DIP1_BP

7/31/2019 DIP1_BP

1/5

7/31/2019 DIP1_BP

2/5

putmedZ .

Level A was able to evaluate whethermedZ a pulse is,

Level B was able to evaluate whetheryxZ , a pulse is. If both

medZ and yxZ , are not pulse, to avoid the unnecessary losses

of the details, the algorithm outputs the valueyxZ , to replace

the median value of the filter window.

In general, the normal median filter has a serious limitationin the processing of the impulse noise with the highly density.

To improve this, the AMF give the method that changing its

maximum sizemaxS .

C. Adaptive Threshold Median Filter (ATMF)To both linear filter and non-linear filter, the decision of

the noise depends on the threshold M. If the difference be-

tween the central pixel and surrounding pixels is more thanM,

then the current pixel is noise.

But for the whole image, the same artificial threshold M

can cause an error in the decision. If the threshold M is

produce by each image itself, moreover, if the thresholdM

can change itself according the image, the filter will more

precise. So the filters performance will more perfect.

1) the value of the threshold M. For any pixel (i,j) in the

image, consider the 55 windows with the pixel ( i, j) in its

center. According the order of the rows and columns in the

matrix, we denote the center pixel by the pixel 13. Thus, for

the 24 pixels surrounding the center pixel, these are pixel 1,

pixel 2,,pixel 12, pixel 14, pixel 15,pixel 24, pixel 25.

We can obtain the difference between the pixel 13 and the

each pixel of the other 24 pixels. Taking absolute value of

above results and sorting them, we denote it by a vectorb.

Define:

4)]7()6()5()4([),( bbbbji +++= (2)Where )4(b is the fourth element in the vectorb, for thesame reason, )7(b is the seventh element in the vectorb.

As a result, for each pixel (i,j), there is ),( ji . So we have

a matrix . Evidently, the matrix has the same scale withthe image. We assume that the scale of the image is NM .

Define:

NMjiM

i

N

j

= = =1 1

),( (3)

[ ] NMjiM

i

N

j

= = =

1 1

2),( (4)

Basing the statistical feature, we define the thresholdMas

follows:

+= M (5)2) the decision of the noise. The procession of decision is

as follow:

If Mji > ),( , the pixel (i,j) is noise, then take the 33

median filter, replace the present pixel by the result.

Or else, the pixel (i,j) is uncorrupted, output the gray of

pixel (i,j).

In brief, if the corresponding ),( ji of pixel (i,j) is more

than the threshold M, then regard present pixel (i,j) as noise,

otherwise, take the pixel (i,j) as uncorrupted.

D. Decision-Based Algorithm for High-Density ImpulseNoises

In [8], Srinivasan and Ebenezer give a new decision-based

algorithm for the high-density impulse noises. Their algo-

rithm, unlike other nonlinear filters, removes only corruptedpixel by the median value or by its neighboring pixel value.

In the algorithm, for any pixel (i,j), consider the 33 win-

dows with the pixel (i,j) in its center. First sorting the 9 pixel

in the widows, denote the result by vectorS. Decision of the

noise depends on the position of the present pixel (i,j) in the

vectorS. If the pixel (i, j) is corrupted, then there are two

cases:

If the vectorSis in the normal order, then the present pixel

(i,j) is a corrupted normal pixel. So, the pixel (i,j) is replaced

by the fifth value of vectorS, that is S(5).

If the vectorSis in the non-normal order, then the present

pixel (i,j) is a noise pixel. So, the pixel (i,j) is replaced by the

value of neighboring pixel value.Or else, left the present pixel (i,j) unchanged.

As a result of this, the proposed method removes the noise

effectively even at noise level as high as 90% and preserves

the edges without any loss up to 80% of noise level.

According the results, the DBAs effect is significant.

However, the restoration is slanted toward the bright region

in the bright. So the DBAs algorithm has its shortcoming in

the restoration of the dark details.

E. Modified Adaptive Median Filter (MAMF)Avoiding the shortcomings of the DBA and the ATMF, we

propose a modified algorithm to deal with impulse noise,

especially for the high-density impulse noises. The algorithmabsorbs both the merit of the DBA and the MAF, and so does

the ATMF. The steps of designing are:

1) modifying the value of the threshold M. Firstly, modi-

fying the method generating vectorb. We consider the 33

windows instead of 55 windows, changing ),( ji as fol-

low,

3)]4()3()2([),( bbbji ++= (6)So we change the matrix similarly. Then we sort the

gray value instead of the absolute value of the difference of

the pixels. Although we have the same equation as (2) and (3)

above, the parameter and has changed, and so on

the += M .2)enhancing the capability of decision on the noise.

