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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
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Figure 3. Voronoi diagrams of the maps
shown in figure 1.
After a Voronoi diagram is formulated, the total area of the map
is tessellated. Let S be the whole area and the tessellation is
defined by 2»/ 712^" | Then probability of a feature can be
determined by the area it holds as follows:
S
P=— 4
! S (4)
H(M)
The entropy of the metric information, . can be defined as
follows:
HM)=H(B,P,P)==Y PnP =-Y (Ins; psy 260
i=l izpek
As to thematic information, they proposed a similar way that
classify a symbol's neighbours according to their thematic type
and calculate the information according to the classification.
All these methods presented above are based upon Shannon's
information theory, and the major difference between them is
the way to calculate probabilities of symbols. When this
difference applies, the probabilities are utilized to calculate
different kind of information, including statistical information,
topological information and (Geo)metric information as
mentioned above. Yet on one hand, it is reasonable to place
some suspicion on whether this probability model based method
can reflect the internal relationship among geographical feature
or not and we can find that it is not so suitable to infer the
information amount with these method mentioned above. On
the other hand, a common drawback of these methods is that
they can only deduce a ‘relative’ relation among all symbols of
the map, and information amount obtained by these methods
only reveals relative relationship among symbols in the same
map. thus these methods do not concern any relationship
between amount of information and amount of data that
contains this information. Suppose the resolution of map is
changed, usually we can expect that with more details can be
discerned, we can obtain more information from this map. But
all methods above can only get the same amount of information
after the resolution is enlarged. The other drawback of these
methods is that they do not take into account the information
actually obtained by users. A symbol may exist in the map but
cannot be concerned by the user, if this symbol is not attractive
or is too small to be perceived, but the entropy of this symbol is
also calculated. From the description above we can see that to
apply the information amount to determining the minimum
amount of data that we should transfer to a user over network a
new approach of calculating information concerning relations
between data and information must be presented.
3. RASTER-BASED MEASUREMENT OF MAP
INFORMATION
3.1 Relationship between GIS data and information
GIS data is the carrier of spatial information and with the
development of remote sensing and other ways of data
collection, huge amount of GIS data is produced day by day,
thus it provides us a plenty data source for information
transmission, share and utilization. As mentioned above, when
the environment of information share is transplanted to Internet,
the function of GIS data to carry spatial information and even
the meaning of information has changed essentially. In the
traditional desktop environment, the spatial information is
strictly in accord with GIS data that contain it. For instance, a
map with lower resolution contains less information than a map
with higher resolution and with the increasing of resolution, the
data amount of the map increases and the information amount
contained by the map increases accordingly. But in a distributed
environment, the relationship between data amount and
information amount is not such a simple linear one. The
resolution of client display device, the bandwidth of the
network connection and other factors cast influence upon this
data-information relationship and inversely this relationship
impacts the principle of data transformation over network,
which is what we must take into account when providing spatial
information service.
3.2 Raster-based measurement of map information
We start our research of map information amount measurement
from a point that concerning map as a media of carrying
geographical information, this way we can find some metric of
information when GIS data is transferred over networks on
purpose of conveying spatial information In computer, or in
other paper-alike media the way on which maps carry
information is in the form of image that is capable of
stimulating visual sentience of human being. There are still
other ways of drilling information from maps such as computer-
associated analysis, but we cannot depend thoroughly on
computer programs even they are powerful. In other words, a
sophisticated expert may obtain what he want by some software,
but a user of GIS on the Web usually can only rely on his eyes,
and Web GIS service providers can not make the assumption
that clients have some GIS software. Usually, clients have only
browsers, and to those who connect to Internet through wireless
or mobile devices, their devices are of limited storage,
computing capacity and display resolution. To these clients, the
only purpose to transfer data to their machine is to display it
and they can then obtain what they want by their eyes.
With the development of remote sensing, communication
satellite and image processing, high-resolution images have
now become more and more available and popular than before
and bring great change to the way people deal with spatial
information. Images of these types are often stored in the
specially designed image databases and processed by computers.
In this way we can get a large amount of information
corresponding to their high resolution and large data size. But if
it comes to human being things changes. Man' eyes have a
relatively low spatial and frequency resolution. a map with
higher resolution may be useful to the computer, but can not
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