An intelligent image agent based on soft-computing techniques for color image processing

An intelligent image agent based on soft-computing techniques

for color image processing

Shu-Mei Guoa, Chang-Shing Leeb,*, Chin-Yuan Hsua

aDepartment of Computer Science and Information Engineering, National Cheng Kung University, Tainan, 701, Taiwan, ROCbDepartment of Information Management, Chang Jung Christian University, Tainan, 711, Taiwan, ROC

Abstract

An intelligent image agent based on soft-computing techniques for color image processing is proposed in this paper. The intelligent image

agent consists of a parallel fuzzy composition mechanism, a fuzzy mean related matrix process and a fuzzy adjustment process to remove

impulse noise from highly corrupted images. The fuzzy mechanism embedded in the filter aims at removing impulse noise without destroying

fine details and textures. A learning method based on the genetic algorithm is adopted to adjust the parameters of the filter from a set of

training data. By the experimental results, the intelligent image agent achieves better performance than the state-of-the-art filters based on the

criteria of Peak-Signal-to-Noise-Ratio (PSNR) and Mean-Absolute-Error (MAE). On the subjective evaluation of those filtered images, the

intelligent image agent also results in a higher quality of global restoration.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: Impulse noise; Image filtering; Fuzzy inference; Genetic algorithm

1. Introduction

Nowadays, the techniques of image processing have been

well developed, but there are still some bottlenecks that are

not solved. For example, many image processing algorithms

cannot work well in a noisy environment, so the image filter

is adopted as a preprocessing module. The process of image

transmission could be corrupted by impulse noise and the

corrupted image is different from the original image. A

number of approaches have been developed for impulse

noise removal. For example, a median filter (Arakawa, 1996)

is the most used method, but it will not work efficiently when

the noise rate is above 0.5. Abreu and Mitra (1995) proposed

an efficient nonlinear algorithm to suppress impulse noise

from highly corrupted images while preserving details and

features. The algorithm is based on detection–estimation

strategy, called Signal-Dependent Rank Ordered Mean (SD-

ROM) filter. SD-ROM filter can achieve an excellent tradeoff

between noise suppression and detail preservation, and

0957-4174/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.eswa.2004.12.010

* Corresponding author. Tel.: C886 6278 5123x2059; fax: C886 6278

5657.

E-mail addresses: [email protected] (C.-S. Lee), [email protected].

ncku.edu.tw (C.-S. Lee).

outperform a number of well-known techniques for highly

corrupted images. Weighted Fuzzy Mean (WFM) filter (Lee,

Kuo, & Yu, 1997) has a better ability for removing high

impulse noise. Especially, when the noise rate is above 0.5,

WFM filter still maintains a steady result. Adaptive

Weighted Fuzzy Mean (AWFM) filter (Kuo, Lee, & Chen,

2000) can improve the WFM filter’s incapability in a low

noisy environment, and still retains its capability of

processing in the heavily noisy environment. Russo (1999,

2000) presented the hybrid neuro-fuzzy filters for images,

which are highly corrupted by impulse noise. The network

structure of the filter is specifically designed to detect

different patterns of noisy pixels typically occurring in highly

corrupted data. The proposed filters are able to yield a very

effective noise cancellation and to perform significantly

better than the other approaches. Wang, Liu, and Lin (2002)

presented a histogram-based fuzzy filter (HFF) to the

restoration of noise-corrupted images, which is particularly

effective at removing highly impulsive noise while preser-

ving image details. Lukac (2003) proposed an adaptive

vector median filter for impulse noise suppression and

outliers rejection in multichannel images. Pok, Liu, and Nair

(2003) proposed a decision-based, signal-adaptive median

filtering algorithm for removal of impulse noise. Chang and

Expert Systems with Applications 28 (2005) 483–494

www.elsevier.com/locate/eswa

http://www.elsevier.com/locate/eswa

Fig. 1. The structure of intelligent image agent.

