Impulse noise Detection and Reduction using Fuzzy ...

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Impulse noise Detection and Reduction using Fuzzy logic and Median Heuristic Filter Mahdi Jampour Computer and IT Department at Kerman Institute of Higher Education Kerman, Iran [email protected]

Mehdi Ziari Computer and IT Department at Payame Noor University (PNU) Mazandaran, Iran [email protected]

Reza Ebrahim Zadeh Artificial Intelligence Department at Azad University of Mashhad Mashhad, Iran [email protected]

Maryam Ashourzadeh Department of Mathematic at Payame Noor University (PNU) Kerman, Iran [email protected]

Abstract- In this paper we proposed a new technique for detects and

removes

impulse

noise

in

grayscale

digital

suitable for real applications. In some algorithms noise detection mechanism isn't absolutely correct and some details in images mistakenly replaced that is not good aim, thus some methods used from fuzzy logic to noise detection such as FIDRM that proposed in [10] this method is one of good methods because it can worked in real application with low time-consuming but FMHF (Fuzzy logic and Median Heuristic Filter) that we present in this manuscript is better than FIDRM because work in low time and have better results in PSNR metric.

images.

Proposed method work in two steps, in first step we detect noisy pixels using fuzzy reasoning with lowest uncertainty, and in second step we replace noisy pixels with a heuristic median filter, our heuristic median's filter is combined with human knowledge

for select

best replacement.

We

analysis

this

method with PSNR (Pick Signal Noise Ratio) metric and visual comparison, the results show this method is very good for noise reduction and image restoration in high level noisy images.

Keywords-component; Impulse Noise; Fuzzy Logic; Noise Detection; Noise Reduction

I.

II.

INTRODUCTION

IN GRAYSCALE IMAGES

A grayscale image represented by a two-dimensional array where a location (i, j) is a position in image and called pixel. Often the grayscale image is stored as an 8-bit integer that giving 256 possible different shades of gray going from black to white [11, 12], pixels can have value in [0-255] integer interval, but some pixels in an image have not correct value and they are noise that their value's is 0 or 255, thus we can present below model for a grayscale image that have impulse noisy pixel in relation (1).

Digital grayscale images acquired through many consumer digital products are often corrupted by impulse noise during image acquisition, transmission and/or recording [1]. Three important types of noise existing: impulse noise, multiplicative noise and additive noise, and available many algorithms for reduction noise of each type. Here we propose and descript a new method that detect and replace noisy pixels. One of most popular filters is the standard median filter (SMF) that is based on order statistic and its nonlinear filter [2] but it has some problem, for example this method mistakenly destroys the edges. Adaptive median filter (AMF) is another method for impulse noise reduction [3, 4] although these methods have been improved, but the quality of restoration image is still not satisfactory. Other methods that they are better performance now available: weighted median filters (WMF) [5], center weight median filter (CWMF) [6], adaptive length median filter (ALMF) [7] and alpha trimmed median filter (ATMF) [8]. Most of these algorithms provide suitable and good results at smaller percent of noise levels and find difficulty with higher level noises. The boundary discriminative noise detection filter (BDNDF) can be improved images that corrupted up to 90% noise [9], but this method is too time-consuming and isn't

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IMPULSE NorSE

imgCi,j)

=

{

ORGCi,j) with probability 1 - pr with probability prl 0 with probability prz 255

(1)

Where ORGO, j) is the original image without noise, prl is probability of corrupted pixel by zero value, pr2 is probability of corrupted pixel by 255 value and pr= prl +pr2. On the other hand we can descript an image with noisy pixel such as relation (2) that 11 (i, j) can be include impulse noises such as 255(pepper) and O(salt).

{

. " ORG(i,j) with probability 1- pr lmgCl,j ) - ( with probability pr rJ i,j) -

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Fuzzy LOGIC IN IMPULSE NOISE DETECTION

All membership functions are types of triangular encountering but the number they are variables in the different nature of the natural parameters such as body temperature is originated. The most important reasons for using fuzzy systems are: 1) Excessive complexity of the real world that ultimately led to a description or approximation for a system model is fuzzy. 2) Need to formulate a model for human knowledge to the legal form and lawful way Insert true the system. In this manuscript fuzzy logic used to help new way in impulse noise detection that has been produced to build the fuzzy model of the effective value can be helpful in the impulse noise detection, so in figure [2] shows membership function of this system.

We use from fuzzy logic and fuzzy reasoning for noise correct detection. Fuzzy logic can be decrease uncertainty in noise detection, thus we introduce fuzzy effective value with assistance of neighborhood for each pixel and decision for noisy pixel that is really noise or not. A.

