TELKOM
NIKA
, Vol. 11, No. 10, Octobe
r 2013, pp. 5
530 ~
55
38
ISSN: 2302-4
046
5530
Re
cei
v
ed Ma
rch 2
9
, 2013;
Re
vised June
20, 2013; Accepte
d
Jul
y
8
,
2013
Color Calibration Model in Imaging Device C
ontrol
using Support Vector Regression
Yang Bo*
1
, Lei Liang
2
, Wang Xue
3
1, 2,
3
School of Electrical
and I
n
formatio
n
Eng
i
ne
erin
g,
Cho
ngq
in
g Uni
v
ersit
y
of Sci
e
n
c
e &
T
e
chnol
o
g
y
(CQUST
)
Univers
i
t
y
T
o
w
n
, 4013
31, Ch
ong
qin
g
, P. R.
Chin
a,
Ph./F
ax: +
8623-65
02
2
172
*Corres
p
o
ndi
n
g
author, e-ma
il: bob
_cq@
16
3.com*
1
, cqlei.l@163.com
2
, saltmaker@163.com
3
A
b
st
ra
ct
In the c
o
lor
sys
tem
of a c
o
mp
uter, the
non
li
n
earit
y of t
he
image
acq
u
isiti
o
n
devic
e
and
the
disp
la
y
devic
e
may r
e
sult in
the
diff
erenc
e b
e
tw
ee
n the c
o
l
o
rs d
i
splay
ed
on th
e
screen
a
nd th
e actu
al c
o
lor
of
obj
ects, w
h
ich
requ
ires for c
o
l
o
r correcti
on. T
h
is p
a
p
e
r intro
duce
d
the S
u
p
port Vector
Re
gressi
on (SVR)
t
o
establish a c
o
lor correction
m
o
de
l for the nonlinear imaging system
.
In the modeling
process, t
h
e
Successiv
e
3
σ
F
ilter w
a
s used to eli
m
in
ate the lar
ge erro
rs
found in the c
o
lor
me
asure
m
ent. Becaus
e th
e
SVR mode
l of
RBF
kernel h
a
s tw
o imp
o
rta
n
t para
m
et
ers (C,
γ
) that nee
d to be d
e
ter
m
i
n
e
d
, this pa
per
app
lie
d
Least
Mean
Squ
a
re
d
T
e
st Errors Al
gorith
m
to o
p
ti
mi
z
e
th
e p
a
ra
meters
to
get t
he
best SVR
mode
l.
Co
mp
ared
w
i
th qu
adratic
p
o
ly
no
mi
al r
egress
i
on, BP
ne
ura
l
netw
o
rk a
nd r
e
lev
ance
vecto
r
machi
ne, SV
R
has better p
e
rformanc
e in col
o
r correctio
n a
nd ge
ner
ali
z
at
i
on.
Ke
y
w
ords
:
c
o
l
o
r re
prod
uctio
n
, sup
port v
e
c
t
or regr
essio
n
, success
ive
3
σ
filter,
least
me
an
squ
a
re
d
test
errors
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
In rece
nt years, ICC (Int
e
r
national Colo
r Con
s
o
r
tium
) colo
r mana
gement is g
r
adually
being receive
d
and ad
opte
d
. The co
re o
f
its manage
ment is to ch
ara
c
teri
ze the
behavior of color
descri
p
tion of
each
device
in imaging
sy
stem
s, nam
el
y, the establi
s
hme
n
t of a functio
n
between
RGB
o
r
CMY
K
of
device control sig
nal values
and
the tris
timulus
values
. This func
tion is
oft
e
n
descri
bed i
n
different
way
s
, su
ch
a
s
L
ook-up
T
abl
e
(L
UT) co
mbi
ned with
the interpol
ation
[
1
],
multiple re
gre
ssi
on [2] and
neural networks [3, 4], etc.
Und
e
r no
rma
l
circum
stan
ces, the Loo
k-up
Table m
e
thod provid
e
s
a preci
s
ion
higher
than othe
r m
e
thod
s, but it requi
re
s a lot
of calib
ration
sampl
e
s. To
redu
ce the dat
a dimen
s
ion
o
f
calib
ration
sa
mples,
Wa
ng
et al u
s
ed th
e col
o
r
co
rrection metho
d
for the
domai
n pa
rtition of
the
multi-chan
nel
printe
r
colo
r co
rrection
[5]. Mult
iple regre
s
sion
wo
rks by m
ean
s of p
o
lynom
ial
approximatio
n to the nonli
near
ch
ar
a
c
t
e
risti
cs
of de
vice color,
fe
atured i
n
a si
mple conversion
relation
shi
p
a
nd the lo
wer
calib
ration
accuracy.
