Research On Equivalency Of Spatial Topological Relations In Multiple Representation

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.