Investigation of the channel capacity of maps with coloured height intervals



Jan Terje Bjørke

Norwegian Defence Research Establishment


Department of Mathematical Sciences and

Technology, Norwegian University of Life Sciences

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

e-mail:, 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







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.