If Mji > ),( , the pixel (i,j) is noise, replace the present

pixel by the mean value of the 33 windows.

Or else, according the following weight matrix, replace the

present pixel by the result of the 33 median filter.

3) improving the final effect of the restoration.

After step 1) and step 2), the effect of the restoration is not

good as expected. So we apply the weighting matrix to the

effect of above, especially to the effect of the DBA and its of

16

7/31/2019 DIP1_BP

3/5

the AMF.

III. EXPERIMENTAL RESULTS AND ANALYSISThe chosen images are as follow: the standard 8-bit

272256 Blood image and the 8-bit 512512 Lena image.

The noise considered in this work is bipolar impulse noise

and its density from 55% to 90%, with the equidistant interval

5%.

Adding the impulse noise to the original image first, we

apply several filters to the corrupted images. The result is

shown in the Fig.1 and Fig.2.

Roughly speaking, with the density of the noise increasing,the entire filters effect debases. We can see the effect of

DBA and MAMF is as the same quality and the same

brightness. The filter AMF is better than the filter ATMF.

And the filter ATMF is the worst one.

When noise density is less than 75%, the effect of AMF is

better than DBA and MAMF. As soon as the density is in-

creasing continuous, the effect of AMF is become terrible

obviously.

Furthermore, in the case of noise density less than 75%, the

effect of MAMF is better than the DBA, as shown in the Fig.1

and Fig.2, especially for the preserving of the darkness de-

tails.

Beyond this, we have found that the brightness of AMF is

lowest; the brightness of the DBA and the MAMF is almost

equal. The change of the brightness of the ATMF appeared to

have been: highlow.

Theoretically the ATMFs effects will better than the

AMFs and DBAs. But the facts run counter to the theory.

There are three reasons: computing of the absolute value of

some pixels, taking certain edge pixels for the noise, choosing

of the threshold M. Of course, all those shortcoming of the

ATMF is born with its algorithm. Unfortunately, these entireshortcomings cannot be eliminated, but be weakened.

For performance measurements, we use the mean square

error (MSE) and the peak signal-to-noise ratio (PSNR) de-

fined as

( )NMjiIjiIM

i

N

j

= = =1 1

2)),(),((MSE (7)

Fig.2. Comparative restoration results of image Blood. From left to

right, the first columns is the corrupted image Lena, from the second to

the fifth one is the effect of the filter of AMF,DBA,ATMF and the

MAMF respectively. From the first row to the last row, the density of

the noise is 55%,60%,65%,70% ,75%,80%,85%,90% respectively.

Fig.1. Comparative restoration results of image Lena.From left to right,

the first columns is the corrupted image Lena, from the second to the

fifth one is the effect of the filter of AMF,DBA,ATMF and the MAMF

respectively. From the first row to the last row, the density of the noise

is 55%,60%,65%,70%,75%,80%,85%,90% respectively.

17

7/31/2019 DIP1_BP

4/5

))),(),((

255(log10PSNR

1 1

2

2

10

= =

=M

i

N

j

jiIjiI

NM

(8)

Where ),( jiI is the original image, ),( jiI is the image

processed by the filter, the size of the image is NM .

From the results of the PSNR and the MSE, one can find

the general law: the effect of filter is inversely proportional to

the density of the noise.

Either the value of the PNSR or the MSE, the MAMF is

better than the DBA.

More directly detail can be found in the PNSR and MSE

curve.

As mentioned previously, there is a downward tendency in

the curves. But, the downward tendency of the DBA and the

MAMF is more gently. On the contrary, even the downwardtendency of the ATMF is gently, it is too low. It is worth

mentioning that the PNSR curve of the DBA and the MAMF

cut the PNSR curve of the AMF between the density of 65%

and the density of 75%.

Assembling the value of PNSR and the value of the MSE

and the effect of filter and the result of restoration, the

MAMF is better than DBA.

IV. CONCLUSIONIn this paper, we propose a new algorithm to deal with

impulse noise. Avoiding the shortcoming of the AMF and the

ATMF, the MAMF algorithm integrates the AMF and DBA

method. The MAMF image filter algorithm has character of

the higher ability of the decision the noises, delicate balanc-

ing act between the noise removal and image quality.

