TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3609 ~ 36
1
5
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.4921
3609
Re
cei
v
ed O
c
t
ober 2
5
, 201
3; Revi
se
d Decem
b
e
r
1, 2013; Accepte
d
Jan
uary 1, 2014
A New Sub-pixel Edge Detection Method of Color
Images
Xiao Feng*
1
, Guo Li
2
, Guo Lina
1
1
School of Co
mputer Scie
nc
e and En
gi
neer
i
ng,
Xi'
an T
e
chnol
ogic
a
l Un
ive
r
sit
y
,
Xi'
a
n, 710
03
2, Chin
a
2
Computer En
g
i
ne
erin
g De
par
tment, Beijin
g Informatio
n
T
e
chno
log
y
C
o
ll
eg
e,
Beiji
ng, 10
00
1
8
, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: xffrien
d
s@1
6
3
.com
A
b
st
r
a
ct
Moder
n i
m
a
g
e
me
asur
e
m
ent
nee
ds to tak
e
full
adv
anta
ge of su
b-p
i
x
e
l e
dge
infor
m
ati
on
of
imag
es. T
h
is
pap
er pr
ese
n
ts a s
ub-p
i
xel
ed
ge
det
ecti
on
method
of
col
o
r i
m
a
ges
bas
ed
on
i
m
a
g
e
di
me
nsio
nal
ity reducti
on an
d the
l
east
s
qua
re meth
od.
F
i
r
s
t of al
l w
e
ge
t the p
i
xel
l
e
v
e
l
edg
e
by Os
tu
alg
o
rith
m a
nd
then co
mbin
e
gray proc
essi
n
g
alg
o
ri
th
m b
a
s
ed o
n
col
o
r spatia
l dista
n
c
e
an
d the l
e
a
s
t
squar
e metho
d
for sub-pix
e
l edg
e locati
o
n
. Experi
m
e
n
tal resu
lts sho
w
that
the alg
o
rith
m pos
ition
i
n
g
accuracy
c
an reach 0.13 pix
e
l
w
h
ich provi
des
a basis
fo
r the sel
e
ctio
n
of color
i
m
ag
e sub-
pixe
l e
d
g
e
positi
oni
ng.
Ke
y
w
ords
: thresho
l
d sel
e
ctio
n, dimens
ion
a
l
i
t
y reducti
on, th
e least squ
a
re
meth
od, col
o
r i
m
a
ge
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Colo
r image
provide
s
more an
d rich
er visual pe
rceptio
n than
grayscale i
m
age
s. At
pre
s
ent th
e
edge
po
sition
ing a
c
cura
cy
of gray-scal
e
image
s
ha
s rea
c
hed
th
e su
b-pixel l
e
vel
whi
c
h i
n
cude
s fitting [1,
2] interpolation
metho
d
[3-5]
mome
nt met
hod [6,
7] a
n
d
so o
n
but t
he
edge
dete
c
ti
on te
chni
que
s of
col
o
r im
age
s a
r
e j
u
st
staying
at th
e pixel level
mainly in
clud
ing
vector a
p
p
r
o
a
ch [8, 9] th
e output fu
sion metho
d
[10] multi-dim
ensi
onal g
r
a
d
ient metho
d
[11].
With the
in
creasi
ngly
wide
spread
u
s
e
o
f
colo
r
im
age
s a
nd th
e a
c
t
ual a
ppli
c
atio
n requi
reme
n
t
s
the sub
-
pixel
edge lo
cali
zat
i
on of colo
r image
s is taken more and
more attentio
n.
Acco
rdi
ng to t
he ima
g
ing
principl
e of the
co
lo
r ima
ge
we
reali
z
e
th
e dime
nsi
on
redu
ction
of image
s [1
2-15]
ba
sed
on
colo
r
spat
ial di
stan
ce t
hen
com
b
ine
ostu
alg
o
rith
m and
the l
e
ast
squ
a
re
s meth
od to
extra
c
t
sub
-
pixel
edg
es
of
colo
r im
age
s. Th
e al
gorithm
takes full adva
n
tag
e
of the colo
r f
eature i
n
form
ation of imag
es
whi
c
h to
some
extent improve
s
the
sub
-
pixel e
d
ge
positio
ning a
c
curacy.
