TELKOM
NIKA
, Vol.13, No
.1, March 2
0
1
5
, pp. 155~1
6
3
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i1.1274
155
Re
cei
v
ed O
c
t
ober 7, 20
14;
Revi
se
d De
cem
ber 23, 20
14; Accepted
Jan
uary 14, 2
015
Color Image E
nhancement Based on
Ant Colony
Optimization Algorithm
Haibo Ga
o, Wenjua
n Ze
ng*
Coll
eg
e of Information Sci
enc
e and En
gi
neer
ing, Hu
na
n Internatio
nal Ec
on
omics Univ
ersit
y
, Ch
angs
ha
410
20
5, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 3780
20
55@
q
q
.com
A
b
st
r
a
ct
In the coll
ectio
n
, transmissio
n
, deco
d
in
g pr
ocess,
the i
m
a
ges are l
i
kely t
o
prod
uce n
o
is
e. Nois
e
mak
e
s the
ima
ge co
lor d
i
storted a
nd th
e arti
culati
on dr
op
p
ed, an
d als
o
a
ffects the imag
e qu
ality. Du
e
to
different ca
use
s
, there are
dif
f
erent
types
of nois
e
, an
d th
e i
m
p
u
lse
nois
e
is
most co
mmo
n
a
m
ong t
h
e
m
w
h
ich exert gr
eat infl
uenc
e o
n
the i
m
a
ge
q
uality. T
h
is p
a
per, accor
d
in
g
to
the char
acte
ristics of the c
o
lor
imag
e, co
mb
in
es the
a
n
t col
ony
alg
o
rith
m
and
w
e
ig
hted vector me
dia
n
filter
met
hod
to put forw
ard
a
n
alg
o
rith
m for the impu
lse n
o
is
e remova
l an
d the co
lor i
m
ag
e enh
anc
e
m
en
t. T
h
is method
finds the o
p
ti
ma
l
filter ba
nk par
a
m
eter
by a
n
t colo
ny opti
m
i
z
a
t
ion (ACO) a
n
d
process
e
s i
m
age
poi
nts po
ll
uted by th
e no
i
s
e
to achiev
e the
purpos
e of ima
ge e
nha
nc
ement an
d
pr
otect the imag
e detai
ls
and
edg
e infor
m
ati
on.
Simulati
on ex
p
e
ri
ment pr
oves
the corre
ctnes
s and val
i
dity o
f
this metho
d
.
Ke
y
w
ords
: ant
colony o
p
ti
mi
zation, w
e
ig
hted
ve
ctor me
dia
n
filter, imag
e e
nha
nce
m
e
n
t
1. Introduc
tion
Noi
s
e can b
e
unde
rsto
od
as vari
ou
s factors inte
rferi
ng with p
eopl
e's u
nde
rsta
n
d
ing o
r
analysi
s
of i
m
age
so
urce
inform
ation
receive
d
by
p
eople’
s visual
org
an
or
system se
nsors.
The
comm
on noi
se
is
the unp
redicta
b
le ran
dom sign
al a
nd it
can
onl
y be
kno
w
n
by mean
s of
the
prob
ability statistical m
e
th
od. Noi
s
e is very
vital fo
r the image
pro
c
e
ssi
ng a
nd affects e
a
ch
image p
r
ocessing
step su
ch as the inpu
t, collecti
on a
nd pro
c
e
s
sin
g
and the ou
tput result [1].
The noi
se
re
moval ha
s b
e
com
e
a ve
ry important
step in imag
e
pro
c
e
ssi
ng.
The
comp
ari
s
on
betwe
en the
gray imag
e
and
colo
r i
m
age
sho
w
s
that the gray image p
r
oce
s
sing m
e
thod
developm
ent
is more m
a
ture, whil
e, the colo
r i
m
age mo
re
worth
studyi
ng with the
rapid
developm
ent of compute
r
i
n
formatio
n proce
s
sing te
ch
nology [2].
Becau
s
e
the
col
o
r imag
e
is multichan
nel
sign
al, n
a
mely the
m
u
ltidimen
sion
al si
gnal,
whi
c
h ma
ke
s the noise re
moval be
com
e
more
com
p
lex. The imp
u
lse n
o
ise is
a very comm
on
and typical n
o
ise
which h
a
s a very big
impact
on th
e image [3]. One of the effective metho
d
s
removin
g
the
impul
se
noi
se is the ve
cto
r
me
dian
f
ilter (VM
F
), h
o
wever, ju
st a
s
t
he me
dian
filter
algorithm, the vector
median filter
still faces s
hort
c
omings,
and, because
of
the
color i
m
age
sign
al’s multi
c
ha
nnel p
r
op
erty, such li
miting factor becom
es in
cre
a
si
ngly more an
d more,
therefore, there still exist great potential to
improve the vector medi
an filter [4].
