Optics and Photonics Journal, 2013, 3, 79-82
doi:10.4236/opj.2013.32B020 Published Online June 2013 (http://www.scirp.org/journal/opj)
Color Image Enhancement by an Integral Mask-filtering
Approach Employing Nonlinear Transfer Function
Ching-Chung Yang
Department of Multimedia Design, Tatung Institute of Commerce and Technology, 253 Mi-Tuo Road, Chiayi City, Chinese Taipei.
Email: yang10.cc@msa.hinet.net
Received 2013
We demonstrate a brand-new method to sharpen a color image by using an integral mask-filtering technique. The de-
rivatives between the target pixel and its neighbors are transferred by the cubic root function instead of the traditional
linear one. The obtained final image has clearer fine characteristics along with much less overshooting.
Keywords: Image Enhancement; Mask-filtering; Transfer Function; Overshooting
1. Introduction
The mask-filtering approach is widely used to sharpen
images by the implementation of the Laplacian operator
[1, 2]. For a 3 3 mask of [-1 -1 -1; -1 8 -1; -1 -1 -1],
when used to sharpen an image f (m, n), the second de-
rivative could be expressed as the following:
2(,) 8(,)[(1,1)
fmnfmnfm n
fm nfm nfmn
mnf mnf mn
fm n
 
 
Eq. (1) could be summed up as th e following:
(,)[(,) (,)]
where (,)(0,0)
mnAf mnfminj
 
 
 (2)
There are totally eight d erivatives calculated in Eq. (2).
This summation is multiplied by a coefficient A. It is
then imposed on the original image f (m, n) to get an
enhanced new one g (m, n) as the following:
(,) (,)(,)
mnf mnf mn (3)
Eq. (3) is commonly used to obtain sharpened pictures
with satisfactory results in general conditions. While this
mask-filtering technique has some annoying drawbacks.
The major problem is that it sums up all the derivatives
between the targ et pixe l and th e su rro und ing ne ighbor s in
a time. Although this summation could no ticeably change
the target’s own grey-level. Such change at times appears
over-exaggerated. In consequence, there is often some
unwanted overshooting happened on the image objects
after this processing.
The conceptual masking filter is qualitatively shown in
Figure 1 with a 4 4 matrix. The target pixel is sur-
rounded by eight neighbors in different directions. When
using this filter with the traditional transferring, it seems
not avoidable to derive a much larger output via big in-
puts. Hence, the nonlinear calculation is substituted here
for the linear one in Eq. (2) to reduce the overshooting.
In this work, the cubic root function is selected as the
substitution. The big inputs are expected to gradually
saturate after the transferring, while the smaller ones
could derive larger outputs. Hopefully, the processed
image would be with less overshooting as well as clearer
fine characteristics.
2. Algorithm
The cubic root function is chosen here for that its curve
increases rapidly in lower values while saturates gradu-
ally in higher ones. Its curve is shown in Figure 2 in
comparison with the linear transferring.
Figure 1. Conceptual diagram of the ma sking filter. The tar-
get pixel changes its value by exploiting its eight neighbors
oriented in different directions.
Copyright © 2013 SciRes. OPJ
-300 -250 -200 -150 -100-50 050100 150 200 250 300
-0. 8
-0. 6
-0. 4
-0. 2
0. 2
0. 4
0. 6
0. 8
[ (f(m ,n)-f(m+i,n+j))/2 55]
[ (f(m ,n)-f(m+i,n+j))/255 ]
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-
11 13
((,) (,))
(,) []
where (,)(0,0)
fmnfm inj
fmn B
 
 (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
(,) (,)
(,) []
where (,)(0,0)
fmnfm inj
fmn C
 
 (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
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-
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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(a) (b)
(c) (d)
Figure 3. (a) The original image. (b) The processed image by using the traditional Eq. (3). (c) The processed image by using
Eq. (5). (d) The processed image by using Eq. (7).
those found in the traditional linear transferring. While
by using the proposed method, such problem could be
distinctly suppressed. The demonstrated technique is
useful for various applications, such as medical image
enhancement, remote sensing, microscopic image sharp-
ening, etc.
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