2. Algorithm
2.1. Color Image Dimensi
onalit
y
Reduction
In the p
r
o
c
e
s
s of im
age
proce
s
sing th
e
colo
r of th
e pi
xel usu
a
lly ta
ke
s the th
re
e
prima
r
y
colo
rs
of RG
B spa
c
e which tend to hav
e very stro
ng
correl
ation a
m
ong them
so it leads to l
o
we
r
pre
c
isi
o
n
of e
dge
dete
c
tion
. In orde
r to
remove th
e
co
rrel
a
tion
amo
ng the
three
compon
ents a
n
d
redu
ce
the
complexity of
the
ope
rati
on thi
s
p
ape
r p
r
e
s
ent
s a
n
imp
r
oved
gray
pro
c
e
ssing
algorith
m
ba
sed on color
spatial dista
n
ce.
For
a colo
r i
m
age th
e o
b
j
ect e
dge
pixels h
a
ve the
larg
est
se
co
nd mo
ment i
n
their
neigh
borhoo
d
s
the
cha
n
g
e
of se
co
nd
moment
i
s
cau
s
e
d
by the differe
nce
s
bet
wee
n
the
brightn
e
ss of the
obj
ect an
d
the ba
ckground
lumi
n
a
n
c
e. T
herefore
the
st
ep
s of
gray p
r
o
c
e
s
si
ng
algorith
m
ba
sed on color
spatial dista
n
ce are a
s
follo
ws:
Step 1:
Cal
c
ulate
the ave
r
age
R
A
vg
、
B
A
vg
、
B
A
vg
of R G B th
ree
comp
one
nts
of all
pixels in the color image.
Step 2:
Calculate
the sta
ndard
deviati
on
R
Dec
、
G
De
c
、
B
Dec
of R
G B co
mpon
ents i
n
the colo
r ima
ge.
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046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3609 – 36
15
3610
Step 3:
Com
pute g
r
ay wei
ghted
coeffici
ent
R
Co
、
G
Co
、
B
Co
o
f
R
G
B co
mp
one
n
t
s
an
d
weig
ht coefficient
R
Wc
、
G
Wc
、
B
Wc
.
Step 4:
Cal
c
ulate the thre
shol
d of the color ima
g
e
R
RG
G
B
B
dT
hr
es
h
h
o
l
d
D
e
c
C
o
D
e
c
C
o
D
ec
C
o
Step 5:
Cal
c
ulate
the di
stan
ce
f
r
om the
gray
val
ue to it
s
correspon
ding
a
v
erage.
R
GB
d
D
ist
D
ist
D
ist
D
i
s
t
Step 6:
A
c
cordin
g to the
magnitude
relation bet
we
en
dD
ist
and
d
T
hr
e
s
hh
ol
d
to get
proje
c
tion val
ues
of ea
ch
pixel. If
dD
i
s
t
d
T
h
re
shho
l
d
the
proje
c
tion val
ue of the
co
rresp
ondi
ng
pixel is:
R
e
0
.
2
9
9
0
.5
87
0.114
RG
B
Gra
y
d
d
Wc
dGreen
Wc
d
B
l
u
e
W
c
.
Otherwise,
[
1
3
,
1
3
,
1
3
][,
,
]
T
Gray
R
G
B
.
It should
be
noted that
wh
en to go
on
weig
hted p
r
o
c
e
ssi
ng fo
r p
a
rtial pixel
s
o
f
image if
we use the
weighted formula dire
ctly
the gray value of the im
age will becom
e
very small
and
very dark whi
c
h will
de
stro
y the edge st
ructu
r
e.