Fuzzy Effective Value

For each of 16 neighbor's pixel of img(i, j) the effective value are calculated and show in relation (3, 4).

Fuzzy if-then rules

C.

With using effective value and other information that I extract from noisy image, rules of fuzzy system are defined as follows:

1) 2)

3) 4) 5) 6) 7) 8)

Figure I : Effective neighbors in the calculated fuzzy gradient value

(") -- t3

VI m,n

tmg . t,]

V2 m,n

img(i,j)

m,n

E

=

(-K.. K}

g

if img(i,j) is if img(i,j) is

N,S,W,E NW,SW,NE,SE

if img(i,j) is if img(i,j) is

NW2,SW2,NE2,SE2

(3)

N2,S2,W2,E2

(4)

9)

Thus Vm,n img(i,j) can be containing an integer value between [0-40], so if all neighbors that show in figure [1] were noisy pixels then Vm,n img(i,j) will be equal by 40. In this subject will be helping us that the fuzzy reasoning can be detect noisy pixel with lowest uncertainty. Figure 2 shows used membership function in this step.

D.

1 2 if V is small and V is small then noise is Large. 2 1 if V is small and V is Medium then noise is Large. 1 2 if V is small and V is Large then noise is Large. if V1 is Medium and V2 is small then noise is Large,

if V1 is Medium and V2 is Medium then noise is Large, if V1 is Medium and V2 is Large then noise is Sma\. if V1 is Large and V2 is small then noise is Large. 2 if V1 is Large and V is Medium then noise is Sma\. 1 2 if V is Large and V is Large then noise is Sma\.

Construction ofFuzzy System

In this System we use from Max-Product for Fuzzy inference engine, singleton Fuzzifier, center average DeFuzzifier and multiplication for algebraic t-norm and max for s-norm, thus inference engine mentioned in Formula 6[13]: 2

Normal

IlB'(y) max;=I[SUP(IlA,(X)I1IlA,(X;)IlB'(Y» ] ;=1

Hi h

=

(6)

I

Thus, system design based on fuzzy inference engine, above the value 7 is calculated [14]: 2

9

10

20

30

40

50

60

70

80

90

f(x)

100

�)I (I1IlA, (X; ) =

1=1

9

1=1

.

lS

AII

,

•••

, xm

. AIm

lS

;=1

I

Y * is center average of fuzzy set of output. In this system

In our method the concepts of critical issues related to the rules and using from relation (5):

if XI

(7)

Where fJ.B'(Y) defined fuzzy membership function, and

Basic Concepts of Fuzzy System

1

'

;=1

I (I1IlA, (x; »

Figure2: Membership function

B.

2

then y

=

BI

we use from singleton Fuzzifier because calculation of FIS is simple, and we use from center average DeFuzzifier because this is most commonly in fuzzy control and fuzzy systems. Properties of this DeFuzzifier is simplicity,

(5)

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Tablel show different between our proposed method by adaptive alpha trim and standard median filter and median based fuzzy reasoning methods.

continuity and explainable. Center average DeFuzzifier mentioned in relation 8 is calculated [15]. 9

y*

=

Lyl,WI

:' ..!.1�-1!":--9

REFERENCES

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IMPLEMENTATION AND RESULTS

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Filtering

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Figure3: calculate average of trim mask

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(75 + 78 +78 +79 +80)/5

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We use from a heuristic median filter for noisy pixels and its neighborhood, this heuristic is similar to trim median filter but this method use from average of neighbor pixels by this concept that good replace pixel is similar to neighbor pixel, in below we introduce this heuristic in 3 step such as: we know there is some noisy pixel in a mask that are zero or 255, thus in step 1 remove all pixels that have 0 or 255 value, then we use from average of other pixels that are not noise in step 2, then in step 3 we replace all noisy pixels that we detect in fuzzy detection mechanism by average that we calculate in step 2. Figure [3] show this idea.

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TABLE I.

RESULT OF FOUR METHOD ADAPTIVE ALPHA TRIM MEDIAN FILTER, STANDARD MEDIAN FILTER, MEDIAN BASED ON FUZZY REASONING AND OUR METHOD ON NOISY DIFFERENT IMAGES.

10% Noise

30% Noise

50% Noise

80% Noise

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Figure4: a is original image, ai, a2,a3 and a4 are Lena images that contained 10%, 30%, 50% and 80% noise, bl to b2 are results of Adaptive alpha trim method, c I to c4 are results of standard median method, and d I to d4 are results of our proposed method.

FigureS: a is original image, ai, a2,a3 and a4 are Boat images that contained 10%, 30%, 50% and 80% noise, bl to b2 are results of Adaptive alpha trim method, c I to c4 are results of standard median method, and d I to d4 are results of our proposed method.

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