Research On Representation And Reasoning Of The Topological Relations Of Convex Regions

Last three decades, spatial reasoning has attracted more and more experts and scholarsfrom different fields of concern, such as computer science, geographic information science,pure mathematics, cognitive science, has carried out detailed models and complex reasoning.In recent years, spatial reasoning has become a cross-disciplinary research priorities and hotspots. The relevant theoretical results and practical applications are also mutually promotedand developed.Research on the topological relations of convex regions is a hot area in spatial reasoning,however, there are still some issues to be addressed. Such as how to use a unified model toexpress the topological relations between points, lines, convex regions, and how to define thedistance of the topological relationships in order to better applications to areas such as imagerecognition, the reasoning of topological relations between the convex regions also needsfurther study.To give the complete set of topological relations between the convex regions, thesix-tuple representation model is proposed, and given the reasoning and further research onthis basis. The main content is organized as follows:(1) Describing the background research and the purpose and the significance of spatialreasoning, and summarizing the convex region topological relations status quo, the existingdeficiencies and problems to be solved.(2) Introduction to the point set topology, basic knowledge and the classical model oftopological relations RCC8and the9-intersectionl and a diagram of the nearest topologicalrelations is given. Further expressing and reasoning the topological relations between a simpleregion and a simple region with a hole.(3) The innovative6-tuple expression model for expressing topological relations betweenthe convex region is proposed and12kinds of topological relations between the straight linesegment and convex region are given which are completed.(4) We obtain a complete classification of topological relations which called RCC32through constraints and the existence theorem. By calculating the cost of transforming onerelation into another, the closest topological relation graph of RCC32is given. (5) Based on RCC32and6-tuple model, for further research of the reasoning of thetopological relations between the convex regions and the inverse reasoning is given byuniqueness.(6) Then the composite reasoning between a simple convex regions and a simple convexregion with a hole is presented through the constraint satisfaction conditions and enumeratingspecific examples.(7) Designed and implemented the convex region topological relations representationand reasoning demonstration system.The6-tuple representation model fully consider the nature of the convex region, theatomic set of topological relations between the convex regions RCC32is given from the pointof view of computational geometry which consisting of constraints. Compared to modelsproposed before, our method expresses fully, theory solid, and be help to integrate theexpression of topological relations of complex spatial objects and further reasoning. Bydefining the measurement of topological relations, the closest topological relation graph ofRCC32is given and the results can be applied to dynamic spatial information processing.Then the inverse reasoning is given, as well as the composite reasoning between a simpleconvex regions and a simple convex region with a hole. The inference results given bindingnature and geometric composition to ensure the complete and accuracy of the results. Finally,the demonstration system is programmed at the conclusion of this article.This study can be applied to spatial data mining, robot navigation, computer graphics,and other fields. In the theory of research and engineering practice our study also has a certainvalue.