Th
erefore
whe
n
p
r
ocessin
g
the
image we can
remove
the g
r
ay
co
efficie
n
t so
the f
o
rmul
ar
chang
es to be
Re
e
n
C
R
CG
CB
Gra
y
d
d
W
d
Gr
e
W
d
B
l
u
e
W
. For the pi
xels which
do not n
eed
to go to
weig
hted p
r
o
c
e
ssi
ng we can re
alize gray pro
c
e
ssi
n
g
usi
ng the a
v
erage val
ue
method. Th
ro
ugh
the above im
provem
ents i
n
crea
se a
s
ymmetry of
image bri
ghtne
ss distri
bution
so that the edge
stru
cture is
well pre
s
e
r
ved
and the e
dge
stand o
u
t. ex
perim
ental re
sults
sho
w
th
at the method
is
effective to keep the e
dge
information
of t
he image
and a g
ood
effect is obtai
ned in p
r
a
c
tical
appli
c
ation.
2.2. Ostu Me
thod fo
r Image Coa
r
se P
o
sitioning
The O
s
tu me
thod is ba
se
d on the pri
n
ciple of lea
s
t
squa
re meth
od it is a bin
a
rization
method of au
tomatically se
lected th
re
sh
old its ba
si
c i
dea is to divi
de the imag
e
into two gro
ups
by using
a pi
xel value wh
en the two
group
s have
th
e maximum v
a
rian
ce th
e value can b
e
the
threshold of b
i
nari
z
ation p
r
oce
s
sing.
Assu
me th
e
gray val
ue
ra
nge
of an
im
age i
s
0
L
the
n
u
mbe
r
of
pixels
wh
ose g
r
ay
value is
i
is
i
n
the total numb
e
r of pixels is
N
the appeara
n
ce p
r
ob
abilit
y of pixels whose g
r
ay
value is
i
is
i
P
s
o
:
1
L
i
i
Nn
(1)
ii
Pn
N
(2)
Acco
rdi
ng to t
he thresh
old
the pixels i
n
the imag
e a
r
e
divided into t
w
o
categ
o
rie
s
is the target
area m
ean
whose gray le
vel is
lowe
r than
and
is the backg
rou
nd regi
on
mean
who
s
e
gray level is highe
r than
the thre
shol
d
thereby we
can o
b
tain the followi
ng
equatio
n:
00
1
1
=/
=/
TL
ii
iT
i
T
iP
w
i
P
w
(3)
Whe
r
e
0
w
and
1
w
are
respecti
vely the probability of
target area an
d the background
area that:
01
0
01
1
TL
ii
ii
T
wP
w
P
w
(4)
Then the ave
r
age of the whole imag
e:
T
0
T
1
T
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A New Sub
-
pi
xel Edge
Det
e
ction Meth
o
d
of Color Im
age
s (Xiao F
eng)
3611
00
1
1
ww
(5)
Acco
rdi
ng to
the theo
ry of
pattern reco
gnition
，
we can
o
b
tain bet
wee
n
-cla
ss
varian
ce
value and
within-cla
ss va
ri
ance value re
spe
c
tively:
22
2
2
01
0
1
0
0
1
1
22
2
00
1
1
BT
T
w
ww
w
w
sw
s
w
s
(6)
Among which
:
2
2
00
0
i
2
2
11
1
i
=/
t=
/
T
i
t
T
i
t
iP
w
itP
w
t
(7)
To sea
r
ch e
a
c
h
gray val
u
e
acco
rdin
g to
a certain
o
r
de
r in th
e
whol
e
gray
scale
ra
nge th
e
pro
c
e
ss of
2
B
maximizing and minimi
zing
2
B
is essenti
a
lly the pr
ocess of auto
m
atically
sele
ct thre
sh
old. Ostu met
hod dete
r
min
e
the optim
al
threshold val
ue T by maximizing o
ne of
the
following formula:
22
2
22
2
B
TB
ww
T
K
(8)
2.3. Least Sq
uare Me
thod
The lea
s
t sq
uare m
e
thod
is an optimal
estima
tion te
chn
o
logy de
ri
ved by the maximum
likeliho
o
d
met
hod
wh
en th
e
ra
ndom
e
rro
r meet
no
rmal
dist
ribution
which
en
able
s
the sum
of th
e
squ
a
re
s of th
e me
asure
m
ent e
rro
rs
re
ach
the
sm
all
e
st
so
it is
consi
dered
as one
of th
e
most
reliabl
e meth
od to g
e
t a se
t of unkno
wn
para
m
eters from a g
r
o
up o
f
measure
m
e
n
ts. Fo
r a giv
e
n
image th
e dif
f
eren
ce val
u
e
of obje
c
t i
s
maximum at
the ed
ge
whi
c
h i
s
th
e cl
assical p
r
in
ciple
of
edge extra
c
ti
on. Acco
rdin
g to the central limit
theore
m
the grey value ch
ang
e of edges
sho
u
ld
be a gau
ssia
n distrib
u
tion.
