the manipulation of image information, Moreover,
the quantitative analysis and the reasoning pro-
cess relied on that theory can simplify the dis-
cussion of many complicated problems. Therefore,
it has been naturally riveted much attention by
the foreseeing photogrammetrists,
The following exposition will focuses on the di-
gitized image of the panchromatic black and white
film which is quite popular in photogrammetric
operations, Because any color film is able to be
formed into three separated monochromic images
with a basic color through the relevant filters,
it can be treated in a similar way to the panch-
romatic film.
2. AN AVERAGE INFORMATION CONTENT
OF THE DIGITIZED IMAGE
A photographic picture is a continuous variation
of the tone between bright and dark on a plane,
which is different sharply from the general maps
Of lineal graphics, Digitizing a photograph can
Just adopt scanning it line by line and one pi-
xel after another. There are lots of available
devices for doing that work. Here we do not in-
tend to describe them in detail. The result of
scan is a fact that the image with continuous
tone variation has been converted into a grey
value matrix arranged in rows and columns. Ma-
thematically, it is equivalent to transform a
two-dimensional function f s I.) from the continu-
ous distribution on certain planar domain into the
discrete values with a limited number, g(m,n), na-
mely
g£(m,n) » f(max,ney (1)
where m-0,1,2,...,M and ve, 1,2 ane, it AX and aÿ re-'
present respectively the lateral and longitudinal
intervals between the proximal scanned points; M
and N are the numbers of row and column resulted
in image discretization in which there are often
taken ax = 44 and M=N,
The scanned image point is called the pixel as
well, The grey value of each pixel g(my,n) is fur-
arf >
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Fig.1. A piece of digital image.
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ther quantified, that is, it, is changed from the
original value into the nearest integer according
to a selected grey unit or level with equal in-
terval, then the continuous image data are per-
fectly converted into separated digital ones. Fi-
gure 1 is an example of digitized image parcel.
As a rule the umber of grey scale division, S
is selected as S = 2%
’
(k 1s a plus integer.) be-
cause the hardware design of cbmputers adopts
the binary coded system and the measure unit of
information takes a logarithm to the base 2
which is called bit in most cases. When k=1,
S=2 implies the grey scale has only two levels,
that is black and white or zero and one, With
k=8 it follows $2256, the grey scale includes
all integers between O and 255, in which O
shows the darkest pixel and 255 the the brigh-
test. Assume the grey level of each pixel to be
a message, the entire frame of digitized ima-
gery may be regarded as a batch of messages.
Therefore, the maximum probable amount of in-
formation content within that frame, Hmax,
would be as follows:
Hmax = MNlog,S = MNk (bits). (2)
The equation (2) is based on an assumption un-
der an ideal condition that all scanned Pixels
have the identical possibility to take any grey
level on the scale and the choice of grey level
for individual pixels is independent of each
other, In fact, the grey value of every pixel
is always related to those of its surrounding
Fixels and influenced by their variation, other-
wise it is impossible of the image data interpo-
lation. It is able to be aware of that the grey
level variation in each row or column of a digi-
tal image belongs in the Markovian process of the
dincrete data from Information theory, thus the
Probabilities of Selecting any grey level for each
Pixel are not exactly equal to 1/S. Alternatively
there is a heterogeneous allocatior of the grey
levels on any actua] Photograph. One can be given
an impression of the unbalanced Frey distribution
through making an examination of the histogram
Frequency
e 127 255
Grey Level
FQ. 2. Histogram
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
