Simulated Evaluation of Adaptive Median Filter for Noise ... · All simulation outcomes are...

VORAPOJ PATANAVIJIT et al: SIMULATED EVALUATION OF ADAPTIVE MEDIAN FILTER FOR NOISE ..

DOI 10.5013/IJSSST.a.19.05.29 29.1 ISSN: 1473-804x online, 1473-8031 print

Simulated Evaluation of Adaptive Median Filter for Noise Removal on SPN and Random-Valued Impulse Noise

Vorapoj Patanavijit Assumption University of Thailand

Bangkok, Thailand e-mail: [email protected]

Kornkamol Thakulsukanant Assumption University of Thailand

Bangkok, Thailand e-mail: [email protected]

Abstract—One of the most impressive and practical noise removal is the (SMF) Standard Median Filter for removing SPN (Salt and Pepper Noise). Based on the SMF, the AMF (Adaptive Median Filter) has been proposed since 1995 and has superior efficiency however its filter is not desired for removing RVIN (random-valued impulsive noise). Consequently, this paper exhaustively analyses the AMF efficiency and its restriction when this AMF is employed in the noise removal for both SPN and RVIN (random-valued impulsive noise). In this simulated outcomes, nine conventional images (Lena, Mobile (10th Frame), Pepper, Pentagon, Girl, Resolution, Baboon, House, Airplane) corrupted under both SPN and RVIN (random-valued impulsive noise) at plentiful distributions are uses to determine the AMF efficiency in both noise detection precision and noise removal efficiency point of view. Moreover, this statistical analysis is used to investigate the AMF efficiency in term of its mean and standard deviation of PSNR.

Keywords- AMF (Adaptive Median Filter), SPN (Salt and Pepper Noise), SMF (Standard Median Filter), Image Denosing

I. INTRODUCTION OF NOISE REMOVAL FOR SPN (SALT

AND PEPPER NOISE)

Traditionally, digital images are contaminated by impulsive noise [3] due to CCD sensor pixel defect, A/D non-synchronization, transmitting flaw or memory located error. By mathematical theory, the impulsive noise can be divided into SPN (Salt and Pepper Noise), which is fix magnitude value, and random-valued impulsive noise), which is random magnitude value. Thereby, noise removal has been researched for more than three decades because of the requirement of advance image processing and computer vison for instant, detection techniques of car license plate, recognized techniques of human face, resolution enhancing techniques, etc. One of the most impressive and practical noise removal is the (SMF) standard median filter [5] that is proposed for suppressing SPN (Salt and Pepper Noise) because (SMF) standard median filter has a fast calculation time. After two decades, many better and more accuracy noise removal algorithms has been invented for SPN and one of these improved algorithms is the adaptive median filter (AMF) [1], which is established on SMF, thereby AMF and noise removal techniques based on AMF are usually implemented on many modern advance image processing and computer vison for suppressing SPN. The AMF is one of the most worldwide for removing SPN as by the reason of its noise removal efficiency and fast calculation time [2,6].

II. MATHEMATICAL THEORY OF AMF (ADAPTIVE

MEDIAN FILTER)

Assume that x is a noiseless image, where ,i jx is a

noiseless image pixel at location ,i j and min , maxi js x s

where min max,s s is the intensity range of this image x . Let

y is a noisy image, which is degraded by SPN, where ,i jy is

a noisy image pixel at location ,i j that can be

mathematically formulated as following equation.

min

, max

,

at probability

at probability

at probability 1i j

i j

s p

y s q

x p q

(1)

where p q is the noise distribution.

Let ,wi jS is a square area of the pixels with the center at

,i j , which is a size w w for calculation.

The calculation procedure of the AMF (Adaptive Median Filter) can be demonstrated as following. 1. Set the square area of the pixels at 3 3 ( 3w ).

2. Determine of minimum of the pixel intensity ( min,,

wi js ),

median of the pixel intensity ( med,,

wi js ) and maximum of

the pixel intensity ( max,,

wi js ) in this square area of the

pixels (,wi jS ).