This p
ape
r, base
d
on ab
ove requi
rem
e
n
t
s, st
udie
s
th
e appli
c
ation
of the vector
median
filter technolo
g
y in the
imp
u
lse
noi
se
re
moval of
th
e
colo
r im
age.
This pap
er a
pplie
s ACO t
o
th
e
colo
r ima
ge’
s vector filte
r
in
g metho
d
an
d finds opt
im
al filter ba
nk
para
m
eter by
ACO to
achieve
the purp
o
se of image en
han
ceme
nt. At first,
th
is pape
r analy
z
es the ch
ara
c
teri
stics of the
impulse n
o
ise, the im
age
’s
weig
hted
vector f
ilter method, and
then studi
e
s
the
ant co
lony
algorith
m
p
r
i
n
cipl
e a
nd b
a
si
c id
ea, b
a
s
ed
on
th
is
,
puts
forwards
the im
ple
m
entation step
s
of
colo
r imag
e filter enh
an
ce
ment ba
sed o
n
ACO al
g
o
rit
h
m, and finall
y
the experim
ental sim
u
lati
on
and the re
sult
analysi
s
.
2. Color Image Filtering
Enhanceme
n
t Methods
Colo
r image
filtering aimsto simulta
n
eou
sl
y achie
v
e the following three o
b
jective
s
:
wea
k
e
n
ing
n
o
ise, m
a
intai
n
ing to
ne
s a
nd p
r
ote
c
ting
edg
es or d
e
tails. Th
e t
h
ree
-
dim
e
n
s
i
onal
spa
c
e
is requ
ired
wh
en
ex
pre
ssi
ng
a
co
lor
pixel. Colo
r
spa
c
e
or
Co
lor m
odel
o
r
Colo
r
coo
r
di
n
a
te
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 1, March 2
015 : 155 – 1
6
3
156
system i
s
th
e thre
e-dime
nsio
nal d
e
scription
of
th
e color pe
rception. Ea
ch
col
o
r
ca
n
be
rep
r
e
s
ente
d
by a dot in the colo
r sp
ace
.
2.1. Chara
c
teristics o
f
Impulse Nois
e
In image p
r
o
c
e
ssi
ng, imp
u
lse
noi
se, that is, salt-p
eppe
r noi
se,
will cau
s
e b
l
ack an
d
white d
o
ts in
the imag
e, esp
e
ci
ally, in part
s
whe
r
e
are ve
ry da
rk
or ve
ry bright. Gene
ral
l
y
speaki
ng, the pixel grayscale value in the image
i
s
a continuous gradation.
The grayscale of
the
impulse noi
se dot is the
sup
e
rp
ositio
n of the no
rmal gray
scal
e of this dot
and the n
o
i
s
e
grayscal
e.
W
h
en
a p
i
xe
l in
th
e image
is in
ter
f
e
r
ed
b
y
th
e impu
ls
e n
o
i
s
e
, its
gr
a
y
s
c
a
l
e
va
lu
e
w
ill
differ greatly from tho
s
e of
the adja
c
e
n
t pixels.
When
the noi
se g
r
ayscale i
s
po
sitive, it appe
ars
in the i
m
ag
e
as
an i
s
ol
ate
d
b
r
ight
dot.