The results of experiments show that the MAMF method is

superior to the conventional methods in the impulse noise,

TABLEIVRESTORATION RESULTS MSE OF IMAGE BLOOD

Filter MethodNoise

density AMF DBA ATMF MAMF

55% 11.083 20.5024 84.3824 16.3465

60% 15.1778 23.061 87.9332 18.5622

65% 20.1933 25.6224 89.4132 20.7571

70% 27.3241 28.9124 92.684 23.8005

75% 32.6815 31.2827 93.7088 25.7927

80% 39.8426 35.1414 96.4275 29.2502

85% 48.1436 39.6576 97.7314 32.7981

90% 56.3428 45.8904 100.513 37.6829

TABLEIIIRESTORATION RESULTS MSE OF IMAGE LENA

Filter MethodNoise


55% 10.3452 21.773 85.1929 17.2936

60% 14.6783 24.1325 87.6957 19.374565% 19.699 26.8546 90.9242 21.7949

70% 25.3029 29.4662 93.0972 24.059

75% 31.8996 33.0084 96.1923 27.2803

80% 39.4652 37.2315 98.9675 30.9506

85% 46.6531 41.678 101.443 34.5656

90% 54.74 47.7409 103.824 39.2798

Fig. 4. The MSE curve. The x label shows the density of the noise, from

55% to 90%. The y axis shows the value of the MSE.

Fig. 3. The PNSR curve. The x label shows the density of the noise,

from 55% to 90%. The y axis shows the value of the PSNR.TABLEII

RESTORATION RESULTS PSNROF IMAGE BLOOD

Filter MethodNoise

density AMF DBA ATMF MAMF55% 61.7348 59.0692 52.5928 60.0527

60% 60.3714 58.5585 52.3541 59.5013

65% 59.1333 58.1014 52.2435 59.0165

70% 57.8216 57.5769 52.0048 58.4225

75% 57.0445 57.2348 51.926 58.0736

80% 56.1847 56.7299 51.7352 57.5279

85% 55.3636 56.2051 51.6368 57.0308

90% 54.6809 55.5715 51.4514 56.4281

TABLEI

RESTORATION RESULTS PSNROF IMAGE LENA

Filter MethodNoise


55% 62.0387 58.8129 52.5549 59.8152

60% 60.5221 58.366 52.3736 59.3212

65% 59.2457 57.9021 52.1625 58.8101

70% 58.1595 57.4991 52.0154 58.3809

75% 57.1541 57.0062 51.8066 57.8351

80% 56.2305 56.4835 51.6279 57.287

85% 55.5042 55.9938 51.4742 56.8073

90% 54.8104 55.4042 51.3219 56.2523

18

7/31/2019 DIP1_BP

5/5

especially for the noise with intermediate-density and

high-density. Meanwhile, the MAMF method provides a

quite stable performance over a wide variety of density of

noise. The downward tendency of the PNSR value of MAMF

is more gently. At the same time, the MAMF has higher

quality than the DBA and the AMF.

REFERENCES

[1] R.C Gonzalez, R.E.Woods. Digital Image Processing. New Jersey:Pearson Education, Inc., 2008, pp.325340.

[2] H. Hwang, R. A. Haddad. Adaptive Median Filters: New Algorithmsand Results,IEEE Transactions on Image Processing, vol. 4, no. 4, pp.

499-502, Apr.1995.

[3] S.M.Lu, H.C.Pu, C.T.Lin. A HVS-directed neural-network-basedapproach for impulse-noise removal from highly corrupted images, in

IEEE International Conference on Systems, Man and Cybernetics,

Washington, 2003, pp.72-77.

[4] G.Pok, J.Liu, A.S.Nair. Selective removal of impulse noise based onhomogeneity level information,IEEE Trans. Image Processing, vol.

12, no.1, pp.85-92, Jan.2003.

[5] S.M.Lu, S.F, Liang, C.T.Lin. A HVS-Directed Neural Network-Based Approach for Salt-Pepper Impulse Noise Removal,Journal ofinformation science and engineering, vol.14, no.4, pp.925-939,

Jul.2006.

[6] B.Jiang, W.Huang. Adaptive Threshold Median Filter for Multi-ple-Impulse Noise,Journal of Electronic Science and Technology ofChina, vol.5, no.1, pp.70-74, Mar.2007.

[7] I.Andreadis, G.Louverdis. Real-time adaptive image impulse noisesuppression,IEEE Trans. Instrumentation and Measurement, vol.53,

no.3, pp.798-806, May. 2004.

[8] K.S.Srinivasan, D.Ebenezer. A New Fast and Efficient Deci-sion-Based Algorithm for Removal of High-Density Impulse Noises,

IEEE Signal Processing Letters, vol.14, no.3, pp.189-192, June 2007.

19

Documents

DIP1_BP