3. If minimum of the pixel intensity ( min,,

wi js ), median of the

pixel intensity ( med,,

wi js ) and maximum of the pixel

†The Portions of this work were presented at The 6thInternational Electrical Engineering Congress (iEECON2017),Krabi, Thailand, March 2018 as "Performance Analysis ofDenoising Algorithm Based on Adaptive Median Filter UnderUnsystematic Intensity Impulse and Salt and Pepper Noise" [7]



intensity ( max,,

wi js ) are min, med, max,

, , ,w w w

i j i j i js s s then go

to Calculation Procedure 5. Otherwise increasing this square area of the pixels at 2w w .

4. If the size of square area of the pixels is less than its maximum or

maxw w then go to Calculation Procedure

2. Otherwise ,i jy is replaced by ( min,,

wi js ), median of the

pixel intensity ( med,,

wi js ).

5. If the noisy pixel intensity is min, max,, , ,

w wi j i j i js y s then

,i jy

is detected as noiseless, else ,i jy is detected as noisy

pixel and, then, is replaced by med,,

wi js or med,

, ,ˆ wi j i jx s .

From the above procedure of the AMF, we can briefly demonstrate this calculation procedure in the flowchart as illustrated in the figure 1.

Figure 1. Flowchart of Adaptive Median Filter (AMF) process

III. EXAMPLE OF AMF CALCULATION

This part reviews the detail of example of AMF calculation in order to obviously demonstrate the calculation of the AMF at each step.

This first example can be shown in the figure 2 where

,i jy is a noisy pixel, which is corrupted by for SPN

(, 255i jy ).

Figure 2. The Computaion of AMF (Adaptive Median Filter) procedure

for example 1 (where ,i jy is a noisy pixel).




for example 2 (where ,i jy is a noiseless pixel).


for example 2 (where ,i jy is a noiseless pixel). (Cont.)

From this computation procedure of AMF, the calculated pixels is detected as an noisy pixel without window size increasing (or fix at 3 3 ) and, then, is replaced by med,

,w

i js thereby, ,ˆ 97i jx .

This second example can be shown in the figure 3 where

,i jy is a noiseless pixel, which is , 100i jy . From this

computation procedure, the calculated pixel is initially processed at window size 3 3 . Later, the computation procedure will compute iteratively with window size increasing (at 5 5 ) for detecting the calculated pixel as a noiseless pixel.

IV. SIMULATION RESULTS

All simulation outcomes are computed by the MATLAB software, which are operated by PC with CPU: Intel i7-6700HQ and RAM Memory: 16 GB. In this simulated section, nine standard tested images (Lena, Mobile (10th Frame), Pepper, Pentagon, Girl, Resolution, Baboon, House, Airplane) under both SPN and RVIN (random-valued impulsive noise) are simulated to measure the maximum AMF efficiency. The first subsection of these simulations investigates the precision efficiency when the AMF is implemented for detecting noisy pixels on both SPN and RVIN (random-valued impulsive noise). Later, the second subsection of these simulations investigates the denoised efficiency when the AMF is implemented for suppressing noisy images.

A. Simulation Outcomes for Detected Precision

This simulation investigates the precision efficiency of AMF when the AMF is implemented for detecting noisy pixels on both SPN and RVIN (random-valued impulsive noise). Initially, the original images (or noiseless images) are contaminated by the impulsive noise. By comparing the noisy image with the original image, the noisy pixel location can be detected as the prior information. Later, the AMF is applied for classifying whether noisy pixels or the noiseless pixels. Finally, the precision efficiency can be determined from comparing the detection outcomes from AMF



TABLE III. THE OUTCOMES OF THE PRECISION EFFICIENCY FOR DETECTING NOISY PIXELS AND NOISELESS PIXELS (SPN)

TABLE IV. THE OUTCOMES OF THE PRECISION EFFICIENCY FOR DETECTING NOISY PIXELS AND NOISELESS PIXELS (RANDOM-VALUED IMPULSE NOISE)

procedure and the prior information. The precision efficiency (in percentage) can be mathematically expressed as

estimated noisy pixels estimated noiseless pixels1 12 2

noisy noiselessnoisy pixels noiseless pixelspixels pixels

ˆ ˆAcc 100

y y

y y

(1)

The simulated outcomes of the precision efficiency of the AMF by applying the SPN and the random-valued impulse noise can be shown in Table I and Table II, respectively.

