C.-C. YANG

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-0. 8

-0. 6

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0

0. 2

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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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