Page 253 - Digital Analysis of Remotely Sensed Imagery

Image Enhancement 215

diagram (Fig. 6.8d) is searched. Since the output DN is discrete, cau-
tion must be exercised here to determine to which DN the observed
probability is closer, if it falls between two DNs. For instance, the
observed probability at DN 4 (17.86 percent) lies between 12.50 percent
at DN 1 and 18.75 percent at DN 2. Since it bears much more resem-
blance to the second percentage than the first one, it is hence
assigned the new DN of 2 in the equalized image. The calculation of
the output cumulative distribution frequency c (k) in col. 6 of
out
Table 6.1 is mathematically expressed as
⎡ c () − c ⎤
k
c k () = round ⎢ in min × (2 b − ) 1 ⎥ (6.7)
out N −
⎣ c min ⎦
where c (k) = input cumulative distribution frequency at level k
in
c = smallest cumulative frequency of the image
min
b = number of bits at which the output image is recorded
Thus,

⎡ c (11 − c ⎤ ⎡39 0 ⎤
−
)
[
.
)
c (11 = round ⎢ in min × (2 − ) 1 = round ⎢ × 15 ⎥ = round 10 45] = 10
4
⎥
⎣ c min ⎦ ⎦ ⎣ 56 − 0 ⎦
out N −
The newly assigned DNs for other levels are given in col. 6 in
Table 6.1.
After the nearest DN in the output image has been determined, it
is time to calculate the number of pixels at these DNs. This process is
a reversal of calculating the cumulative frequency, namely, to multi-
ply the observed net frequency, defined as the cumulative frequency
at the current DN level minus that at the previous DN level, by the
total number of pixels in the input image. For instance, the cumula-
tive frequency of DN 0 is observed at 5.36 percent. This translates into
3 pixels, or
56 × 5.36% = 3
Similarly, at DN 10 there are

56 × (69.64% − 64.29%) = 3 (pixels)
The scaled frequency at all other DNs is provided in the last
column of Table 6.1. The equalized histogram of the output image is
shown in Fig. 6.8b. There are three disparities between the distribu-
tion in this figure and that in Fig. 6.8a:
• First, the number of DNs at which there are pixels has been
reduced from 14 to 10. This reduction is achieved through
amalgamation of pixels at adjoining values, for instance