From the simulated outcomes in Table I (and Figure 4) for SPN, the noise detection based on AMF has good and powerful efficiency for SPN thereby the mean and standard



Figure 4. The Outcomes of The Precision Efficiency for Detecting Noisy Pixels and Noiseless Pixels (SPN)

Figure 5. The Outcomes of The Precision Efficiency for Detecting Noisy Pixels and Noiseless Pixels (RVIN)

deviation of the precision efficiency is 92.18971.8253 % for all noisy density levels. The precision efficiency slightly decreases when the noisy density increases therefore these simulation outcomes implies that the precision efficiency does not depend on the noise density.

From the simulated outcomes in Table II (and Figure 5) for random-valued impulse noise, the noise detection based on AMF has not good efficiency for random-valued impulse noise thereby the mean and standard deviation of the

precision efficiency is 65.21028.1585 % for all noisy density levels. The precision efficiency dramatically decreases when the noisy density increases.

B. Simulation Outcomes for Noise Removal

This simulation investigates the noise removal efficiency of AMF when the AMF is implemented for detecting noisy pixels on both SPN and random-valued impulsive noise. Initially, the original images (or noiseless images) are



contaminated by the impulsive noise. Later, the AMF is applied for suppressing noisy image. Finally, the noise removal efficiency can be determined from comparing the noise removal outcomes from AMF procedure and the original image (or noiseless image) in term of quality measurement (PSNR). For indicating the noise removal performance, many state-of-art algorithms for noise removal for instant, Median filter [5], Mean filter [3], and Bilateral filter (BF) [4] are applied on noisy images in order to compare in all simulation. The noise removal efficiency (in PSNR) can be mathematically expressed as

2

10 2

original denoising

10 logˆ

MAXPSNR

x

x x

(2)

where

originalx is the original image (or noiseless image),

denoisingx̂ is processed image by a noise removal technique

(from y ) and MAXx is the maximum intensity value of the

image. From the simulation outcomes in Table III, the noise

removal technique by using AMF can produce the better quality expected noiseless image than many state-of-art algorithms for noise removal. In PSNR perspective, the AMF is better efficiency than SMF about 4.45651.3835 dB, Mean filter about 10.87744.1411 dB and BF about 10.36434.6957 dB, respectively.

From the simulation outcomes in Table IV, the noise removal technique by using AMF has the ineffective efficiency for random-valued impulsive noise. The overall noise removal efficiency is lower than SMF about 4.15192.5141 dB and BF about 1.73791.8031 dB but higher than Mean filter about 1.82501.5606 dB.

From the confines of number of publication slides, these simulation outcomes are illustrated for only three conventional images (Lena, Pepper and Baboon) in order to show the superior efficiency of the noise removal for SPN in term of image quantity (visional outcomes) in Fig. 6, Fig. 7 and Fig. 8, respectively. From these visional outcomes, it can summarize that the expected noiseless image from AMF is clearly better than expected noiseless images from other techniques.

