Research On The Representation Models For Uncertain Spatial Directional Relations

The theory on the modeling of spatial data and relationships is the fundamental properties of GIS and the basis of spatial reasoning and cognition. Spatial relationships include topological relations, metric relations and directional relations. Directional relationship is the spatial relations most widely used in natural language and relative orientation. Comparing with topological relations, the study on directional relations is laggard. The crux is the uncertainty of directional relations. The uncertainty leads to the difficulty of directional representation and reasoning. Directional relations uncertainty may include two factors:the vagueness in directional relations concepts and the uncertain of boundary. Vagueness of directional relations concepts is caused by the ys of representation of directional relations. Directional relations are most commonly represented with qualitative representation model and quantitative representation model. The quantitative models represent direction relationships by angle (quadrant angle or azimuth), and the qualitative models use ordered classes. The uncertainty conversion model between qualitative directional relation concepts and quantitative directional relation numerical values is the crux problem of the directional relations concepts. The uncertain of boundary is caused by the randomness or the vagueness of spatial objects. Randomness of spatial objects contains the inaccuracy, error and imprecision during the course of the observation and surveying. Vagueness results from the imprecise knowledge or inherent uncertainty of spatial objects.Different kinds of spatial relations are not isolated and restricted each other. The restricted relationship causes the effect of topology and distance on the representation of directional relations. The category mechanism based on the topological relations and distance may improve the accuracy of the directional description.Based on the analysis of the uncertainty of directional relations, this thesis focused on the effect of topology and distance on the directional relations representation, the conversion between qualitative directional relation concepts and quantitative directional relation numerical values and the formalism of the directional relations between vague objects. Different models are presented for quantitative, qualitative and fuzzy representation of directional relations in the thesis. The main efforts include:(1) Presented a coordinate-based quantitative directional relations model, which is based on the restricted by the topology and distance. This quantitative model, which changes the angle-based quantitative way of directional relations, is based on the coordinates and is more sensitive to the factors including location, distance, size and shape. Furthermore, statistic model and quantitative similarity assessment method are defined by the metric parameters based on the coordinate-based directional relations model.(2) Proposed a topology-based multi-levels directional qualitative model, which based in the way of project-based models. The levels are according to different directional regions. Directional regions can be classed into four tiles, that is, I (interior), B (boundary), OE (exterior of MBR) and E (exterior). According to four tiles, four directional relations matrix are built to represent the directional relations in different regions. The computational models, going with the description of natural language, are defined to convert directional relations coordinates to qualitative matrix. In order to improve the ability of the model, metric statistic directional relations are built. Based on the mathematics concept of fuzzy similarity, we define a method to assessment the similarity of directional relations.(3) To overcome the limitation of hard class, defined a fuzzy directional relations matrixes to different regions. This model, which combined the methods of cone-based models and projection-based models, can distinguish the directional relations in the same direction tile. The fuzzy membership functions of straight directional tiles are defined in the way of projection-based models and one of other tiles are defined in the way of cone-based models. For example, the fuzzy membership functions of straight north are built on the east and west coordinates. The results of operations prove the ability of the model to descript the directional relations uncertainty.(4) The definition of fuzzy boundary is crux of the formalism of directional relations between fuzzy objects. There are different definitions of fuzzy boundary in fuzzy topology. After the analysis of characters of these definitions, this thesis select one as to create directional relations models between fuzzy objects. Based on a computational fuzzy topology for computing the interior, boundary and exterior, we define quantitative, qualitative and fuzzy directional relations models. These models transfer the topological fuzzy caused by the fuzzy object to the representation and improve the resolution of directional relations models.This thesis focus on the uncertainty of directional relationship and proposed quantitative, qualitative and fuzzy directional relations models·between crisp objects and fuzzy objects based the classification of topological regions. These models realize multi-levels directional relations representation and conversion between quantitative directional values and qualitative directional concepts.