Whe
n
th
e
im
pulse n
o
ise g
r
ayscale
is n
egative, it ap
pears
as an i
s
olat
ed da
rk d
o
t. Impulse n
o
i
s
e dot an
d
the typical va
riation
cha
r
a
c
teri
stics of the
neigh
borhoo
d
pixel graysca
l
e of are sh
o
w
n in Figu
re
1 (a) a
nd (b
):
(a)
(b)
Figure 1. Impulse n
o
ise model
2.2 Weigh
t
e
d
Vector
Direction
Dista
n
ce Filtering
o
f the Image
The natural image is no
n-stati
ona
ry. The premi
s
e of filteri
ng ope
ra
tion is that the image
can
be divide
d into seve
ra
l smalle
r a
r
e
a
s, an
d ea
ch
area
ca
n be
rega
rd
ed a
s
stationa
ry. The
smalle
r im
ag
e a
r
ea
is det
ermin
ed
by the
sup
port
wi
ndo
w. Filter
wind
ow is
an
impo
rtant p
a
rt of
spatial filteri
n
g, whi
c
h i
s
rel
a
ted to the
si
ze of
the
win
dow, di
re
ctio
nality and pa
rtition, etc. All the
pixels
12
,,
,
N
Wx
x
x
in a windo
w aro
und
the cente
r
pixel, is sho
w
n i
n
Figure 2:
Figure 2. Pixels in the wi
n
dow
In 1993, Tra
hania
s
put fo
rwa
r
d the Ba
sic Ve
ct
or
Di
rectio
nal Filte
r
(BVDF
)
, wh
ich is
a
method
ba
se
d on th
e di
re
ction i
n
form
ation in
col
o
r v
e
ctors. In
19
95, Karakos
put forwa
r
d t
h
e
Directional-di
stance Filt
ers (DDF
),
whi
c
h integ
r
ate
s
t
he m
e
t
hod
s of
Vecto
r
M
e
dian Filter (V
MF)
and BVDF. T
hey have a common d
r
a
w
back, that is,
t
hey all negle
c
t that the pi
xels in the filter
x1
x2
x3
x4
x5
x7
x8
x9
i
or
j
i
or
j
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Colo
r Im
age Enhan
cem
e
n
t
Based on A
n
t Colon
y
Opt
i
m
i
zation Algorithm
(Haib
o
Gao)
157
wind
ow
are
also
relate
d t
o
sp
ace di
stance. Thi
s
crucial
point
wi
ll affect the result of im
ag
e
filtering. Ho
wever, weig
hted vector
dire
ction
di
stance filter can make up
this dra
w
b
a
ck.
Weig
hted ve
ctor filte
r
me
ans that ea
ch pixel in
the
weig
hted ve
ctor filte
r
ha
s a corre
s
po
n
d
ing
weig
ht value.
The filter re
sult is rep
r
e
s
e
n
ted
throug
h
the sp
ace di
stance
s
b
e
twe
en the
pixels
in
the filter wind
ow [5].
In weighte
d
vector di
re
ctio
n distan
ce filter
, each pixel
in the same
filter windo
w
has two
corre
s
p
ondin
g
weig
ht value, which co
ncern
s
two fa
ctors, o
ne is ve
ctor di
re
ction,
and the othe
r i
s
vector
dista
n
c
e. In the
filter
wind
ow,
suppo
se th
ere
are
k
pixels
,,
,
,
12
1/
2
,,
,
,
p
qp
q
p
q
p
q
K
K
ZZ
Z
Z
,
usin
g
12
,,
K
ww
w
to re
pre
s
ent th
e
coeffici
ent of
the
vecto
r
distan
ce wei
ght
value,
u
s
ing
1,
2
,
,
r
wr
K
to re
pre
s
e
n
t the real n
u
m
ber,
who
s
e
ran
ge i
s
[0,
1
], multiplying wei
ghte
d
vector di
stan
ce with weig
hted angle di
stan
ce, wh
ose prod
uce ca
n be rep
r
e
s
e
n
ted with
,
pq
r
,
,
pq
r
represents th
e weig
hted vector di
re
ctio
n distan
ce, a
s
sh
own in the followin
g
:
1
1
11
11
1
,,
,
,
,
11
1
11
,1
,
2
,
KK
y
pq
pq
pq
pq
pq
rr
r
r
r
r
r
rr
rr
r
r
wz
z
w
A
z
z
r
K
(1)
In the filter
windo
w, u
s
ing
re
pre
s
e
n
t ve
ctor di
stan
ce
and
ve
ctor
angle, th
at i
s
, the
output. If each pixel
,
1,
2
,
pq
r
zr
K
in
,
p
q
is
seq
uen
ce
d in
an a
s
cendi
n
g
ord
e
r
acco
rding
to the vector di
stan
ce
,
ij
r
in (1
), and g
a
in the re
sult after seq
uen
ci
n
g
,,
,
,
12
1/
2
,,
,
,
pq
pq
p
q
pq
K
K
zz
z
z
, then
,
,
1
p
q
pq
Yz
rep
r
e
s
ents that the
filter
keep
s calculating
till
gainin
g
the correct re
sult. Therefore, su
ch filter
ing i
s
called weigh
t
ed vector di
rection di
stan
ce
filtering [6].