TABLE III. NOISE REMOVAL EFFICIENCY OUTCOMES FOR SPN



TABLE IV. NOISE REMOVAL EFFICIENCY OUTCOMES FOR RANDOM-VALUED IMPULSE NOISE

V. CONCLUSION

This research article exhaustively analyses the AMF efficiency and its restriction when this AMF is employed in the noise removal for both SPN and random-valued impulsive noise. In this simulated experiment, nine noisy images (Lena, Mobile (10th Frame), Pepper, Pentagon, Girl, Resolution, Baboon, House, Airplane) under both SPN and random-valued impulsive noise at plentiful distributions are used to evaluate the maximum AMF efficiency in both noise detection precision and noise removal efficiency perspective. Form the simulated experiment, we can summarize that the AMF has a better efficiency for SPN but the AMF has a limited efficiency for the random-valued impulse noise.

ACKNOWLEDGMENT

The research project was funded by Assumption University.

REFERENCES [1] H. Hwang and R. A. Haddad, Adaptive Median Filters New

Algorithms and Results, IEEE Transactions of Image Processing, 1994.

[2] R. H. Chan, C-W Ho and M. Nikilova, Salt&pepper Noise Removal by Median-Type Noise Detectors and Detail-Preserving Regularization, IEEE Transactions of Image Processing, Vol. 14, No. 10, 2005.

[3] R. C. Gonzalez and R. E. Woods, Digital Image Processing, Prentice-Hall,Upper Saddle River,NJ, USA, 2nd edition, 2002.

[4] V. Patanavijit, The Bilateral Denoising Performance Influence of Window, Spatial and Radiometric Variance, ICAICTA2015, 2015.

[5] W. K. Pratt, “Median filtering,” Tech. Rep., Image Proc. Inst., Univ. Southern California, Los Angeles, Sep. 1975.

[6] Yiqiu Dong, Raymond H. Chan, and Shufang Xu, A Detection Statistic for Random-Valued Impulse Noise, IEEE Trans. on IP, April 2007

[7] Vorapoj Patanavijit, Performance Analysis of Denoising Algorithm Based on Adaptive Median Filter Under Unsystematic Intensity Impulse and Salt&Pepper Noise, The 6th International Electrical Engineering Congress (iEECON2017), Krabi, Thailand, March 2018. (IEEE Xplore)



(c-2) (D=30%)

Corrupted Image

(PSNR=10.8971dB)

(c-3)

3 3 Median Filter

(PSNR=23.6811dB)

(c-5)

7 7 Bilateral Filter

(PSNR=12.7455dB)

(c-5)

25 25 AMF Filter

(PSNR=27.9141dB)

(e-2) (D=50%)

Corrupted Image

(PSNR=8.6553dB)

(e-3)

3 3 Median Filter

(PSNR=15.4758dB)

(e-5)


(PSNR=8.6652dB)

(e-6)

25 25 AMF Filter

(PSNR=20.5725dB)

(a-2) (D=10%)

Corrupted Image

(PSNR=15.6564dB)

(a-3)

3 3 Median Filter

(PSNR=30.7076dB)

(a-5)


(PSNR=19.0151dB)

(a-6)

25 25 AMF Filter

(PSNR=35.3032dB)

(a-4)

3 3 Mean Filter

(PSNR=19.3812dB)

(c-4)

3 3 Mean Filter

(PSNR=14.5829dB)

(e-4)

3 3 Mean Filter

(PSNR=12.2146dB)

(b-2) (D=20%)

Corrupted Image

(PSNR=12.6389dB)

(b-3)

3 3 Median Filter

(PSNR=27.6257dB)

(b-5)


(PSNR=15.0831dB)

(b-6)

25 25 AMF Filter

(PSNR=32.1558dB)

(b-4)

3 3 Mean Filter

(PSNR=16.3208dB)

(d-2) (D=40%)

Corrupted Image

(PSNR=9.6481dB)

(d-3)

3 3 Median Filter

(PSNR=19.0080dB)

(d-5)


(PSNR=11.0367dB)

(d-5)

25 25 AMF Filter

(PSNR=23.7903dB)

(d-4)

3 3 Mean Filter

(PSNR=13.2479dB)

(a-1 - e-1)

Original Image

Fig. 6. The simulation outcomes of SPN expected noiseless images (for Lena)



