Research On Reasoning And Topological Relations Between Spatial Region With Holes And Simple Unclosed Line

In recent years, researches on theory and application on spatial information are getting more and more attentions in Artificial Intelligence(AI), Geographical Information System(GIS), Spatial Database and other relating fields. The relations of spatial objects are various, and sometimes rely on the domain specific applications. The research on cognition, description and representation of spatial relations are the basis of an effective application.Topological relation is the most elementary relation in space, and is one of the basic problems in qualitative spatial reasoning.In Practical applications,some spatial phenomena have cavities and islands, which require geometric representations of regions with holes when they are modeled in geographic information systems. Most prominent geographic examples are the territorial configurations of Italy (which completely surrounds San Marino and the Vatican City). Hence, relations between complex objects and simple objects have been focused on for practical applications. it is meaningful to study topological relation between spatial regions with holes and a simple line.In this article we will discuss the topological relationship between spatial region with Holes and simple unclosed lines in two ways.1.Treat the inside of simple unclosed line as integrity. For spatial regions with a single hole, based on the thinking of Egenhofer, the 2×5 intersection matrices model was raised, and the 93 kinds of topological relationships between Spatial regions with holes and simple unclosed line were defined.2. Regard the inside of the simple unclosed line as connections of many linear lines.we established the inference table of topological relationship using the method of combinatory description of topological relationship. We also described the 254 kinds of topological relationships of regions with holes and simple unclosed lines more specifically.The concrete work content and research results of this article 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, introduce the theoretical basis involved in this research articles. Arround the mainstream of description of spatial relationships and focusing the most elementary topological relationships, some main research work about the quantitative relationships and topological relationships among spatial objects was analyzed and summarized in both logical method and algebraic method. These research work include the n-intersection model. Meanwhile, the method of combinatory inference using elementary spatial topological relationships by Guo Qingsheng and etc was introduced.Thirdly, based on the thinking of the nine-intersection model and the structural traits of regions with holes(single hole only),we proposed the 2×5 intersection model describing topological relation between spatial region both with one hole and simple unclosed line on the basis of Egenhofer's methods. And by means of 2×5 intersection model we defined 93 kinds of relations. between spatial region both with one hole and simple unclosed line,and a complete diagram about these 93 kinds of spatial topological relations is listed.fourthly, the denotative method about 93 spatial topological relations between spatial region with holes and simple unclosed line were presented by 2×5 intersection model,this paper gave algorrithm H_L and 9 basic topological relation and proved that algorrithm H_L is correct.Based on the essential 2×5 intersection model which was the main method to represent the topological relation between spatial region with holes and simple unclosed line. we find that these topological relations can be reduced to 9 basic topological relations of 93 topological relations . Based on the theory about matrix operation, we brought forward algorithm H_L, give the ADL representation about algorithm H_L, the reasoning process and illustrating diagram that reason about other relations from five basic topological relations.Fifthly,Regard the inside of a line as connections of multiple linear lines. 11 kinds of elementary relationships were defined, using the combination of which we described the topological relationship between spatial region with holes and simple simple unclosed lines. We also gave the principles of the combination, according to which we got the 254 kinds of topological relationships between spatial region with holes and simple simple unclosed lines. The inference table of topological relationships was established and the 254 kinds of topological relationships were charted. The correspondence table between the 93 kinds of topological relationships of a line and spatial region with holes (when regarding the inside of a line as integrity) and the 254 kinds of ones (when regarding the inside of a line as combination of multiple lines) were also given.Sixthly, we designed and implemented a demonstrating system of model TSC. The demo system is composed of three main functions, that is, demonstrating, distinguishing and reasoning of topological relations.The 2×5 intersection matrix model based on the thinking of Egenhofer can describe the topological relationships between spatial region with holes and a line accurately and concretely. H_L algorithm can solve the topological relationship matrix of a new line and the same single spatial region with holes. The 9 elementary topological relationships between spatial region with holes and a line based on the H_L algorithm has equal expressing ability with the 93 topological ones based on the 2×5 intersection model,but more simple and brief. In addition,more specific topological relationships can be gained when treating the inside of a line as combination of multiple linear lines. The 254 kinds of topological relationships can differentiate the following four circumstances between a line and spatial region with holes:simple contingence, overlapping contingence, simple intersection , and overlapping intersection. According to the chart and combination table of the 254 kinds of topological relationships between spatial region with holes and a line , the spatial topological relationships can be queried and decided directly,thus it has good operability in processing two-dimension spatial data. Using the correspondence table between the 254 kinds of topological relationships and the 93 ones,the multiple circumstances when spatial region with holes and a line have intersections can be queried.In a word, the study results of the paper are of both theoretical and practical benefit to further researches in spatial relations on spatial reasoning, spatial query language and geographic information system (GIS).