S.-M. Guo et al. / Expert Systems with Applications 28 (2005) 483–494484

Chen (2004) proposed a classifier-augmented median filter

for impulse noise removal from images. Liu (2002) presented

a representation of digital image by fuzzy neural network, by

which the predetermined fuzzy system can be constructed to

express a given two-dimensional (2D) digital image. Tsai

and Yu (1999, 2000) proposed adaptive fuzzy hybrid

multichannel filters for removal of impulsive noise from

color images. Lin and Hsueh (2000) proposed a multichannel

filtering by gradient information. Barni, Buti, Bartolini, and

Cappellini (2000) proposed a quasi-Euclidean norm to speed

up vector median filtering. Vardavoulia, Andreadis, and

Tsalides (2001) proposed a new vector median filter for color

image processing.

Intelligent agents are a new paradigm of modern

Artificial Intelligence (AI) research in computer science.

An agent is a physical or virtual entity, which is capable of

acting in an environment and communicating directly with

other agents (Ferber, 1999). Soft computing differs from

conventional (hard) computing in that, unlike hard comput-

ing, it is tolerant of imprecision, uncertainty and partial

truth. Neural network theory, fuzzy logic, probabilistic

reasoning, genetic algorithms, chaos theory and parts of

learning theory all are in soft computing. Fuzzy inference is

the process of formulating the mapping from a given input

to an output using fuzzy logic. The mapping then provides a

basis from which decisions can be made, or patterns

discerned. The process of fuzzy inference involves member-

ship functions, fuzzy logic operators, and if–then rules.

In this paper, we propose an intelligent image agent to

remove impulse noise from highly corrupted images. The

proposed filter consists of a parallel fuzzy composition

mechanism, a fuzzy mean related matrix process, and a fuzzy

adjustment process. The genetic learning approach proposed

by Cord’on, Herrera, and Villar (2001) and Lee and Pan

(2004) is applied to tune the parameters of the membership

functions. The intelligent image agent performs better than

our previous AWFM operator (Kuo, Lee, & Chen, 2000) and

is able to largely outmatch state-of-the art methods in the

literature. The rest of this paper is organized as follows.

In Section 2, we briefly introduce the knowledge base of the

image agent. Section 3 describes the novel structure of the

intelligent image agent. Section 4 focuses on parameter

encoding and genetic learning. The experimental results for

intelligent image agent are described in Section 5. Finally, we

make the conclusion in Section 6.

Fig. 2. The luminance fuzzy variable with five linguistic terms.

2. Knowledge base construction for intelligent

image agent

An intelligent image agent is a special fuzzy system

having an image knowledge base and a fuzzy inference

mechanism. Fig. 1 shows the structure of the intelligent

image agent.

In this system, the RGB color space is adopted to

represent color images. X(i,j) denotes the color image that

may be corrupted by impulse noise, and Y(i,j) is the output

image after filtering. R($), G($) and B($) are the functions to

produce the projections of X(i,j) in the red axis XR(i,j), green

axis XG(i,j), and blue axis XB(i,j), respectively, i.e. the

functions can be represented as following formulas:

Xði; jÞ Z ðXRði; jÞ;XGði; jÞ;XBði; jÞÞ (1)

RðXði; jÞÞ Z XRði; jÞ (2)

GðXði; jÞÞ Z XGði; jÞ (3)

BðXði; jÞÞ Z XBði; jÞ (4)

After filtering in individual color channel, the function

T($) aggregates the partial results to construct the filtered

color image Y(i,j), that is,

Yði; jÞ Z TðFFðXRði; jÞÞ;FFðXGði; jÞÞ;FFðXBði; jÞÞÞ (5)

In this paper, we propose a new construction algorithm of

image knowledge base (IKB), where the trapezoidal

function is adopted to be the membership function of

fuzzy sets. Eq. (6) denotes the membership function fA(x) of

fuzzy set A.

fAðxÞ Z

0 x!aA

ðx KaAÞ=ðbA KaAÞ aA%x!bA

1 bA%x!cA

ðdA KxÞ=ðdA KcAÞ cA%x!dA

0 xRdA

8>>>>>>><>>>>>>>:

(6)

The trapezoidal membership function of fuzzy set A is

denoted by the parameter set AZ[aA,bA,cA,dA]. Fig. 2

illustrates an example for luminance fuzzy variable with five

linguistic terms. The membership degree is usually a value

S.-M. Guo et al. / Expert Systems with Applications 28 (2005) 483–494 485

in the range [0, 1], where ‘1’ denotes a full membership and

‘0’ denotes no membership.