The expressi
on of
gau
ssi
a
n
cu
rv
e is
2
2
1(
)
ex
p(
)
2
2
x
y
where
is the averag
e
is the stand
ard deviation .We u
s
e gau
ssian curve to do som
e
tran
sform
a
tion lo
garithm on b
o
th
side
s then
we
can get the followin
g
form
ula:
2
2
()
1
ln
ln
2
2
x
y
(9)
As ca
n be
see
n
the a
b
o
ve equ
ation
is qu
adratic curve
abo
u
t
x so we
can u
s
e
logarith
m
ic v
a
lue
s
to fit th
e para
bola a
nd then fi
nd the vertex coo
r
dinate
s
so the comp
utatio
n is
greatly sim
p
lified.
The cu
rve eq
uation which is used to fit edge si
gnal
is
2
y
ax
b
x
c
we can o
b
tain the
values of
a
b c by th
e l
east
sq
ua
re
method
so t
hat tne
sum
of
squ
a
re
e
rro
rs
can
be
the
minimum.
2
1
(y
ax
bx
)
n
ii
i
i
Sc
(10
)
Ca
culate the
partial deriv
atives of a b cr
e
s
pe
ctivel
y and make
the values of
partial
differentives
be 0 then we can g
e
t that:
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ISSN: 23
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046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3609 – 36
15
3612
2
11
1
1
(a
)
nn
n
ii
i
ii
i
de
f
g
a
hd
g
g
fg
a
b
d
cy
x
b
x
n
(11
)
Among which
:
2
11
1
22
11
1
11
1
32
11
1
42
2
11
1
nn
n
ii
i
ii
i
nn
n
ii
i
i
ii
i
nn
n
ii
i
i
ii
i
nn
n
ii
i
ii
i
nn
n
ii
i
ii
i
dn
x
x
x
en
x
y
x
y
f
nx
y
x
y
g
nx
x
x
hn
x
x
x
(12
)
It shoul
d b
e
noted th
at th
e ab
ove-o
b
ta
ined
sol
u
tion
is o
b
taine
d
b
y
the log
a
rith
m of th
e
origin
al G
a
u
s
sian
curve. In
anoth
e
r word the val
ue
o
f
a pixel
after loga
rithm i
n
accordan
ce
with
the qua
drati
c
curve
so th
e
pixel gray val
ues i
n
the formula shoul
d
be in
stead
ed
by the loga
rithm
values thu
s
g
e
t the values
of
and
:
(2
a
)
1
2
b
a
(13
)
The value of
is the su
b-pix
e
l value.
Due to the im
age ha
s the
rotation invari
ant at the sa
me deg
e and
as a result there i
s
no
spe
c
ial re
quirements
for select strai
ght dire
cti
on
wh
e
n
cal
c
ul
ates the subpixel
coordi
nate
s
a
n
y
direction will
be OK.
