地图概括中空间目标几何信息传递模型研究

A Transmission Model of Geometrical Information for Individual Spatial Objects in Cartographic Generalization

地图概括是实现多比例尺地图生产和更新的一种重要理论方法。目前,国际国内制图学界对地图概括的研究主要集中在发展地图概括算法方面,在地图概括的质量评价方面的研究还很少。为此,本文以信息论为理论基础,以地图概括中空间目标几何信息的传递问题为研究对象,以相应空间目标几何信息的传递效率来度量地图概括中单个空间目标的概括质量。首先,建立了地图概括的空间信息传递模型,描述不同比例尺地图之间空间信息的传递过程。进而提出了地图概括过程中空间目标(即:线和面目标)几何信息的传递模型,并且对地图概括中空间目标几何信息的传递状况进行了评估,给出了具体的计算和实现方法。最后,通过实验初步验证了地图概括中空间目标几何信息传递模型的可行性。

Cartographic generalization is an important approach for the production and updating of multi-scale maps.Maps with different scales contain different amounts of spatial information.From the view of spatial information transmission,cartographic generalization may be regarded as a process of information transmission from a larger-scale map to a smaller-scale map.Currently,the scholars from the international cartographic association pay more attention to the algorithms of cartographic generalization.However,there is still a lack of quality assessment for the results by different generalization algorithms.For this purpose,the information theory is utilized in this paper to build a comprehensive transmission model for the geometrical information of individual spatial objects from a larger-scale map to a smaller-scale map,where the transmission ratio of geometrical information is utilized to measure the quality of generalization algorithm.Obviously,the description of geometric complexity for a spatial object is very key to further measure its geometrical information.In this paper,three geometrical indictors,i.e.,angle,vertical distance and length,are taken to express the complexity of individual spatial objects in the process of generalization.On the basis of this,the computation method of geometric information for individual spatial objects is developed,where mutual information as a measure is employed to depict the geometrical information.In the process of implementation,the Shannon communication model is at first given based on the information theory and three information measure indicators（i.e.,information entropy,conditional entropy and average mutual information） are described and used to measure map information.The transmission model of map information is further developed according to the process of cartographic generalization after a simple introduction of communication characteristics of cartographic generalization.On this basis,a general computational model is proposed for individual spatial objects（i.e.lines and areas） to track their geometrical information transmission with cartographic generalization,and the quality of transmission is evaluated by using three quantitative indictors,i.e.,information transmission ratio,information loss ratio,and information incrementation ratio.It is shown by a practical example that the proposed transmission model is valid and correct.