Calculation And Evaluation Of Spatial Relations Similarity Degree In Cartographic Generalization

The similarity judgment is the most important concept in human cognition, throughout the total process of the spatial perception, spatial object cognition, spatial pattern cognition. The similarity judgment of spatial relations is the basic content of spatial cognition, which plays an important role in the spatial cognition. In the field of Geographic Information Science, it is an ordinary problem to judge the differences between spatial relations, when integrating and matching data from different versions, different sources and different scales. In addition, the similarity measurement of spatial relations is also the foundation of some other application problems, such as the query and retrieval of spatial data, spatial data mining, and cartographic generalization and so on. It is an important restriction to keep the consistency of spatial relations before and after the cartographic generalization. The cartographic generalization is a process of spatial information abstraction usually generating the problem of spatial data quality. However the study about the similarity of spatial relations is based on the qualitative measurement of conceptual neighborhood, lacking the quantitative measurement and intellectual assessment of the consistency of spatial relations in cartographic generalization.Aiming at the similarity judgment of spatial relations, the paper trys to build a quantitative model to express and calculate whether two spatial relations are similar, and further to judge the similarity degree. The study establishes a method to find the conflicts and inconsistency of spatial relations within the multi-scales expression of geographic objects and build an evaluation method for consistency of spatial relations in cartographic generalization. Thus it can guide to choose the multi-scales expression scheme of spatial objects and to evaluate the quality of generalization results.This paper explores the questions above presenting the following works:1. Analyzing the background in associated fields on spatial relations similarity. Every field of spatial information science has a specific need for the similarity measurement of spatial relations, on the basis of which, the paper analyses and summaries the study progresses and conditions about the similarity measurement of spatial relations from different viewpoints including theories of similarity, similarity of spatial relations and cartographic generalization.2. Elaborating systematically the theoretical bases in support of the research for spatial relation similarity. The basic theories of spatial relations are discussed, including classification, representation model and characteristics of spatial relations. It examines the theories of similarity, including the conception and definition of similarity, measurement model, similarity of spatial relations. It also discusses the mathematical model supporting the similarity of spatial relations, including Delaunay triangulation and Voronoi graphic in computational geometry and conceptual neighborhood of spatial relations. 3. Exploring the conceptual schema of cartographic generalization about spatial mapping. The study extends the conceptual schema of cartographic generalization, elaborating the concepts and classifications of spatial relation mapping, and analysis the expression of spatial relations mapping in cartographic generalization. Two types of spatial relation mapping are distinguished, one is the coarsening expression of spatial relations under the low resolution, the other is correcting about the conflicts of spatial relations produced by entity mapping.4. Summarizing the cases of spatial relation destroying in cartographic generalization from the point of operator view. The operators generating inconsistency spatial relations involves simplification, combination, displacement, exaggeration, collapse, deletion and so on. The analysis depicts possible contradictions, conflict and inconsistency of spatial relations among points, lines and polygons, with the combinations of pictures and texts.5. Exploring the difference measurement of spatial relations in condition of the topological consistency based on the analysis of the characteristics about consistency of spatial relations in cartographic generalization. It establishes a sequence of quantitative models which are used to compare and calculate the similarity degree of spatial relations among objects with different scales:(1) For the conceptual neighborhood and similarity calculation of topological relationship takes the object-oriented topological relationship of polygons for example, it will coarsen and refine the basic topological relationship of 8 resolution. It establishes the difference matrix of conceptual neighborhood of the topological relationship among polygons with multi-resolutions. And through the definition of the maximum difference value, it establishes a computation formula about difference degree of multi-resolutions topological relationships between polygons based on difference matrix of conceptual neighborhood.(2) The calculation model of similarity degree of spatial proximity relation:with the target group as study objects, Delaunay triangulation and Voronoi graphic as research tools, based on the analysis of gradual movement rules of single object and the theory of determining similarity degree according to the number of the same characteristic between two things, establish the similarity models of spatial proximity when position change of one or more objects. It can get the idea of the near-far level among metric objects, though the "relation curve with the same distance" got from the boundary of Voronoi graphic among targets with different classes specific to the particular target. It also establishes the similarity model of proximity relation based on the relation curve with the same distance.(3) The calculation model of quantitative similarity degree integrated by directional relation and distance relation:referring to the idea that using arc length corresponding to angle to express the angle error in survey adjustment theory, we combine angle error and distance error into positional error. In this paper, when integrated difference of directional relation and distance relation is studied, arc length corresponding to azimuth is used to express directional relation so that the units of directional relation and distance relation can be unified into measurement units. Polar coordinates is set up which is appropriate to the integrated representation of relations of direction and distance. Calculation method is put forward to calculate the integrated difference of directional relation and distance relation. According to the above model and human’s cognitive characteristics to spatial relations, visual model is got from the integrated difference by six kinds of directional relation and distance relation with multi-scales and multi-resolutions. Finally, calculation method and process are demonstrated by specific examples, which show the integrated difference and similarity by several objects’directional and distance relation on the average.(4) Similarity of qualitative spatial relations based on the integrated difference model of direction and distance. On basis of existing quantitative calculation model, which is integrated by directional and distance relation, the paper researches the transformation among spatial relations from quantitative to qualitative under different resolutions, and gets other semantic description set of directional and distance relations, whose similarity is different from the referring relations, with different scales and resolutions.6. Theories and methods for assessments about the consistency of spatial relations in cartographic generalization are studied. Based on the analysis of characteristics, contents and research status of qualitative assessments in cartographic generalization, the paper discusses the assessments about the consistency of spatial relations based on the knowledge inference, mainly including the methods and process to evaluate consistency of spatial relations, assessment about the consistency of spatial relations and classifications of knowledge during the build of the knowledge base, the structured expression of knowledge, table structural design of knowledge base and inference mechanism and so on. At last, the feasibility of calculation model and evaluation methodology for spatial relations similarity is verified by the instances.