2.4. Steps of the Algorith
m
The main i
d
e
a
of this alg
o
rithm i
s
that use O
s
tu m
e
thod to obt
ain all po
ssib
le edg
e
points of pix
e
l level firstl
y and then
use g
r
ay
pro
c
e
ssi
ng alg
o
r
ithm ba
sed
on col
o
r
spa
t
ia
l
distan
ce to re
duce the dim
ensi
o
n
s
of the image
a
nd
finally on the proje
c
ted im
a
ge use the pi
xel
level edge p
o
ints which h
a
ve been o
b
tained to re
ali
z
e sub-pixel edge lo
cation
combini
ng the
least
squ
a
re
method. T
h
e flow
ch
art
of su
b-
pixel
edge
dete
c
t
i
on alg
o
rithm
of col
o
r i
m
age
pre
s
ente
d
in the pap
er a
r
e
is follows:
Co
lor
I
m
a
g
e
Im
age
a
f
t
e
r
pr
oce
ssi
ng
pr
epr
oce
ssi
n
g
Im
age
wi
th
P
i
x
e
l
Edg
e
Os
tu
met
hod
Pr
oj
e
cti
on
Ima
ge
Im
age
wi
t
h
S
u
b
-
p
i
xel
Ed
ge
Th
e l
eas
t s
qua
r
e
m
e
t
hod
Figure 1. The
Flow Ch
art o
f
Sub-pixel Edge Detectio
n of Color Im
age
s
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046
A New Sub
-
pi
xel Edge
Det
e
ction Meth
o
d
of Color Im
age
s (Xiao F
eng)
3613
3. Experiment and Resul
t
Analy
s
is
Evaluation cri
t
eria
fo
r sub
p
i
x
el
algo
rithm is
to
co
nsi
der the p
r
e
c
i
s
ion
of the
algo
rit
h
m the
pre
c
isi
on of t
he alg
o
rithm i
t
self mu
st use the ide
a
l im
age to eval
ua
te so that it can elimin
ate the
influen
ce
of n
o
ise
we
can
n
o
t obtain
ima
ges by
cam
e
ras
be
cau
s
e
t
he im
age
pa
rameters
ca
n
not
be d
e
termi
n
e
d
lea
d
ing
to t
he
referen
c
e
is n
o
t a
c
curate an
d the
im
age
obtain
e
d
by the
came
ra
s
will inevitably introdu
ce no
ise. The
r
efore we
use co
mputer to ge
nerate a
sta
ndard image
by
simulatin
g
the actual ima
g
i
ng pro
c
e
s
s a
nd we ta
ke
it as the ba
si
s of test locali
zation accu
ra
cy of
locali
zation
a
l
gorithm. A
s
sho
w
n i
n
Fi
gure
2 u
s
e
CCD ima
g
in
g prin
cipl
e to simul
a
te
color
stand
ard lin
e
a
r imag
es
wh
ose
slop
es
k are respe
c
tively 0,1, 2, 4.
(a) k=
0
(b) k=
1
(c
)
k
=
2
(d) k=
4
Figure 2. Standard Col
o
r L
i
ne Image
s
Cal
c
ulate th
e
averag
e di
stance btween
t
he su
b-pixe
l edge
obtain
ed by the p
r
opo
sed
algorith
m
an
d the actual
sub
-
pixel ed
g
e
whi
c
h
is th
e positio
ning
accura
cy of the image. T
h
e
expre
ssi
on of
positioni
ng a
c
cura
cy is:
1
n
i
i
d
m
n
(14
)
Whe
r
e
i
d
is the
distan
ce b
e
twee
n the det
ected e
dge
p
o
sition of the
sub
-
pixel an
d the
actual
sub
-
pi
xel edge
is the numb
e
r of
detected e
d
g
e
points.
