Color Image Enhancement by an Integral Mask-filtering Approach Employing Nonlinear Transfer Function

doi:10.4236/opj.2013.32B020

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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: [email protected]

Received 2013

ABSTRACT

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)

(1,)(1,1)(,1)

(,1)(1,1)(1,)

(1,1)]

fmnfmnfm n

fm nfm nfmn

mnf mnf mn

fm n

 

 





(1)

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.

C.-C. YANG

-300 -250 -200 -150 -100-50 050100 150 200 250 300

-1

-0. 8

-0. 6

-0. 4

-0. 2

0. 2

0. 4

0. 6

0. 8

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

((,) (,))

(,) []

255

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

(,) (,)

(,) []

2255

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

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

C.-C. YANG

(a) (b)

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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C.-C. YANG

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