International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
give more information to a man with low physical resolution
because the resolution added can not be perceived. This
resolution-limitation suggests that what a user can get from a
map by eyes is not always the same as what the map contains.
Maybe this limitation is not so important when we access a
local image database and analysis images with corresponding
software, but this situation changes dramatically if it is in the
distributed environment and Internet.
Suppose there is a user with normal sight and he sends an
HTTP request that contains a request for a certain map on the
server. If server responds with a map whose resolution is lower
than client machine, usually the user can only get part of the
information he wants because some details are missed. Through
some progressive schema, server can transfer more data to
improve the map's resolution. After this stage, usually the user
can get more information when he perceives more and more
details of the map. But up to some certain resolution if the .
server transfers more data to improve the resolution and quality
of the map, the user cannot get more information even when he
is given more data. Obviously, server should stop transfer data
on this certain resolution to avoid wasting of bandwidth.
Then our job is to find this resolution. Firstly and obviously,
this resolution must be lower than the client machine's
resolution, for higher resolution details cannot be displayed on
the client's machine. We can find even this simple rule is useful.
We can add some header into the request HTTP message to
include the information about client machine's resolution, and
then server can send data according to this resolution.
But this simple rule is not enough. We need some rules that are
more precise. Suppose there is a map as follows, if we raster it
with different resolution, what we get is listed in Fig 4.
| | | Wi
(a) (b) (c) (d)
Figure 4. A map rastered with different resolution (only bi-level,
grayscale not considered)
In (b), we can only find the line feature passes left-up corner of
the map, which is implied by three black pixels. Then we refine
the resolution from 2*2 to 4*4, as shown in (c). More details
are now displayed and we can get more information about this
feature. But if the resolution is refined from 4*4 to 8*8, the
information increment that we can get is less than previous step.
If the resolution becomes finer and finer, users almost no longer
get more information.
From this process we define a new way of raster-based
information measurement method. From the point of human
sentience, the reason that a pixel can stimulate human eyes is
because its color is different with its context, which is the
collection of pixels adjacent to it as shown in Fig 5., and if the
contraction between it and its context is sharper, it can give
human eyes more stimulus, thus more information accepted by
human eyes. Then we can extract this difference and define the
information of a pixel P as follows:
368
Information, = > (Difference between Pand its context) (6)
C C HIC
C Pic
C C rc
Figure5. A pixel’s context
Information obtained by this approach is relevant to the map’
resolution, and the data size of the map ultimately. We can
utilize the metric of this information to determine how much
data should we transfer to a client with certain resolution. A
QoS map service can be implemented based on this method.
3.3 Features of raster-based information
Then what is the relationship and difference between this new
information measurement and Shannon’s concept of entropy?
Shannon’s entropy is a measurement of ‘uncertainty’, which is
what we want to obtain from the data to be transferred through
communication channel. To a certain map, if the purpose of
transferring it is just for display, to eliminate this ‘uncertainty’
completely, the number of pixels we need is related to both the
display device’s resolution and the map itself. If this map is of
high resolution, some part of ‘uncertainty’ cannot be
determined by a low-resolution display device, then it is useless
to transfer more details beyond this client resolution to the
client. If the map itself is relatively simple (i.e. it contains few
features and the shape of features is straightforward) and do not
contain many details, a lower resolution (may be lower than the
resolution of display device and the original map) can
determine all the ‘uncertainty’ in the map and a higher
resolution is unnecessary. From the point of information theory
the original map contains a certain amount of information, but
what the information theory do not consider is whether all of
this information can be received by the user or not. It is not
adequate to use only information theory to be guidance on how
to deal with data and information, especially on the distributed
environment.
We can infer from the discussion above that a quantitative
relation between information and data must exist. A brief
analysis of this relation is presented as follows. Let us begin by
one single pixel. If the whole map is rastered to only one pixel,
then the data size is the minimum, and the information amount
is 0 due to this pixel has no context. It is obvious for we can
know nothing from a single pixel. That is where we begin. Then
we improve the resolution, and the map becomes finer and finer
as discussed before. In this process, usually information amount
is keep arising. But to a certain resolution, the information will
not arise with the resolution improved for all the details can be
determined with this resolution and the finer version of data is
unnecessary. The curve that describes this relation must usually
be mono-modal with a single peak and where the peak lies
depends on the map itself and resolution of user's display
device. We find this relation through experimental research and
further we can use this relation as a rule to determine how much
data should we transfer through the network, which is what
Section 4 does.
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