterior correlative regions. According to importance of components and shape feature, spatial topological relations are abstracted by deletion, amalgamation and collapse operations. Using simplification methods of Delaunay Triangulation Networks and observing visualization feature of point objects, simplification method for point group, which can keep equivalency between topological relations, is presented. Based on basic principle of graph theory, abstraction method of linear objects group is discussed. Abstraction methods of area objects are discussed and reasoning rules of relation matrix simplification are given.?Equivalency evaluation model of topological relations in spatial scene are established. Every spatial scene is composed of different types of spatial objects, the number and configuration of these spatial objects could have much distinction, but topological relation between them must keep equivalent in multiple representations. The content of multiple representation is very widely, however, only equivalency of topological relations in multiple scales representations is studied here, i.e., equivalency evaluation of topological relations in spatial abstraction. In this dissertation, conceptions about equivalency of topological relations in spatial scene are debated. By analyzing residential area and correlative spatial objects, spatial topological relations between these factors that make up of spatial scene are determined. Combining with some rules about spatial relations manipulation in cartographic generalization, equivalency calculation models, which are used to calculate equivalency of topological relations between different types of spatial objects or objects groups in spatial abstraction are given. Based on this, a synthetic model, which can be used to calculated topological relation equivalency in spatial scenes has been built. At last,
the applied field of these evaluation models and abstraction method is discussed, and an example of application of the models is given.This dissertation aims to discuss abstraction rules of spatial topological relations, build up equivalency evaluation models of topological relations in the process of spatial abstraction, which could provide theoretical basis for equivalency maintenance of spatial topological relations in cartographic automated generalization. The work should be keep up in the future. We hope more researchers would pay attention to this field, and more outstanding achievements would be made out.
引文
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