The image knowledge base consists of the parameters

of the membership functions. In this paper, we define

five fuzzy sets for an image including very dark (VDK),

dark (DK), medium (MD), bright (BR) and very bright

(VBR) shown in Fig. 2. The membership functions of

fuzzy sets VDK, DK, MD, BR and VBR for color

image are denoted as VDKz Z ½azVDK ; b

zVDK ; c

zVDK ; d

zVDK�,

DKzZ ½azDK ; b

zDK ; c

zDK ; d

zDK�, MDzZ ½az

MD; bzMD; c

zMD; d

zMD�,

BRz Z ½azBR; b

zBR; c

zBR; d

zBR� and VBRz Z ½az

VBR; bzVBR; c

zVBR;

dzVBR� where zZ[R, G, B] means the three axes of color

image, respectively. The fuzzy sets describing the

intensity feature of a noise-free image can be derived

from the histogram of the source image. Now we describe

the construction algorithm for the image knowledge base

as follows:

Construction Algorithm for the Knowledge Base of

Intelligent Image Agent:

Input: The histogram of sample image or noise-free

image.

Output: The parameter of the membership functions.

Method:

Step 1:
Decide the overlap range of the fuzzy sets,
respectively.

Step 1.1: Set czVDK of z axis be the first sz

k such that

gzk O0, az

DK )czVDK .

Step 1.2: Set bzVBR of z axis be the last sz

k such that

gzk O00, dz

BR )bzVBR.

Step 1.3: Set

rangez )ðbz

VBR KczVDKÞ

2,Nzf K3

$ %

where Nzf is the number of fuzzy sets of z

axis.

Step 1.4: Set azVDK )0, bz

VDK )0.

Step 1.5: Set czVBR )0, dz

VBR )255.

Step 2:
Decide the parameter values of the membership
function f zVDK of fuzzy set VDK in z axis:

dzVDK )cz

VDK Crangez.

Step 3:
function f zDK of fuzzy set DK in z axis by the

following sub-steps:

Step 3.1: Set bzDK )dz

VDK .

Step 3.2: Set czDK )rangez Cbz

DK .

Step 3.3: Set dzDK )rangezCcz

DK .

Step 4:
function f zMD of fuzzy set MD in z axis by the


Step 4.1: Set azMD )cz

DK .

Step 4.2: Set b2MD )d2

DK .

Step 4.3: Set czMD )rangez Cbz

MD.

Step 4.4: Set dzMD )rangezCcz

MD.

Step 5:
function f zBR of fuzzy set BR in z axis by the


Step 5.1: Set azBR )cz

MD.

Step 5.2: Set bzBR )dz

MD.

Step 5.3: Set czBR )bz

BR Crangez.

Step 6:
function f zVBR of fuzzy set VBR in z axis:

azVBR)cz

BR.

Step 7:
Stop.
Then we can apply the construction algorithm to perform

the red channel, green channel and blue channel in color

image, respectively.

3. The structure of the intelligent image agent

In this section, we describe the structure of the intelligent

image agent. The proposed agent operates on a 3$3

neighborhood in order to restore image data highly

corrupted by impulse noise. Fig. 3 shows the architecture

of the intelligent image agent for the impulse noise removal.

The intelligent image agent consists of a parallel fuzzy

inference mechanism, a fuzzy mean related matrix process

and a fuzzy adjustment process. Now, we describe them as

follows.

3.1. Parallel fuzzy inference mechanism

The architecture of parallel fuzzy inference mechanism is

shown in Fig. 3. In Fig. 3, the structure consists of five

layers. Now, we will describe each layer in details.