3. Principle
and Applica
t
ion of An
t Colon
y
Algorithm
3.1. Basic pr
inciple and idea of an
t c
o
lon
y
algorithm
(1) Ba
sic id
ea
Ant colony al
gorithm i
s
the imitation of
ant foragin
g
behavior in t
he natu
r
e. During the
ant foragi
ng
pro
c
e
ss i
n
th
e nature, alth
ough th
ere are
many
ba
rri
ers
between
ant ne
st and
food
sou
r
ce, a
n
ts
have al
way
s
been
abl
e to
bypass
ob
sta
c
le
s a
nd fin
d
the sho
r
test
p
a
th bet
wee
n
t
he
nest an
d so
urce to acqu
ire food. Wh
en the ex
teri
or environme
n
t is cha
nge
d, the ants can
quickly ada
pt to such ch
an
ge to find ne
w optimal
p
a
th. The main reason lie
s in the mechani
sm
of commu
nication amon
g the ants. Thi
s
me
chani
sm
is the phe
ro
mone which is an imp
o
rta
n
t
cha
nnel fo
r
ants to
com
m
unicate
with ea
ch
other, which at th
e sa
me time
also
ma
ke
s ant
s
alway
s
tend to sele
ct the path with hig
her ph
er
omo
ne den
sity in the pro
c
e
ss
of sea
r
chi
ng
for
food.
(2) Ant’
s path
search
Such a p
o
siti
ve feedba
ck
mech
ani
sm
will also occur when a
n
ts meet obsta
cles. As
sho
w
n i
n
the
followin
g
Fig
u
re
1, assu
m
e
that A
is th
e ant n
e
st a
n
d
D th
e food
sou
r
ce, when
the
ant rea
c
he
s
B from A, th
e ant will rea
c
h C by
sel
e
cting ra
ndom
ly to pass E or F, and lea
v
e
pheromo
n
e
s
along
the
wa
y. At first, wi
th the
sam
e
prob
ability, al
l ants will
se
lect E
or
F t
o
bypass the o
b
sta
c
le, in thi
s
way, the ph
erom
one
den
sity on path B
E
and BF are
same i
n
a
sh
ort
perio
d of time
. But with the
passa
ge of ti
me an
d the
p
hero
m
on
e vol
a
tility, phero
m
one
den
sity on
path BE is relatively low than BF due to the path BE is longer than path BF. In selecting
the
path, sub
s
eq
uent ants will
tend to sele
ct path
BF, and in this wa
y, the phero
m
one de
nsity
on
path BF
will f
u
rther in
crease,
while, the phero
mone
density on path BE
will sharply decrease
due to
the
a
n
t numb
e
r se
lecting
path
BE decrea
s
e
s
, an
d the
n
t
he a
n
t num
b
e
r
sele
cting
such
path will sha
r
ply redu
ce, th
us a ne
w p
o
sitive feedback me
cha
n
ism
will be form
e
d
and finally
all
ants tend to select on
e sh
o
r
test path to b
y
pass ob
stacl
e
s in orde
r to rea
c
h the foo
d
sou
r
ce [7].
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 1, March 2
015 : 155 – 1
6
3
158
Figure 3. Ant colo
ny foragi
ng sketch ma
p
We
ca
n see
that du
ring
the fora
ging
pro
c
e
ss,
all ants co
ordi
n
a
te
with ea
ch
othe
r.
Although, the
ant nu
mbe
r
i
n
the e
n
tire
a
n
t col
ony
is n
u
merou
s
, the
entire
ant
col
ony refle
c
ts the
self-o
rg
ani
zin
g
characte
ri
stic, a
nd fol
l
owin
g
p
r
in
ci
ples shoul
d
be m
e
t to
co
mplete
such
c
h
ar
ac
te
r
i
s
t
ic:
(1) Sea
r
ch ra
nge
The i
ndividua
l ant i
s
ve
ry tiny and
its pe
rcept
ive
range is very limit
ed. Us
ually, the range
that one
ant
is
able
to o
b
se
rve i
s
a
che
c
kered
world. T
h
is ra
nge i
s
th
e 3
*
3
che
c
k wit
h
8
d
i
r
e
c
t
io
ns
and
its
ad
va
nc
in
g
d
i
s
t
a
n
c
e
of o
n
l
y 1
.