Fu
rth
e
rmo
r
e, the p
o
lynomial a
s
a global fu
nct
i
on
may lead
to t
he lo
cal
di
sto
r
tion to
be
ex
tended
to the
wh
ole
col
o
r
spa
c
e. A
n
eff
e
ctive
way i
s
to
narro
w the
range
of
co
rrection, th
at i
s
,
corre
c
ti
on
pa
rtition [6,
7]. The
o
retically, the
ne
ural
netwo
rk
ca
n approximate any
nonli
nea
r relation
shi
p
, so it ha
s a
hi
gh ap
plicability when
used
for
colo
r
co
rrecti
on. On
e
co
n
c
ern i
s
th
e
difficulty
to d
e
termin
e the
internal
stru
cture
of
neu
ral
netwo
rks, su
ch as the hid
d
en layer.
In re
cent yea
r
s,
sup
port v
e
ctor ma
chin
e ba
sed
on t
he stati
s
tical
learni
ng the
o
r
y ha
s
been pl
ayin
g a big
rol
e
in term
s
of pattern
reco
gnition, i
m
age
cla
ssif
i
cation, fun
c
t
i
o
n
approximatio
n, etc. And it also
finds its way to be applie
d in the field of color co
rrectio
n
[8].
Ho
wever, research in this area is al
so
relati
vely less. Thi
s
pap
er presented
an attempt to
introdu
ce
a
suppo
rt ve
ctor ma
chin
e mo
del fo
r e
s
t
abl
ishin
g
colo
r correctio
n
,
wit
h
corre
c
tion
of
experim
ental
data bein
g
used to te
st the accuracy of the model.
2. Color Corr
ection Progr
am
In the gene
ra
l colo
r syste
m
of a comp
uter, as
sho
w
n in Figu
re 1,
the colo
r of an obje
c
t
wa
s captu
r
ed
by CCD
ca
mera i
n
stan
dard
lighting
con
d
ition
s
(e
.g. the D50 li
ght so
urce
),
and
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TELKOM
NIKA
Vol. 11, No
. 10, Octobe
r 2013 : 553
0 –
5538
5531
pre
s
ente
d
on
the screen th
rough th
e com
puter. ICC
i
s
respon
sibl
e to define
col
o
r captu
r
e
and t
o
displ
a
y the device-i
nde
pe
ndent colo
r spa
c
e, plu
s
t
hat now the
r
e are m
any acq
u
isitio
n a
nd
displ
a
y devi
c
es th
at supp
o
r
t color ma
na
gement,
su
ch
as ga
mma
correctio
n
, col
o
r
balan
ce,
e
t
c
.
Non
e
thele
s
s, due to the
chara
c
te
risti
c
s of indi
vidual
equipm
ent, color di
spl
a
y o
n
the scree
n
of a
computer
still have differences in t
he
color
system f
r
om the actual
color,
so color correction
is
need
ed.
In the color system of a compute
r
, the color corre
c
tion can b
e
done in two st
eps, a
s
s
h
ow
n
in
F
i
gu
r
e
1
,
a
)
, b)
be
lo
w
.
Figure 1. Col
o
r cali
bration
model
First i
s
th
e n
eed to
create
col
o
r
co
rrecti
on mo
del. In
Figure 1a
), th
e a
c
tual
colo
r on the
stand
ard
col
o
r card
was kno
w
n,
a
nd marked with the
ch
rom
a
ticity
coo
r
din
a
tes (
t
xi
, t
yi
). In the
D50 standard illumination
conditions
, the standard card
had the colors
displ
a
yed on the
screen
throug
h the came
ra, an
d
that are usu
a
lly different
from the act
ual col
o
r of the ca
rd. Screen
s
h
ow
ed
its colo
r
s
b
y
th
e colo
r
s
us
in
g a
sp
e
c
tro
r
adiom
eter, referred
to here a
s
th
e screen
colo
rs
or me
asurin
g
colo
rs, m
a
rked with th
e color
coo
r
di
na
tes (
p
xi
, p
yi
). The e
s
tabli
s
h
m
ent of a
col
o
r
corre
c
tion
m
odel
actually
mean
s to
est
ablish the
m
appin
g
relatio
n
shi
p
bet
wee
n
mea
s
u
r
em
ent
colo
r
T
a
nd
the actu
al co
lor
P
. As d
e
s
cribe
d
in
se
ction I, this
mappin
g
rela
tionshi
p can
be
establi
s
h
ed with the help of the look-up t
able, mu
ltiple
regressio
n
o
r
neu
ral net
work m
e
thod
s. In
this pap
er, suppo
rt vector regr
essio
n
wa
s employe
d
to establi
s
h the mappi
ng relatio
n
sh
ip,
whe
r
e the
sta
ndard color
card u
s
e
d
to establi
s
h color corre
c
tion m
odel was h
e
re kno
w
n a
s
t
he
training sam
p
le.