Layer 1 (Input linguistic layer): The nodes in the first

layer just directly transmit input values to the next layer. If

the input vector is ðxz1; x

z2;.; xz

9Þ, where xzi is denoted as

input value of the ith pixel. Then, the output for this layer

will be

m1;zij Z xz

ij; i Z 1;.; 9; j Z 1;.; 5; (7)

where xzij is input value of the jth linguistic term for the ith

pixel from z axis.

Layer 2 (Input term layer): Each fuzzy variable of the

second layer appearing in the premise part is represented with

a condition node. This layer performs the first inference step

to compute matching degrees. If the input vector of this layer

is ððxz11; x

z12;.; xz

15Þ; ðxz21; x

z22;.; xz

25Þ;.; ðxz91; x

z92;.; xz

95ÞÞ,

then the output vector will be

m2;zij Z f z

AjðxzijÞ; i Z 1;.; 9; j Z 1;.; 5; (8)

where f zAjðx

zijÞ is the membership degree of the jth term for the

ith pixel.

Layer 3 (Rule layer): The third layer is called the rule

layer, where each node is a rule to represent a fuzzy rule.

The links in this layer are used to perform precondition

Fig. 3. The Structure of the intelligent image agent.


matching of fuzzy logical rules. If the input vector of this

layer is ððf zA1ðx

z11Þ; f

zA2ðx

z12Þ;.; f z

A5ðxz15ÞÞ; ðf

zA1ðx

z21Þ; f

zA2ðx

z22Þ;.

; f zA5ðx

z25ÞÞ;.; ðf z

A1ðxz91Þ; f

zA2ðx

z92Þ;.; f z

A5ðxz95ÞÞÞ then the output

vector will be

m3;zij ZMINff z

AjðxzijÞ; f

zAjðy

zmeanÞg; i Z1;.;9; j Z1;.;5 (9)

Layer 4 (Subrulebase layer): Let m4;zi be the output of the

ith node (iZ1,.,9). The node function is defined by

MAXjZ1;.;5

fm3;zij g; i Z1;.;9 (10)

Layer 5 (Output Linguistic Layer): The final output v is

evaluated by means of the following relation:

v Zm5;z ZX9

iZ1

ðm4;zi !xz

i Þ (11)

3.2. Fuzzy mean related matrix process

The fuzzy mean related matrix process performs the

fuzzy mean of input variables. Eq. (12) denotes the

computing process with fuzzy interval F_mean from z

axis for fuzzy mean related matrix process.

yzmean Z

P9iZ1 f z

F_meanðxzi Þ,xz

iP9iZ1 f z

F_meanðxzi Þ

; ifP9

iZ1 f zF_meanðx

zi Þ

O0

0; otherwise

8<:

(12)

where f zF_mean Z ½0;az;bz; 255�. Then, we set the fuzzy

mean related matrix f zAjðy

zmeanÞ, jZ1,.,5. The fuzzy mean

related matrix is used to evaluate input variables and

perform weighted input variables.

3.3. Fuzzy adjustment process

There are four computation functions including f zKð,Þ,

f z,1ð,Þ, f z

,2ð,Þ, f z

sumð,Þ and two membership functions

including f zsmall and f z

large utilized in fuzzy adjustment process.

Now we briefly describe them as follows:

f zKðm5;z; xz

5Þ Z jm5;z Kxz5j (13)

f z,1ðv; f z

largeðfz

Kð,ÞÞÞ Z m5;z !f zlargeðf

zKð,ÞÞ (14)

f z,2ðxz

5; fzsmallðf

zKð,ÞÞÞ Z xz

5 !f zsmallðf

zKð,ÞÞ (15)

Fig. 4. The architecture of genetic learning process of the intelligent image agent.


f zsumðf

z,1ð,Þ; f z

,2ð,ÞÞ Z f z

,1ð,ÞC f z

,2ð,Þ (16)

The fuzzy sets of small and large denote smallZ[0, 0,

sz, lz] and largeZ[sz, lz, 255, 255] for the fuzzy adjustment

process. The parameters s and l for fuzzy sets small and

large are defined as follows:

sz Z lz,f zF_meanðx

z5Þ (17)

The final output y of fuzzy decision process is the

computing result of f zsumð,Þ. The membership functions f z

large

and f zsmall define the detail preserving process of the filter. It

basically executes full correction of large amplitude noise

pulses, partial correction of median amplitude noise

pulses, and no correction of small amplitude noise pulses.