T
h
e
a
n
t
s
t
ep
se
arc
h
is
on
ly w
i
th
in
su
ch
a sma
l
l
rang
e.
(2) Ant search environ
men
t
The environment where artificial ants are
in
i
s
a virtual world in
whi
c
h the ant will
also
encounte
r
ob
stacl
e
whe
n
sea
r
ching, an
d this obsta
cl
e is also a ki
nd of visual e
x
isting form
s. In
orde
r to make the ants ha
ve large se
arch ra
nge po
ssibly, we assume a volatile mech
ani
sm
for
the ph
eromo
ne
rele
ase
d
by ants d
u
rin
g
the
movi
ng
process to
make
the
virt
ual e
n
viron
m
ent
more
clo
s
e to
the ant’s env
ironm
ent in the nature p
o
ssibly.
(3) Sea
r
ch rul
e
Search
whet
her th
ere
is a
n
y food in
th
e
ra
nge t
hat
can
be
perce
ived by ea
ch
ant, and
get over if th
e
r
e i
s
food,
oth
e
rwi
s
e,
ch
eck whet
h
e
r th
ere is
any ph
eromone. Sel
e
ct the point
with
the most p
h
e
r
omo
n
e
s
with
in the ra
nge t
hat ca
n be
p
e
rceived a
nd
move to this
point with la
rger
prob
ability, that is to
say, e
a
ch
ant
will
make
mista
k
es in
sm
all p
r
obability an
d
doe
s not
always
move toward
s the p
o
int wi
th the mo
st p
hero
m
on
es.
The rule that
ants findi
ng t
he ne
st is
si
milar
to the above, but it only respond
s to ne
st phero
m
on
es.
(4) Mov
e
rule
Each
ant moves towards the di
rection with
the mo
st pheromones in larger probability,
but when there i
s
no
pheromone
to gui
de,
the ant will
move on accordi
ng
to
t
he
original
m
o
ve
dire
ction
and
there
may
be
small
ra
ndom
distu
r
b
a
n
c
e
along
the
mo
ve direction.
In o
r
de
r to
av
oid
circling a
r
o
u
n
d
, the ant can
rememb
er a
nd avoi
d the
positio
n wh
ere it has gon
e whe
n
moving
.
(5) O
b
sta
c
le
avoidan
ce rul
e
If there are
obstacles bl
ocki
ng the
direction
where the ant is t
o
move, the ant will
rand
omly ch
o
o
se a
nothe
r
dire
ction, and
will mo
ve according to th
e rule
s of foraging b
ehavi
o
r
unde
r the gui
dan
ce of the pheromo
ne.
(6) Di
ssemin
ating phe
rom
one rul
e
The phe
rom
o
ne dissemi
n
a
t
ed by each a
n
t at t
he time
when it finds the food or the nest
is the mo
st, which b
e
come
s fewe
r and f
e
we
r as the
moving dista
n
ce in
crea
se
s.
Acco
rdi
ng to
these few si
mple rule
s, there i
s
no di
rect relation
ship amon
g a
n
ts, but
each ant interacts
with the environ
ment
and is
a
s
so
ci
ated togethe
r by the phero
m
one bo
nd[8,
9].
3.2. Basic an
t colon
y
alg
o
rithm applied to TSP
Acco
rdi
ng to
the phe
romo
ne upd
ate strategy, t
he pri
n
cipl
e that the ant-cycle al
gorith
m
is appli
ed to TSP problem
s is a
s
follows:
First, rand
om
ly
place
m
ants in
n
citie
s
, an
d ea
ch
ant
1,
2
,
,
kk
m
g
enerates on
e
action path
with
1
n
steps
k
Tt
accordin
g to rule
s of prob
ability transform
ation, and its le
ngth
is
k
L
t
.
m
paths wi
ll be gene
rat
ed wh
en all
ants have
co
mpleted the t
r
avel aroun
d for on
e
A
B
C
E
d=1
d=0
5
(a)
(b)
(c)
A
B
C
E
A
B
C
E
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TELKOM
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ISSN:
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930
Colo
r Im
age Enhan
cem
e
n
t
Based on A
n
t Colon
y
Opt
i
m
i
zation Algorithm
(Haib
o
Gao)
159
time. The shortes
t
path
Tt
will be g
a
ine
d
after comp
aring l
ength
s
of
m
paths.
