C.-C. YANG
80
-300 -250 -200 -150 -100-50 050100 150 200 250 300
-1
-0. 8
-0. 6
-0. 4
-0. 2
0
0. 2
0. 4
0. 6
0. 8
1
f(m,n)-f(m+i,n+j)
[ (f(m ,n)-f(m+i,n+j))/2 55]
[ (f(m ,n)-f(m+i,n+j))/255 ]
1/3
Figure 2. Comparison of two different transfer functions.
The solid line is for the transfer curve in Eq. (2), while the
dash line is for that in Eq. (4).
When choosing this new transfer function, we modify
the target pixel increment from Eq. (2) to be the follow-
ing:
11 13
11
((,) (,))
(,) []
255
where (,)(0,0)
ij
fmnfm inj
fmn B
ij
(4)
Meanwhile, this increment should multiply together a
coefficient B to adapt to different processed picture. And
Eq. (3) is then changed to the following:
(,) (,)(,)
mnf mnfmn (5)
The term f (m, n) – f (m+ i, n+ j) in Eq. (4) actually
represents the high frequency component as we men-
tioned before [3-9]. But the low frequency component of
the image, the term f(m, n) + f( m+ i, n+ j), is not yet
introduced into the masking. That means the brightness
distribution of the whole image still remains unadjusted
after th e above pro cessing.
Hence, we introduce a second mask to take into ac-
count this consideration as the following:
11 1110
11
(,) (,)
(,) []
2255
where (,)(0,0)
ij
fmnfm inj
fmn C
ij
(6)
The term (f( m, n) + f( m + i, n+ j))/2 in Eq. (6) repre-
sents the low frequency component of the image, and
coefficient C would affect its amplitude. The power 11/10
here could be replaced by larger value in case that the
picture is non-uniformly illuminated. Therefore, the il-
lumination adjusting of the full image is going to be ac-
complished by using this second mask. The result image
g (m, n) is finally obtained by an integral mask-filtering
as the following:
(,) 2(,)(,)(,)
mnf mnfmnfmn (7)
Eq. (7) means that a much better enhanced image
could be acquired by subtracting the primary low fre-
quency components alongside of imposing the crucial
high frequency ones.
The coefficients A, B and C in the above equ ations a re
experimentally determined here to obtain better output
results.
3. Experiment
We use Matlab 7.0 to deal with this experiment. The
HSV color system is selected here owing to its conven-
ient acquisition from the Matlab to ol box. A color image
in this system is considered to comprising three compo-
nents including hue, saturation, and value. The value
component represents the brightness of a colorful image.
It is similar to the gray-level magnitude of a colorless
picture. Then we can apply the mentioned algorithm onto
the colored images scope.
The input image shown in Figure 3(a) has a 256 256
dimension., We use the traditional mask-filtering ap-
proach to get Figure 3(b), which is derived by using Eq.
(2) and Eq. (3) with coefficient A = 1/3. There we could
see many unwanted overshooting happened on the object
edges in the picture. Figure 3(c) is the processed result
by Eq. (4) and Eq. (5) with coefficient B = 12. There the
fine characteristics are better enhanced with much less
overshooting. And Figure 3(d) is the final result by us-
ing Eq. (6) and Eq. (7) with coefficient C = 35. The im-
age sharpening is now further reinforced by adjusting the
image illumination.
4. Discussions and Conclusions
By comparing Figure 3(b)-(d), some merits are found
upon the usage of our proposed method. The most im-
portant is that this integral masking is capable of reveal-
ing more details along with less overshooting .
In Figure 3(c), there is much less overshooting hap-
pened on the tree branches and leaves. While its grass
and buildings are clearer than those in Figure 3(b). This
could be deduced that the nonlinear transferring rather
than the linear one is more promising when using the
mask-filtering approach. And by adjusting the illumina-
tion, Figure 3(d) shows that the attic roof is better dis-
tinguished. This is because that the local visibility has
been improved by reducing the low frequency compo-
nents.
Although the increments in Eq. (2), (4) and (6) are
scalars, there are directional messages hidden inside
them. For that they are summations of derivatives along
different directions. But these hidden messages tend to
distort once their values easily got saturated, just like
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