In fact, the quantity f zKð,Þ can be interpreted as measure

of the modification process by previous layers. If this

measure is large, a full correction is allowed. If this measure

is small, on the contrary, the correction is further reduced in

order to better preserve the quality of fine details and

textures.

Fig. 5. (a) Encoding of fuzzy sets and parameters. (b) Encoding of the

linguistic modifiers of the linguistic terms.

4. Parameter encoding and genetic learning

This section introduces the genetic learning for intelli-

gent image agent. As previously mentioned, we adopt a

supervised learning method based on the genetic learning

for the fuzzy filtering system shown in Fig. 4.

The important questions when using the genetic learning

are how to encode each solution, how to evaluate these

solutions and how to create new solutions from existing ones.

In order to adopt a genetic learning method we encode the set

of fuzzy sets and the linguistic modifiers of the linguistic

terms. Here, we apply the learning approach proposed by

Cord’on et al. (2001) to learning image knowledge base

containing image DB and image RB for the next behavior

learning.

The three components of image knowledge base to be

encoded are the membership functions of the fuzzy

variables and the linguistic modifiers of the linguistic

terms. This chromosome is composed of the following sub-

parts CSza and CSz

b shown in Fig. 5.

1.
CSza is that a 23-gene which encodes the fuzzy set
parameters.

2.
CSzb is that a 5-gene which encodes the linguistic
modifiers of the linguistic terms.

Next, a linguistic modifier used in IKB is a function with

the parameter d that lets us alter the membership functions.

Two of the most well known modifiers are the erosion

linguistic modifier ‘very’ (dZ2) and the dilation linguistic

modifier ‘more-or-less’ (dZ0.5) (Lee & Pan, 2004).

Eqs. (18) and (19) denote the functions of the two modifiers

used in this paper:

mveryðxÞ Z ðmðxÞÞ2 (18)

mmore�or�lessðxÞ Z ðmðxÞÞ0:5 (19)

Fig. 6. The experimental website for intelligent image agent.

Fig. 7. (a) Original ‘Lena’ image, (b) noise image corrupted by impulse noise (

Fig. 8. (a) The fuzzy sets of ‘Lena’ image constructed by t


The factors of the luminance considered here are

the fuzzy variables VDK, DK, MD, BR, and

VBR, represented as ½azVDK ; b

zVDK ; c

zVDK ; d

zVDK�, ½az

DK ; bzDK ;

czDK ; d

zDK�, ½az

MD; bzMD; c

zMD; d

zMD�, ½az

BR; bzBR; c

zBR; d

zBR� and

½azVBR; b

zVBR; c

zVBR; d

zVBR�. The simple genetic algorithm

(Lee & Pan, 2004) operates as follows. The method

starts with a randomly generated population of individ-

uals and produces the subsequent populations by means

of reproduction, crossover, and mutation operators. The

individuals having the best fitness have more chances to

be reproduced. The object function F, which

measures the fitness of each individual, is based on the

mean-absolute error (MAE) between the processed and

prob. 0.4), and (c) result yielded by genetic learning after 50 generations.

he construction algorithm. (b) The tuned fuzzy sets.

Table 1

The parameters of fuzzy sets for ‘Lena’ image constructed by the intelligent image agent