Upd
a
te
pheromo
n
e
s
on m path
s
a
fter an iterati
on,
and
con
d
u
ct such iterative pro
c
e
s
s for
N
times
to
finally get th
e
glob
al
sho
r
te
st path
T
. Prob
lems should
be p
a
id
atten
t
ion to
duri
n
g
the ite
r
ative
p
r
oc
es
s
ar
e
as
fo
llo
ws
:
(1) Ant mem
o
ry
function
Ants in the artificial ant col
ony system
h
a
s the mem
o
ry function ca
lled Tabu Li
st
which
is
us
ed to remember the
c
i
ty s
e
t
k
i
J
that
has bee
n visi
ted by nu
mb
er
k
ant. With
this
lis
t, the
ant’s re
petitive visit of one same
city will be avoided.
(2) Phe
r
om
on
e and he
uri
s
tic guid
a
n
c
e fu
nction
The phe
rom
o
ne
ij
on the path rep
r
e
s
ent
s the intelle
ctual
desire by tra
n
sferrin
g
fro
m
city
i
to c
i
ty
j
, wh
ich
refle
c
ts t
he expe
rie
n
ce a
c
cumulati
on of the
an
t in the p
r
o
b
l
em solving
pro
c
e
ss, a
n
d
this paramet
er is dyn
a
mi
c and
cha
n
g
eable in the
pro
c
e
ss
of algorithm ite
r
at
ion.
Heu
r
isti
c g
u
id
ance fun
c
tion
ij
al
so
call
ed t
he visi
bility function
represents the heur
i
s
tic desire
of
the ant
k
from
c
i
ty
i
to c
i
ty
j
, w
h
ich is u
s
e
d
to guide the a
n
t search, an
d its definition is related
to practi
cal problem
s, and it
is defined as the re
ciprocal
1/
ij
ij
d
of the distance betwe
e
n
citie
s
in the TSP problem
s[10].
(3) T
r
an
sfe
r
r
u
le
The tran
sfer
rule
on
whi
c
h the a
n
t ba
sed
to sele
ct the path
fro
m
city
i
to c
i
ty
j
is
sho
w
n in Fo
rmula (1
):
0
k
i
ij
ij
k
i
k
il
i
l
ij
lJ
k
i
t
j
J
t
pt
j
J
(2)
In whic
h,
and
are t
w
o p
a
ram
e
ters th
at can
be a
d
justed,
whi
c
h
are
re
spe
c
tively
weig
ht facto
r
s of th
e
phe
romo
ne
stre
ngth a
nd
he
uristi
c
guida
nce
fun
c
tion
to the
ant
path
sele
ction [11]
.
(4) Phe
r
omo
ne upd
ate
After the
nu
mber
t
iteratio
n, the
ant
k
wi
ll disse
m
inate
ce
rtain
ph
eromone
k
ij
t
on
the path
,
ij
. The cal
c
ulatio
n formul
a of
k
ij
t
is sho
w
n in Fo
rmula (2
):
/,
0,
kk
k
ij
k
QL
t
i
j
T
t
t
ij
T
t
(3)
In which,
k
Tt
is the path pa
ssed by numbe
r
k
ant durin
g the numb
e
r
t
iteration, an
d
k
L
t
is the length
of this path a
nd
Q
is a pre
s
e
t
paramete
r
[12].
If there is n
o
volatile mech
anism
of the
pher
omo
ne, the initializatio
n ran
dom flu
c
tuation
will be
caused to further enlarg
e, thus,
the algorithm
converges
t
o
the non-optimal
solution.
In
orde
r to
gua
rantee
the fu
ll sea
r
ch of t
he
soluti
on
space, simil
a
r to the real
ant colony,
we
introdu
ce
the
phe
romo
ne
volatile me
cha
n
ism. Int
r
odu
ce the
p
hero
m
on
e vo
latile co
effici
ent
01
in the alg
o
ri
thm to simul
a
te the volati
le pro
c
e
s
s. T
he ph
ero
m
on
e volatile rul
e
of
each path is
as sho
w
n in
Formul
a (3
):
1
ij
ij
ij
tt
t
(4)
In which,
1
m
k
ij
i
j
k
tt
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Vol. 13, No. 1, March 2
015 : 155 – 1
6
3
160
In orde
r to m
a
ke th
e ant
search
su
ccessfu
lly start, th
e phe
rom
one
initial value
on ea
ch
path ca
n not be ze
ro. Du
ri
ng the sp
ecifi
c
init
ialization
,
the pherom
one on e
a
ch
path ca
n be
set
as on
e small
positive con
s
tant
0
.