Positionin
g
a
c
cura
cy is
sh
own i
n
Figu
re
3 amon
g the
m
the dotted
line is th
e po
sitionin
g
accuracy of tradition
al alg
o
rithm and th
e solid li
ne is the sub-pixel location a
c
cura
cy usin
g the
prop
osed
alg
o
rithm
whi
c
h
firstly minimi
ze convert
s
co
lor im
age
to p
r
oje
c
tion i
m
a
ge a
nd th
en
u
s
e
the least
squ
a
re m
e
thod t
o
reali
z
e
sub
p
ixel edge
l
o
cation. Expe
rimental re
sult
s sho
w
that the
highe
st p
o
sit
i
oning
a
c
curacy of
the
prop
os
ed
al
gorithm
can
re
ach 0.1
3
pixels while
the
maximum p
r
eci
s
ion
of traditional
alg
o
rithm i
s
j
u
st 0.2 pixel
s
.
Thus the
propo
sed
algo
rithm
make
s full u
s
e of charact
e
risti
c
inform
ation of
col
o
r image
s so t
hat it improv
es the ima
g
e
of
sub
p
ixel edg
e locatio
n
accura
cy.
Figure 3. The
Locatio
n Accura
cy Com
p
a
r
iso
n
Ch
art
n
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Vol. 12, No. 5, May 2014: 3609 – 36
15
3614
In orde
r to
verify the propo
sed al
go
rithm we selected te
a service i
m
age
in the
experim
ent a
s
sh
own in Figure 4 a
nd we did
a com
p
arison bet
we
en the pro
p
o
s
ed algo
rithm and
traditional
alg
o
rithm. Amon
g whi
c
h
The
Figure 4
(
a)
is the ori
g
inal i
m
age Fi
gu
re
4(b
)
is the
su
b-
pixel edge im
age obtai
ned
by traditional
algorith
m
and
Figure 4(c) i
s
the sub
-
pix
e
l image g
o
t by
the propo
se
d
algo
rithm. Experime
n
tal result
s sh
o
w
t
hat the p
r
op
ose
d
alg
o
rith
m ca
n obtai
n
a
more
a
c
curat
e
subpixel
ed
ge
comp
are
d
with tradition
al algo
rithm t
he latter exist
s
di
scontinuiti
es
it is be
ca
use
the tra
d
ition
a
l algo
rithm
use
s
a
spe
c
ific formula fo
r colo
r im
age
gray p
r
o
c
e
ssi
ng
thereby ig
no
re the color chara
c
te
risti
c
s info
rmatio
n
of the col
o
r i
m
age o
n
im
age pixel l
e
vel
coa
r
se p
o
siti
oning
edg
e l
o
catio
n
a
c
curacy i
s
lo
we
r
ultimately affect the
po
sitioning
accu
ra
cy of
sub
p
ixel. whi
l
e the p
r
op
o
s
ed
algo
rith
m is o
n
the
basi
s
of m
a
ximize th
e
image fe
ature
informatio
n convert proj
ection image a
nd then for
subsequ
ent ca
lculatio
ns. So
the accu
ra
cy of
the prop
osed
algorith
m
is superi
o
r to the
traditional de
tection alg
o
rit
h
m.
(a)The O
r
igin
al Image
(b) T
he Edge
Image of
Traditio
nal Algorithm
s
(c) The Edg
e
Image of the
Propo
se
d Algorithm
s
Figure 4. Edge Dete
ction Re
sult
s of the Tea Service
In ord
e
r to fu
rther verify th
e supe
riority
and
rep
eatab
ility of this al
gorithm
we choo
se
anothe
r mo
re com
p
lex fruit imag
e to do exp
e
ri
ment. Figu
re
5(a
)
~(c) th
ree imag
es
are
respe
c
tively origin
al imag
e sub
-
pixel e
dge ima
ge o
b
tained by traditional met
hod sub
-
pixel
edge
image
got
b
y
the p
r
op
osed m
e
thod
It is
obviou
s
t
hat the
prop
ose
d
al
gorith
m
can
gen
erate
clea
re
r and m
o
re a
c
curate sub
-
pixel ed
g
e
comp
ared
with the tradit
i
onal metho
d
.