Axis Terms Before tuning After tuning

[a, b, c, d] d l a b [a, b, c, d] d l a b

Red VDK [0, 0, 53, 81] 1 72 28 224 [0, 13, 28, 46] 0.5 40 3 234

DK [53, 81, 109, 137] 1 [28, 62, 84, 112] 0.5

MD [109, 137, 165, 193] 1 [84, 112, 112, 168] 0.5

BR [165, 193, 221, 249] 1 [133, 168, 168, 218] 0.5

VBR [221, 249, 255, 255] 1 [171, 224, 255, 255] 0.5

Blue VDK [0, 0, 1, 35] 1 72 28 224 [0, 1, 3, 69] 0.5 72 7 236

DK [1, 35, 69, 103] 1 [35, 79, 81, 112] 0.5

MD [69, 103, 137, 171] 1 [83, 116, 140, 168] 1

BR [137, 171, 205, 239] 1 [140, 168, 196, 224] 0.5

VBR [205, 239, 255, 255] 1 [219, 224, 255, 255] 1

Green VDK [0, 0, 8, 39] 1 72 28 224 [1, 1, 2, 66] 2 7 72 193

DK [8, 39, 70, 101] 1 [46, 67, 75, 118] 1

MD [70, 101, 132, 163] 1 [84, 121, 136, 182] 1

BR [132, 163, 194, 225] 1 [140, 183, 188, 221] 0.5

VBR [184, 225, 255, 255] 1 [198, 240, 249, 254] 1

Fig. 9. Values of fitness obtained during the learning process and effects of different choices of genetic parameters for ‘Lena’ image.


Fig. 10. MAE curves of the proposed method and others on the color images corrupted by salt-and-pepper impulse noises with the noise corruption rate p,

where pZ0.1–0.8.

Fig. 11. PSNR curves of the proposed method and others on the color images corrupted by salt-and-pepper impulse noises with the noise corruption rate p,

where pZ0.1–0.8.


the original noise-free image:

F Z

P256iZ1

P256jZ1 jy

Rði; jÞKsRði; jÞj

256!256

C

P256iZ1

P256jZ1 jy

Gði; jÞKsGði; jÞj

256!256

C

P256iZ1

P256jZ1 jy

Bði; jÞKsBði; jÞj

256!256

! 3

Table 2

PSNR values of the compared approaches for salt-and-pepper impulse noisy “Le

Filters pZ0.1 pZ0.2 pZ0.3 pZ0.4

Russo 48.09 42.81 38.90 34.04

AWFM 29.86 28.68 27.37 26.13

Median 30.22 29.89 29.37 28.08

Lin 30.73 26.42 23.46 20.62

Proposed 39.37 37.82 36.35 34.62

The learning process stops when an assigned number

of generations have been evolved or when a satisfactory

value of fitness has been obtained.

5. Experimental results

There are many different methods for removing impulse

noise from corrupted images. In this paper, we compare our

approach with other famous filters including Russo’s filter,

na” image with the corruption rate p, where pZ0.1–0.8

pZ0.5 pZ0.6 pZ0.7 pZ0.8

29.94 25.33 21.23 18.15

25.04 23.59 21.36 19.50

25.79 22.69 18.74 15.82

18.04 16.00 14.07 12.83

33.25 31.90 30.17 27.46

Table 3

PSNR values of the compared approaches for salt-and-pepper impulse noisy ‘House’ image with the corruption rate p, where pZ0.1–0.8

Filters pZ0.1 pZ0.2 pZ0.3 pZ0.4 pZ0.5 pZ0.6 pZ0.7 pZ0.8

Russo 51.96 44.09 40.37 36.54 31.49 26.92 22.84 19.72

AWFM 33.79 31.44 29.35 27.67 26.14 24.13 21.44 19.45

Median 33.30 32.65 31.42 29.61 26.76 23.00 19.04 16.05

Lin 31.27 27.29 24.00 21.07 18.18 15.59 13.83 13.02

Proposed 50.28 45.11 42.48 39.75 37.21 35.62 33.22 30.25


AWFM, Median and Lin filter to test the performance of the

intelligent image agent. In the noise model for experiments,

the noise-free image is corrupted by additive identical

independent distribution (i.i.d.) impulse noise with the

corruption rate p, and the impulses take on positive and

negative values with an equal p/2, i.e. the x is a Bernoulli

random variable (Kuo, Lee, & Chen, 2000), as follows:

xði; jÞ Z

sði; jÞCnði; jÞ with corruption rate p=2

sði; jÞKnði; jÞ with corruption rate p=2

sði; jÞ with probability ð1 KpÞ

8><>: (21)