(c-2) (D=30%)

Corrupted Image

(PSNR=10.6242dB)

(c-3)

3 3 Median Filter

(PSNR=22.0663dB)

(c-5)


(PSNR=18.2898dB)

(c-5)

25 25 AMF Filter

(PSNR=26.7650dB)

(e-2) (D=50%)

Corrupted Image

(PSNR=8.3843dB)

(e-3)

3 3 Median Filter

(PSNR=14.8506dB)

(e-5)


(PSNR=8.4139dB)

(e-6)

25 25 AMF Filter

(PSNR=20.2203dB)

(a-2) (D=10%)

Corrupted Image

(PSNR=15.3798dB)

(a-3)

3 3 Median Filter

(PSNR=30.6116dB)

(a-5)


(PSNR=25.0013dB)

(a-6)

25 25 AMF Filter

(PSNR=36.0391dB)

(a-4)

3 3 Mean Filter

(PSNR=19.0677dB)

(c-4)

3 3 Mean Filter

(PSNR=14.1748dB)

(e-4)

3 3 Mean Filter

(PSNR=11.8117dB)

(b-2) (D=20%)

Corrupted Image

(PSNR=12.3593dB)

(b-3)

3 3 Median Filter

(PSNR=26.5888dB)

(b-5)


(PSNR=21.4752dB)

(b-6)

25 25 AMF Filter

(PSNR=31.6485dB)

(b-4)

3 3 Mean Filter

(PSNR=15.9804dB)

(d-2) (D=40%)

Corrupted Image

(PSNR=9.3998dB)

(d-3)

3 3 Median Filter

(PSNR=18.4321dB)

(d-5)


(PSNR=9.4404dB)

(d-5)

25 25 AMF Filter

(PSNR=23.4995dB)

(d-4)

3 3 Mean Filter

(PSNR=12.9076dB)

(a-1 - e-1)

Original Image

Fig. 7. The simulation outcomes of SPN expected noiseless images (for Pepper)



(c-2) (D=30%)

Corrupted Image

(PSNR=10.5359dB)

(c-3)

3 3 Median Filter

(PSNR=20.3469dB)

(c-5)


(PSNR=17.3238dB)

(c-5)

25 25 AMF Filter

(PSNR=23.9710dB)

(e-2) (D=50%)

Corrupted Image

(PSNR=8.2874dB)

(e-3)

3 3 Median Filter

(PSNR=14.4515dB)

(e-5)


(PSNR=8.3008dB)

(e-6)

25 25 AMF Filter

(PSNR=18.9240dB)

(a-2) (D=10%)

Corrupted Image

(PSNR=15.3487dB)

(a-3)

3 3 Median Filter

(PSNR=23.6544dB)

(a-5)


(PSNR=21.9311dB)

(a-6)

25 25 AMF Filter

(PSNR=27.2354dB)

(a-4)

3 3 Mean Filter

(PSNR=18.7999dB)

(c-4)

3 3 Mean Filter

(PSNR=13.9923dB)

(e-4)

3 3 Mean Filter

(PSNR=11.6301dB)

(b-2) (D=20%)

Corrupted Image

(PSNR=12.3118dB)

(b-3)

3 3 Median Filter

(PSNR=22.4812dB)

(b-5)


(PSNR=19.7091dB)

(b-6)

25 25 AMF Filter

(PSNR=26.2472dB)

(b-4)

3 3 Mean Filter

(PSNR=15.8097dB)

(d-2) (D=40%)

Corrupted Image

(PSNR=9.2209dB)

(d-3)

3 3 Median Filter

(PSNR=17.3112dB)

(d-5)


(PSNR=9.2359dB)

(d-5)

25 25 AMF Filter

(PSNR=21.2088dB)

(d-4)

3 3 Mean Filter

(PSNR=12.6294dB)

(a-1 - e-1)

Original Image

Fig. 8. The simulation outcomes of SPN expected noiseless images (for Baboon)

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