关键词: 空间关系, 空间相似性, 多尺度, 点群, 层次分析法

Abstract:

Similarity relation is one of the focal spatial relations in the community of geographic information science and cartography. The spatial similarity calculation in multi-scale map spaces is a research hot spot in Geographic Information Systems (GIS). Point cluster object contains plenty of structured information in its spatial distribution. Its similarity is widely used in the retrieval and query of spatial databases and is also used to analyze and process the spatial data, to recognize the spatial objects from image and to describe the spatial features on maps. Point clusters can be taken as a simple spatial object in geographic space and with studying its similarity we are able to evaluate the result of computer drawing and to calculate complex clusters' similarity, such as the spatial line clusters, the spatial polygon groups and a mixture of points, lines and polygons. Previous theoretical researches mainly focus on a single factor that could impact the point group target, then analyze the impact factor of the point clusters, and in the end, carry out a calculation model without considering the effect of mixing factors. However, so far these researches have hardly made any significant achievements. In this paper, with the consideration of the Gestalt principles from visual cognition, incorporating predecessors' research results, a calculation model is proposed to comprehensively grasp the point clusters similarity in detail. In order to calculate the similarity between different point clusters in the multi-scale map spaces, the main factors that could affect the similarities of point cluster objects were integrated, including the topological relation, the distribution range, the direction relation, the distance relation and the distribution density. Then, this paper discusses the calculation methods of the topological relation, direction relation, distance relation, distribution range and distribution density for point clusters in the multi-scale map spaces. According to the calculations of the five factors, this paper describes the topological relation using the concept of topological neighbor, represents the distribution range by stripping the outside triangles after triangulation, uses the trend of main skeleton for point clusters to express the direction relation, indicates the distance relation by calculating the mean distance between each point and the distribution center for each point cluster, and expresses the distribution range by the overall relative density. Their complete similarity calculation models were put forward respectively at the same time. Analytic Hierarchy Process (AHP) analysis method was adopted for weight assignment, which is a qualitative and quantitative method and can be systematic. Hierarchical analysis method of weighting factor was integrated to address the impact of weight problem. It only uses a small amount of quantitative information, with the help of mathematical methods, complex issues can be simplified. The importance of different factors were taken into account, and the topological relation weight, the direction relation weight, the distance relation weight, the distribution range weight and the distribution density weight were calculated. Finally, the integrated similarity calculation model with the influential factors' weights for point clusters in multi-scale map spaces was established. The validation results of an example shows that the model can accurately calculate the spatial similarity of point clusters in multi-scale map spaces, meanwhile the model is proved to be feasible and effective , which can be applied to evaluate the quality of map generalization.

Key words: spatial relations, spatial similarity, multi-scale point clusters, Analytic Hierarchy Process (AHP)