ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
164 
QUANTITATIVE MEASURES FOR SPATIAL INFORMATION OF MAPS 
Zhilin LI and Peizhi HUANG 
Dept, of Land Surveying and Geo-Informatics 
The Hong Kong Polytechnic University 
Kowloon, Hong Kong 
e-mail: Lszlli@polvu.edu.hk 
KEYWORDS: Spatial information, quantitative measure, information content, maps, topological information, thematic information. 
ABSTRACT 
Map is media for recording geographical information. The information contents for a map is of interest to spatial information scientists. In 
this paper, existing quantitative measures for map information have been evaluated. It has been pointed out that these are only measures 
for statistical information and some sort of topological information. However, these measures have not taken into consideration of the 
spaces occupied by map symbols and spatial distribution of these symbols. As a result, a set of new quantitative measures is proposed, i.e. 
for metric information, topological information and thematic information. Experimental evaluation is also conducted. Results show that the 
metric information is more meaningful than statistical information and the new index for topological information is also more meaningful than 
the existing one. It is also found that the new measure for thematic information is also useful in practice. 
1. INTRODUCTION 
For many centuries, map has been as a media for recording and 
presenting geographical information and has played an important 
role in human activities. On a map, geographical information is 
expressed with cartographic symbols. As map is regarded as a 
communication tool, cartographers are interested in the 
effectiveness of map design and the information content of a 
map (e.g. Knopfli 1983, Bjprke 1996). The former can be 
studied either through theoretical analysis or through map 
evaluation experiments similar to a clinic survey. However, it is 
outside of the scope of this study and no further discussion will 
be conducted in this paper. Indeed, this paper is to discuss the 
information content of a map. 
The interest in map information dated back to later 1960s after 
the publication of the work on quantitative measures of 
information by Shannon (1948) and Shannon and Weaver 
(1949), which is normally termed as “information theory” and was 
applied in communication theory. 'Entropy' is a quantitative 
measure for the information content contained in a message. 
The pioneering work in quantitative measurement of map 
information was done by Sukhov (1967, 1970), who considered 
the statistics of different types of symbols represented on a map. 
That's the entropy of these symbols are computed. This is a kind 
of direct application of Shannon's information measure in 
cartography. This is indeed a kind of statistical information. 
Later, Neumann (1987, 1994) did some work on topological 
information of maps. Neumann (1994) demonstrated the 
measurement of topological information for a contour map using 
the information concept developed in communication theory. In 
his work, a dual graph is formed to record topological relationship 
between neighbouring contour lines, and then the entropy of the 
dual graph is computed. Quantitative measures for map 
information has bee used for comparing the information contents 
between maps and images, maps at different scale, evaluation of 
map design and so on (Knopfli 1983, Bjarke 1996). 
However, it is clear that spatial information is more than simple 
statistical information and topological information. It may also 
contain geometric and thematic information. In other words, the 
spatial position and distribution of map symbols should also be 
considered when a quantitative measure is designed for spatial 
information. In this study, Voronoi regions of symbols have been 
employed to model the spatial distribution of map symbol and 
then a new set of quantitative measures for spatial information on 
a map. 
This introduction is followed by an evaluation of existing 
measures (Section 2). Based on the evaluation results, a set of 
new quantitative measures is then introduced (Section 3) and 
these new measures are experimentally evaluated (Section 4). 
Finally, some conclusions are made (Section 5). 
2. EVALUATION OF EXISTING QUANTITATIVE 
MEASURES FOR MAP INFORMATION 
As stated in the introduction section, two important pieces of 
work on map information have been done previously, one for 
statistical information and the other for topological information. In 
order to introduce new measures, it seems pertinent to conduct 
an evaluation on existing work to reveal the advantages and 
shortcomings of such measures. 
2.1 The quantitative measure of information in 
communication: Entropy 
Shannon (1948) was the first person to introduce entropy in the 
quantification of information. He employed the probabilistic 
concept in modelling message communication. He believed that 
a particular message is one element from a set of all possible 
messages. If the number of messages in this set is finite, then 
this number or any monotonie function of this number can be 
regarded as a measure of the information when one message is 
chosen from the set, all choices being equally likely. Based upon 
this assumption, information can be modelled as a probabilistic 
process. He then introduced the concept of 'entropy' to measure 
the information content. 
Let X be the random message variable, the probabilities of 
different message choices are Pi, P 2 , ... Pi, ... P n . The entropy 
of X can be computed as follows: 
H(X) = H(P„p r ,...p n ) = -f j PMP i ) m 
i=\