Investigation
of the channel
capacity of maps with coloured height intervals

#### Jan Terje Bjørke

Norwegian Defence Research
Establishment

and

Department of Mathematical Sciences and

Technology, Norwegian University of Life Sciences

Address: FFI, P.O. Box 115,
NO-3191 Horten,
Norway

e-mail: jtb@ffi.no, fax: +47 33 04 78 34,
phone: +47 33 03 38 37

#### Kjetil Sæheim

Department of Mathematical Sciences and

Technology, Norwegian
University of Life Sciences

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### ABSTRACT

What are the optimum
number of contour levels in a map with coloured height intervals? This
question is answered in terms of information theory. Shannon information theory
computes the channel capacity of an information source as R=H(Y)-H(Y|X), where
H(Y) is the entropy of the interpreted map and H(Y|X) is the amount of
confusion, i.e., the equivocation of the received message Y when information
source X is used. The computation of H(Y|X) requires
that the transition probabilities are known, i.e., we must know the probabilities
that the different map colours are misinterpreted as well as correctly
interpreted.

In order to get the probabilities considered, an experiment was carried
out. From a digital seafloor model a series of maps were constructed. The topography
of the seafloor was visualized as coloured depth intervals. The number of depth
intervals

varied in the range from 4 to 10. The colour scale from dark blue to light
blue was used to symbolize the depth intervals. Since the visual variable
colour lightness was used to portray the information, we obtained a logical
relation between the selected visual variable and information variable;
according to the recommendations of Bertin. Twenty
five subjects participated in the investigation.

The figure shows how the R value changes as
the number of depth intervals increases from one to ten. The blue line
represents a smoothed curve through the observed values. The maximal R value,
i.e., the channel capacity occurs at 7 classes. An interesting perspective of this
result is that seven classes corresponds to what often is

recommended at the maximum number of classes in choroplet
maps.

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