ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001
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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=\
