Research On The Combination Method Of Topological Relations And Metric Relations Of Spatial Regions

Spatial relation is the relation with spatial character between spatial objects. It usually consists of topological relations, metric relations and order relations. Theses relations are the bases of spatial data organizing, querying, analyzing and reasoning. Spatial relation is one of the most important theoretical problems in the fields of spatial reasoning, Geographical Information System (GIS), computer vision and spatial databases.All spatial relations are not entirely independent of each other. They express an internal constraint among spatial data. All spatial relations depict correlational characters of spatial objects in different aspects. There are very close connections among these spatial relations, and we need to consider multiple spatial relations in many practical applications. Now the researches on single spatial relation have have already rich accumulation, it is a hot issue on current spatial reasoning researches that how to combine multiple spatial relations to represent spatial objects. Most of the existing methods focus on the combination of topology and orientation, distance and size, distance and direction, position and direction. However, there are less works on the combination of metric relations and other relations.This paper focuses on the combination of topological and metric relations of regions and their representation. Firstly, we summarized and analyzed the study of spatial relation among objects in recent years. Based on splitting and closeness measurements between line-region and line-line presented by Egenhofer, we proposed the measurements between two regions. On this basis we gave the combination diagram and combination algorithm on topological relations and metric relations of regions. We shows the application of combination method through examples, this combination method can be applied for spatial analysis in GIS. Finally we gave therepresentation of topological relations and metric relations of regions on the basis of classifying invariant and topological attribute set of regions presented by Clementini and Egenhofer.The main work and results included in this paper are as follows: Firstly, it is a short introduction on background and significance of this paper. We summarized and analyzed the state of arts on spatial relation among objects in recent years.Secondly, some basic theories including n-intersection model and measurements are introduced. n-intersection model is one of the models which are used to represent topological relations among spatial objects, and measurements between line-region and line-line including splitting and closeness measurements are presented by Egenhofer.Thirdly, we proposed splitting and closeness measurements between regions on the basis of Egenhofer's methods. Splitting measurements are used to describe the splitting degrees of region's interior, boundary and exterior, if they have non-empty intersections. Closeness measurements are used to describe the closeness degrees of all disjoint parts between regions. By analyzing the content and type of intersections which are formed by the intersection of all parts of regions, we found that the length and area measurements can be used to represent the splitting and closeness degrees of all parts of regions. Based on these analyses, we difined four types of splitting and one closeness measurement values, and these five values can describe topological relations of regions in detail.Fourthly, we studied the combination of topological and metric relations of regions. Based on the measurements of two regions, we gave the combination diagram and combination algorithm about topological relations and metric relations of regions, and also gave the algorithm's basic idea and its ADL language description. Combination algorithm can compute twoarbitrary regions'metric tables according to their intersection matrixes. We illustrate the application of combination method in spatial analysis of GIS from three aspects including quantitative information, error handling and uncertainty, dynamic information.Fifthly, we gave the representation of topological relations and metric relations of regions on the basis of classifying invariant and topological attribute set of regions presented by Clementini and Egenhofer. At first, we gave the classifying invariant for representing topology of two arbitrary regions, which is called CI ( R1 ,R2). Then splitting measurements of regions are added into classifying invariant, and the resulting invariant are called as metric-enhanced classifying invariant MCI ( R1 ,R2), it can express any two arbitrary regions'topological and metric information. This representation structure establishes good foundation for formal representation and reasoning of spatial regions.Finally, we designed and implemented Combniation algorithm system. This system is based on the MVC design ideas, and uses Java 5.0 and SWT technology. The modules of this system have low coupling between each other, and the interior of the modules has stronger cohesion. The whole system is of high efficiency.The measurements of regions proposed in this paper are refinements of qualitative element value in n-intersection matrix, which can describe spatial relation of regions more accurately and detailedly. The combination method of topological and metric relations between regions can not only distinguish different topological relations of two pair of regions qualitatively, and also quantitative difference between two pair of regions can be made under the same topology. This representation structure establishes good foundation for formal representation and reasoning of spatial regions.In a word, the study results of this paper have both theoretical and practicalbenefits, it can be applied to represent and analyze the spatial relations among objects in spatial reasoning, spatial query language and geographic information system.