where s(i,j) is the gray level of the noise-free pixel on

location (i,j), n(i,j) is the noise amplitude corrupted on

location (i,j), and x(i,j) is the gray level of the noisy pixel for

s(i,j). In the beginning, we analyze the properties of the

intelligent image agent, then verify the noise removal

capability of the intelligent image agent by comparing with

the other filters. To decide the parameter set of the

intelligent image agent for the experiment, we adopt the

well-known 256!256 ‘Lena’ color image to be the sample

image to construct image knowledge base. In addition, we

also produce a salt-and-pepper noisy ‘Lena’ color image

with a corruption rate 0.4 for the intelligent image agent. We

have chosen a small population of 20 individuals and set the

parameters of genetic learning as follows: crossover

probability 1.0, mutation rate 0.005 and 50 generations.

We have implemented an experimental website to test

Fig. 12. Results of color image ‘Lena’ with pZ0.8 impulse noise.

Table 4

Runtime (in s) consumed at various noise densities p using the intelligent

image agent and other filters based on ‘Lena’ image

Filters pZ0.1 pZ0.3 pZ0.5 pZ0.7

Russo (3!3) 11.87 11.80 11.75 11.90

AWFM (3!3) 1.67 1.63 1.54 1.60

Median (3!3) 1.32 1.36 1.30 1.33

Lin (3!3) 1.26 1.23 1.24 1.25

Proposed (3!3)

(filtering time) (s)

6.62 6.33 6.40 6.64

Proposed (3!3)

(tuning time) (min)

149.2 152.7 150.6 150.3

Fig. 13. Results of color image ‘House’ with pZ0.8 impulse noise.

Fig. 14. Results of color image ‘Lena’ with pZ0.8 impulse noise.


the performance of the proposed approach. Fig. 6 shows the

experimental website.

Fig. 7(a)–(c) shows the noise-free ‘Lena’ image, noise

‘Lena’ image with probability 0.4 and result image by the

intelligent image agent, respectively.

Fig. 8(a) illustrates the fuzzy sets of ‘Lena’ color image

constructed by the construction algorithm. The tuned fuzzy

sets are shown in Fig. 8(b).

Table 1 shows the parameters of fuzzy sets for ‘Lena’

color image constructed by the intelligent image agent.

In order to analyze the behavior of the intelligent image

agent, we choose the well-known ’Lena’ color image to test

the convergence for the intelligent image agent. In addition,

we also choose a small population of 20 individuals and 50

generations and set the crossover probability 0.9, 0.6 or 1.0,

the mutation rate 0.05, 0.1, or 0.005. Fig. 9 shows the fitness

curves of the intelligent image agent with various

parameters for ‘Lena’ color image.

By this experimental result, we can see that genetic

learning is robust for various parameters and images. Next,

we analyze the filtering capability of the intelligent image

agent. We compare the noise removal capability of Russo,

AWFM, Median, Lin and the intelligent image agent in

Fig. 15. Results of color image ‘House’ with pZ0.8 impulse noise.


the following experiments. The parameters of Russo’s

method are setting as follows: M1Z4, M2Z2, crossover

probability 1.0, mutation rate 0.005, population size with 40

individuals and 50 generations. Figs. 10 and 11 show the

MAE and PSNR curves of all compared approaches for

‘Lena’, and ’House‘ images, respectively.

The extrapolated PSNR value of ‘Lena’ image and

‘House’ color image resulted from using various filters at

different noise densities, ranging from 0.1 to 0.8, are shown

in Tables 2 and 3, respectively.

The runtime analysis of the intelligent image agent and

other concerned filters were conducted for ‘Lena’ image

using Pentium IV 2.4 GHz Personal Computer and docu-

mented in Table 4.

Figs. 12 and 13 show the salt-and-pepper noisy ‘Lena’

and ‘House’ images with a corruption rate 0.8, the results of

the intelligent image agent and other filter, respectively.

Figs. 14 and 15 show the subjective evaluation on edge

detection results of Figs. 12 and 13, respectively. By the

results, we can see that the intelligent image agent can

preserve the fine details and textures better than the other

approaches.