(a)The O
r
igin
al Image
(b) T
he
Edge Image
of
Traditio
nal Algorithm
s
(c
) The
Edg
e
Image of the
Propo
se
d Algorithm
s
Figure 5. Edge Dete
ction Result
s of the Fruit Image
4. Conclusio
n
This p
ape
r p
r
esents
a su
b-pixel e
dge
detectio
n
alg
o
rithm of
col
o
r ima
g
e
s
co
mbined
gray p
r
o
c
e
ssi
ng alg
o
rithm
based o
n
color
spatial
d
i
stan
ce a
nd t
he lea
s
t squ
a
re m
e
thod t
h
e
algorith
m
u
s
es O
s
tu m
e
thod to
cal
c
u
l
ate maximu
m varian
ce
betwe
en
cla
s
s an
d minim
u
m
intercl
a
ss variance of targ
et and ba
ckg
r
oun
d so
tha
t
it can dire
ctly obtain the optimal colo
r
threshold
fina
lly ideal subpi
xel pixel wa
s
obtaine
d by combinin
g sub
p
ixel edg
e de
tection m
e
tho
d
of gray imag
es. Experim
ental re
sults sho
w
that the algo
rithm
can avoid repeat dete
c
ti
on
pro
c
e
ss fo
r the thre
sh
old
we can get t
he optimal
th
reshold valu
e
dire
ctly by usin
g the O
s
tu
method
red
u
c
e
s
the
run
n
i
ng time.At the sa
me time
the metho
d
combi
n
e
s
the
advantag
es
of
sub
-
pixel
edg
e dete
c
tion
o
f
gray im
age
s its dete
c
tio
n
effect i
s
go
od it i
s
con
d
ucive to
furth
e
r
image a
nalysis an
d proce
ssi
ng. Howe
ver ho
w to o
b
tain the sub
-
pixel ed
ge o
f
color im
age
s
whi
c
h contain
noise i
s
nee
d to study in the future.
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TELKOM
NIKA
ISSN:
2302-4
046
A New Sub
-
pi
xel Edge
Det
e
ction Meth
o
d
of Color Im
age
s (Xiao F
eng)
3615
Ackn
o
w
l
e
dg
ements
This wo
rk
wa
s
finan
cially suppo
rted by
Natu
ral Sci
e
n
c
e Ba
si
c Research Pla
n
in
Shaanxi
Province of
Chin
a (201
3
J
M80
4
3
)
, Th
e Prin
cip
a
l
Fund
of Xi'
an T
e
ch
nolo
g
ical
University
(XAGDX
JJ12
18).
Referen
ces
[1]
Ma Yu G
u
Xia
o
don
g W
a
n
g
Y
uan
yu
a
n
ect.F
eature
fu
sio
n
method
for e
d
ge
detecti
on
of color
ima
ges
.
Journ
a
l of Systems E
ngi
ne
eri
ng an
d Electro
n
ics.
200
9; 20(
2): 394-3
99.
[2]
Lin
hai J
i
n
g
Qiu
m
ing
Che
ng. A
n
ima
ge fus
i
o
n
method
takin
g
into
accou
n
t p
hen
olo
g
ic
al a
n
a
lo
gies
an
d
haze. Intern
ati
ona
l
Jour
ma
l o
f
Remot
e
Sens
ing
. 20
11; 32(
6
)
: 1675-1
6
9
4
.
[3]
T
Hermosilla
E
Berme
jo A
Ba
l
agu
er ect.
Non
-
line
a
r fo
urth-o
rder im
ag
e i
n
te
rpol
ation
for s
u
bpi
xel
ed
ge
detectio
n
an
d l
o
caliz
atio
n.
Image a
nd Vis
i
on
Computi
n
g
. 20
08; 26: 12
40-1
248.
[4]
L Z
han
g
XL. W
u
An e
dge-
gui
ded im
ag
e inte
rpol
ation
alg
o
ri
thm via dir
e
ctio
nal filter
in
g an
d data fus
i
o
n
.
IEEE Transactions on I
m
age
Processing
. 20
06; 15: 22
26-2
238.