Ant colony al
gorithm flo
w
cha
r
t is shown in Figure 4:
Figure 4. Ant colony alg
o
ri
thm flow cha
r
t
Star
t
Param
e
ter initi
alization
k=1
Select form
ula and ne
xt city
a
ccording t
o
a
n
t searc
h
path
Correct the ant
visibility
m
e
te
r
Num
b
er
k
ant t
r
averses all cities
Co
rr
ect ph
erom
o
n
e
d
e
nsity on
an
t p
a
th
K<
m
K=K+
1
C
o
r
r
ect the
glo
b
al p
h
e
r
om
one
de
nsity
Nc=Nc+
1
N
c=Nc
ma
x
Out
put calculating
result
En
d
No
No
No
Yes
Yes
Yes
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TELKOM
NIKA
ISSN:
1693-6
930
Colo
r Im
age Enhan
cem
e
n
t
Based on A
n
t Colon
y
Opt
i
m
i
zation Algorithm
(Haib
o
Gao)
161
4. Color Image Filtering
Enhan
ceme
n
t Ba
sed on
ACO Algorithm
The ba
si
c tho
ught of this p
aper i
s
to usi
ng ACO al
go
rithm to opti
m
ize the
wei
ght value
coeffici
ent ve
ctor of the
filter in
the
weig
hted ve
ct
ors,
so
as to find
t
he o
p
timize
d
filter pa
ramet
e
r
to eliminate the noi
se.
4.1. Population design
Usi
ng
K
to repre
s
ent
the
size of the median filter
windo
w, then, the search is
K
dimen
s
ion
a
l, in other
wo
rks, there
are
K
weig
hted coe
fficient vectors in the m
edi
an filter to b
e
optimize
d
, which fo
rm
s a
n
ant in
divid
ual in A
C
O.
A set of
wei
ght value
co
rrespon
ds an
ant
individual to
be optimi
z
ed. Different
filters
a
r
e
rep
r
e
s
ente
d
by differe
nt weig
ht value
combi
nation
s
of real numb
e
r co
de, he
re
,
01
r
w
refe
rs to the
range of the
weig
ht value.
4.2. Fitness function
Mean A
b
solu
te Erro
r
(MA
E
) an
d Me
an
Squa
re E
rro
r (MSE
) a
r
e f
r
equ
ently u
s
e
d
color
image qu
ality evaluation function
s. Equation (5
) re
fers to MAE, and equ
ation (6) refers
to
(MSE).
3
11
1
3
PQ
ir
ir
ri
M
AE
o
y
PQ
(5)
3
2
11
1
3
PQ
ir
ir
ri
M
SE
o
y
PQ
(6)
The
M
AE
or
M
SE
of the origi
nal n
o
i
s
ele
s
s imag
e
and the filte
r
i
ng outp
u
t ima
ge can b
e
rega
rd
ed a
s
the targ
et function. The mi
nimum of th
e
target functi
on is the
sea
r
ch ta
rget of
the
ant algo
rithm. The fitness functio
n
i
F
it
is sho
w
n in e
quatio
n (7),
whi
c
h i
s
the fitness f
unctio
n
after
norm
a
lization
.
ma
x
1
i
i
M
AE
Fit
MA
E
(7)
i
F
it
refers to the fitness value
of individual
i
.
i
M
AE
refers to the mean ab
so
lute erro
r
betwe
en the weig
hted ima
ge and the origi
nal noi
sele
ss ima
ge of individual i.
max
M
AE
referd to
the mean ab
solute e
rro
r b
e
twee
n the noise ima
ge a
nd the origin
al noisel
e
ss i
m
age. The la
rge
r
the
i
F
it
, the better the image fil
t
ering result.
4.3. Algorith
m
procedur
e
The algo
rithm
procedu
re i
s
as follo
ws:
(1) i
n
itialization: the me
di
a
n
filter wi
ndo
w si
ze i
s
K
, the individual
di
mensi
on i
s
K
. The
individual po
sition and velo
city are ra
ndo
mly initialized
real num
bers in within [0, 1].
(2) calculate
the vecto
r
di
stance
an
d a
n
g
le
di
stan
ce:
cal
c
ulate
the
vector dista
n
c
e
and
angle di
stan
ce betwe
en an
y vector in the
median filte
r
wind
ow a
n
d
other vecto
r
.