6. Conclusions

In this paper, we present an intelligent image agent

including a parallel fuzzy composition mechanism, a fuzzy

mean related matrix process and a fuzzy adjustment process

to remove impulse noise from highly corrupted color

images. The intelligent image agent will receive sample

images or the noise-free color image, then construct image

knowledge base for the filter. It will also adjust the

parameters of fuzzy sets for getting the optimal image

knowledge base. From the experimental results, we observe

that the PSNR and MAE curves of the intelligent image

agent achieve the most efficient results than other

approaches including Russo’s method, AWFM, median

and Lin for removing heavily corrupted additive impulse

noise. Subjective evaluation of the intelligent image agent

also shows a higher quality of global restoration.

Acknowledgements

This work was partially supported by the National

Science Council of TAIWAN (ROC), under Grant NSC

90-2213-E-309-007 and NSC 92-2213-E-309-005.

References

Abreu, E., & Mitra, S. K. (1995). A signal-dependent rank ordered mean

(SD-ROM) filter. Proceedings of IEEE International Conference

on Acoustics, Speech and Signal Processing, ICASSP-95, Detroit ,

2371–2374.

Arakawa, K. (1996). Median filter based on fuzzy rules and its application

to image restoration. Fuzzy Sets and Systems, 77, 3–13.

Barni, M., Buti, F., Bartolini, F., & Cappellini, V. (2000). A quasi-

Euclidean norm to speed up vector median filtering. IEEE Transactions

on Image Processing, 9, 1704–1709.

Chang, J. Y., & Chen, J. L. (2004). Classified-augmented median filters for

image restoration. IEEE Transactions on Instrumentation and

Measurement, 53, 351–356.

Cord’on, O., Herrera, F., & Villar, P. (2001). Generating the knowledge

base of a fuzzy rule-based system by the genetic learning of the data

base. IEEE Transactions on Fuzzy System, 9, 667–674.

Ferber, J. (1999). Multi-agent systems. New York: Addison-Wesly.

Kuo, Y. H., Lee, C. S., & Chen, C. L. (2000). High-stability AWFM filter

for signal restoration and its hardware design. Fuzzy Sets and Systems,

114, 185–202.


Lee, C. S., Kuo, Y. H., & Yu, P. T. (1997). Weighted fuzzy mean filters for

image processing. Fuzzy Sets and Systems, 89, 157–180.

Lee, C. S., & Pan, C. Y. (2004). An intelligent fuzzy agent for

meeting scheduling decision support system. Fuzzy Sets and Systems,

142, 467–488.

Lin, R. S., & Hsueh, Y. C. (2000). Multichannel filtering by gradient

information. Signal Processing, 80, 279–293.

Liu, P. (2002). Representation of digital image by fuzzy neural network.

Fuzzy Sets and Systems, 130, 109–123.

Lukac, R. (2003). Adaptive vector median filtering. Pattern Recognition

Letters, 24, 1889–1899.

Pok, G., Liu, J. C., & Nair, A. S. (2003). Selective removal of impulse noise

based on homogeneity level information. IEEE Transactions on Image

Processing, 12, 85–92.

Russo, F. (1999). Hybrid neuro-fuzzy filter for impulse noise removal.

Pattern Recognition, 32, 1843–1855.

Russo, F. (2000). Noise removal from image data using recursive

neurofuzzy filters. IEEE Transactions on Instrumentation and

Measurement, 49, 307–314.

Tsai, H. H., & Yu, P. T. (1999). Adaptive fuzzy hybrid multichannel filters

for removal of impulsive noise from color images. Signal Processing,

74, 127–151.

Tsai, H. H., & Yu, P. T. (2000). Genetic-based fuzzy hybrid

multichannel filters for color image restoration. Fuzzy Sets and

Systems, 114, 203–224.

Vardavoulia, M. I., Andreadis, I., & Tsalides, Ph. (2001). A new vector

median filter for colour image processing. Pattern Recognition Letters,

22, 675–689.

Wang, J. H., Liu, W. J., & Lin, L. D. (2002). Histogram-based fuzzy filter

for image restoration. IEEE Transactions on Systems, Man and

Cybernetics, Part B, 32, 230–238.

Documents

An intelligent image agent based on soft-computing techniques for color image processing