[5]
Ning
Li H
u
i Ju
Yuqi
nYa
o
ect. A sub-pi
xel e
d
ge d
e
tection m
e
thod
base
d
o
n
improv
ed ca
nn
y o
perator t
o
detect co
pper
stripsize.
Proc
eed
ings
of 2
0
1
1
Intern
ation
a
l
Confer
ence
o
n
Mana
ge
ment
Scienc
e a
n
d
Intelli
gent C
ont
rol
. 201
1; 4: 59
2-59
5.
[6]
T
J
Bin Ao Lei Cui Ji
w
e
n. Sub
p
i
x
el e
d
g
e
loca
tion bas
ed on
orthog
on
al F
o
u
r
ier–Me
lli
n mo
ments.
Im
age
and Vis
i
on C
o
mp
utin
g
. 200
8; 26: 563-5
69.
[7]
Qu Ying-
Don
g
Cui
Che
ng-S
ong
Che
n
Sa
n
-
Ben ect. A fa
st subpi
xel
ed
ge d
e
tectio
n
method
usi
n
g
Sobe
l-Z
e
rnik
e moments op
er
ator.
Imag
e an
d Visio
n
Co
mp
uting.
20
05; 23
: 11-17.
[8]
Pabitra M Sha
n
kar BU, Sank
ar KP. Segmen
tation of
multis
pectral rem
o
te sensi
ng ima
g
e
s
using activ
e
supp
ort vector machi
nes.
Pattern Rec
ogn
itio
n Letters
. 200
4
;
25(9): 106
7–1
074.
[9]
PE T
r
ahani
as
AN Venets
ano
pou
los. Vector
Order
Statistics Operators as
Color E
dge D
e
tectors
. IEEE
T
r
ansactio
n
s On Systems Ma
n And Cyb
e
rn
e
t
ics-Part B.
1996;2 6(1): 1
35-
143.
[10]
Ma Yu Gu
Xia
odo
ng W
a
n
g
Yuan
yu
a
n
ect.F
eat
ure fusi
on
method for
edg
e detecti
o
n
of colo
r
imag
es.
Journ
a
l
of Systems En
gin
eeri
ng a
nd
Electron
ic
s. 20
09;20(
2):39
4
-3
99.
[11]
B Bouda L
h
. Masmou
di D Abouta
j
di
ne.
Cubic
a
l vo
xels
and virtua
l el
ectric field mo
del for ed
g
e
detectio
n
in co
l
o
r imag
es.
Sig
nal Proc
essin
g
. 2008; 11
5-11
9.
[12]
LJP Maat
en E
O
Postma, HJ
Herik. D
i
m
ens
i
ona
lit
y re
ductio
n
:a com
parativ
e revi
e
w
.
Til
b
u
r
g Un
iversit
y
Technic
a
l Re
p
o
rt TiCC-TR
. 2009-
005
200
9.
[13]
PN Belh
ume
u
r
,
JP Hespan
h
a
, DJ Kriegm
an. Ei
ge
nface
s
vs fisherfaces; recogn
itio
n
using cl
ass
specific li
ne
ar proj
ection.
IEEE Trans Pattern Anal. Machine Intell
. 20
08; 19(7): 71
1-7
2
0
.
[14] SC Ch
en
g, T
L
W
u
. Subp
i
x
el
edg
e d
e
tectio
n
of
col
o
r im
ag
e
s
usin
g m
o
me
nt-preserv
ing
techn
i
qu
e
and
princi
pa
l a
x
is a
nal
ysis.
Pattern Recognition
.
200
5; 38(4): 52
7–5
37.
[15]
Don
g
Li. A
n
im
prove
d
al
gor
ith
m
for non
li
near
dime
nsio
na
lit
y reducti
on
in i
m
age
proc
essi
ng.
T
he 201
2
2nd Intern
atio
n
a
l Co
nferenc
e
on Cir
c
u
its System a
nd Si
mu
l
a
tion
. 20
12; 46
: 183-18
9.
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