(3)
cal
c
ulate
the individual
fitness: fitne
ss fu
nctio
n
i
F
it
is cal
c
ulated t
h
rou
gh e
quat
ion
(7), a
c
co
rdin
g to ste
p
(2
)
cal
c
ulate th
e
vector
dista
n
c
e a
nd a
ngle
distan
ce,
cal
c
ulate i
ndivid
ual
fitness th
roug
h equatio
n.
(4) g
a
in the current optimal
of the i
ndividual and the a
n
t group th
ro
ugh compa
r
i
s
on.
(5) u
pdate th
e individual p
o
sition a
nd velocity.
(6) algo
rithm compl
e
tion condition:
if
th
e
co
rrespon
di
ng solution
of the overall o
p
timal
^
y
is figure
d
out, that is the final optimize
d
weig
ht coefficient
12
,,
K
ww
w
w
, then, th
e algorith
m
is com
p
leted,
otherwi
se, tu
rn to st
ep
(2
), and continu
e
the cal
c
ulatio
n.
(7) g
a
in the o
p
timized filteri
ng output ima
ge.
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ISSN: 16
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TELKOM
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Vol. 13, No. 1, March 2
015 : 155 – 1
6
3
162
4.4. Simulation experime
n
t
Und
e
r the M
a
tlab environm
ent, we
ap
pli
ed a
u
tumn.tif
to test th
e im
age, a
nd
add
ed 1
0
%
impulse noi
se to the imag
e, then ado
pted the AC
O para
m
eter
op
timization p
u
t forwa
r
d by t
h
is
pape
r to co
n
duct weighte
d
vector me
dian filter
ing
operation. Th
e gaine
d filtering results a
r
e
s
h
ow
n
in
F
i
gu
r
e
5
.
(a)
(b)
(c
)
Figure 5. Image filtering re
sults
It can
seen
from the a
b
o
v
e figure th
a
t
t
he method
put forward
by this p
a
p
e
r
can
effectively adj
ust the
filterin
g weight to
p
r
oce
s
s the
im
pulse n
o
ise i
m
age. Its me
an a
b
solute
e
rro
r
and m
ean
sq
uare
e
rro
r
de
viation are
re
latively smal
l
e
r. It can
red
u
ce
or elimi
n
ate the
noi
se
in
the image to achi
eve the o
p
timized filteri
ng and g
a
in b
e
tter colo
r im
age en
han
ce
ment effect.
5. Conclusio
n
This
pap
er a
pplie
s ACO to the p
a
ra
me
ter
optimi
z
ati
on of the
wei
ghted ve
ctor
media
n
filter. Method
put forward in this pape
r can bette
r
ad
just the filter weig
ht
s to proce
s
s the noi
se
image, furth
e
r
improves t
he imag
e qu
ality to
better achi
eve the
purp
o
se of
the col
o
r im
a
ge
enha
ncement
with rel
a
tive small
mea
n
ab
solute e
rro
r an
d me
an squa
re e
rro
r. Simulati
on
experim
ent shows that the
method in this pap
er
ha
s g
ood detail a
n
d chromati
city-kee
ping eff
e
ct.
Ackn
o
w
l
e
dg
ments
This work wa
s su
ppo
rted
by Hunan Provincial
Edu
c
ation Scien
c
e
five-year pla
n
funded
proje
c
t (XJK
0
14BGD046
) a
nd Natio
nal Natural Sci
e
n
c
e Found
ation
of China (NO.
5130
4076
).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Colo
r Im
age Enhan
cem
e
n
t
Based on A
n
t Colon
y
Opt
i
m
i
zation Algorithm
(Haib
o
Gao)
163
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ces
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g-C
hun
g
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Ima
ge E
nha
ncem
ent b
y
A Mo
difie
d
Mask-F
i
lterin
g Ap
proa
ch.
Optik -
Internatio
na
l Journ
a
l for Li
ght
and Electro
n
Optics.
2012; 1
23(1
9
): 176
5-1
767.
[2]
Soha
il M, A
y
yaz H, M Arfan J,
T
ae-Sun C. Co
lor Differ
ences Bas
ed
F
u
zz
y
F
ilter fo
r Extremel
y
Corrupt
ed Co
lo
r Images.
Appli
ed Soft Co
mp
u
t
ing
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