S. Wang, Z. Wang, Q. Du

School of Resource and Environmental Science, Wuhan University, Wuhan, China



As map serves as important carrier conveying geographic information, it's evident that the characteristic of information capacity is its inevitable attribute. By measuring the information on the map, map user can evaluate the quality of maps, and then improves the technology of map designing. After about 50 years of research on quantitative measure for special information of maps, there have yielded some results and improvements, most of them put their emphasis on the statistics for map information, Li and Huang made a measure based on the Voronoi diagram, and solved the problem of measuring the metric information of the map methodology. However, this method does not treat map as a systematic set of symbols, namely, does not reflect different levels of map symbols occupy space in the difference. The maps show important differences in the quality of character (multi-type) and differences of the number (multi-level).

For multi-level elements, higher-level geographic objects hold a more important status in the human cognition and contain a smaller indefinite degree, a less entropy of self-information. Fortunately, this situation tallies with the spatial division property of weighted Voronoi diagram. According to the related weight functions we could compute each weight value, and then control the scope and size of each level. Owing to classics information measure, this paper brings forward a measure of the entropy of metric information for multi-level elements, then gives a new definition of entropy base on the arrangement of the initial point, the limitation that in the same position build different levels place geographic objects, the results obtains same metric information is improved.

As to multi-type elements, the paper points out the competition of spatial influence between different kinds of geographic objects, blending building-up Voronoi diagram is unreasonable. Considering the layered property of maps, we should calculate their metric information respectively.

This paper is an attempt which carries on the quantitative discussion using mathematics method to measure the map information characteristics. The experiment indicated that, this method conforms to the entropy related conclusion, simultaneously conforms to person's spatial cognition characteristic.