In color
pre
d
i
c
tion sta
ge, as sho
w
n in
Figure 1b), t
he col
o
r of the un
kno
w
n
sampl
e
s
coul
d b
e
me
asu
r
ed
u
s
ing
the
spe
c
troradiomete
r
re
gardi
ng th
e
color
displaye
d via the
ca
mera
and scree
n
,
whi
c
h wa
s
m
a
rked with
P’
(
p’
xi
, p
’
yi
). A
well-esta
blish
ed mod
e
l of
colo
r corre
c
tion
coul
d
b
e
use
d
to obtain th
e predi
cted color
A
(
a
xi
, a
yi
), which can
be use
d
to estimate the actual
value
T
for the unkno
wn color sampl
e
s.
As evidence
d
later in the
experim
ent, by selectin
g the
approp
riate color co
rrectio
n
mod
e
l,
the
predi
cted
col
o
r
A
, com
pared
to
th
e screen display color
P’
,
was able
to better esti
mate the actu
al colo
r of un
kno
w
n
sampl
e
s
T
.
b) Col
o
r p
r
edi
ction
Predicte
d
Color (
a
xi
, a
yi
)
Measur
ed
Color (
p’
xi
, p’
yi
)
color
calibr
a
tio
n
mode
l
a) Co
nst
r
u
c
ting the col
o
r calibratio
n
mo
del
Real
Color (
t
xi
, t
yi
)
Measur
ed
Color (
p
xi
, p
yi
)
CCD
camera
screen
computer
D50
lamp
standar
d
color
patch
spectrora
d
iom
eter
color ca
libr
a
tio
n
mode
l
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TELKOM
NIKA
ISSN:
2302-4
046
Colo
r Cali
brat
ion Model in I
m
aging De
vice Control usi
ng Suppo
rt Vector
Reg
r
e
s
sion (Y
ang B
o
)
5532
3. Suppor
t V
ector
Regre
ssion
for
Co
lor Calibra
ti
on ba
sed
on
Lea
s
t
Mean
Square
d Te
st
Errors Algor
ithm
a. Support Ve
ctor
Reg
r
e
ssi
on (SVR)
In its
pre
s
e
n
t form, th
e S
V
machine
is a n
onlin
ear
gene
rali
zatio
n
of th
e G
e
n
e
rali
zed
Portrait algo
ri
thm largely d
e
velope
d at AT&T Bell Laborato
r
ie
s by
Vapnik an
d co-wo
r
kers [9
]. I
t
is firmly
gro
u
nded
in the
framewor
k
of statistical l
earn
i
ng the
o
ry, o
r
VC the
o
ry [1
0]. In a n
u
tsh
e
ll,
VC theory ch
ara
c
teri
ze
s p
r
ope
rtie
s of learni
ng ma
chine
s
whi
c
h
enabl
e them
to gene
ralize
well
to unse
en d
a
ta. Due to
the indu
strial
c
ontext, SV research
ha
s up to date
had a soun
d
orientatio
n towards
real
-world ap
plications. In
reg
r
e
ssi
on ap
plica
t
ions, excell
e
n
t perform
an
ce
s
were obtain
e
d
[11, 12].
b. Successive 3
σ
Filter
3
σ
rul
e
u
s
e
s
the fact that
99.73% of all
va
lues of a
norm
a
lly dist
ributed p
a
ram
e
ter fall
within th
ree
stand
ard
dev
iations of the
avera
ge [1
3
]. Although t
he 3
σ
ru
le
us
es
th
e n
o
rma
l
distrib
u
tion a
s
a ba
sis, the
same i
s
true
of other dist
ri
bution
s
[14].
In the acqui
sition pro
c
e
ss of the col
o
r
coo
r
din
a
te m
easure
m
ent
value an
d th
e actu
al
value, the li
ght, mea
s
uri
ng in
strum
e
nts an
d recordin
g p
r
o
c
e
ss
may be
ran
dom to
the
introdu
ction o
f
random e
r
ro
r. This stu
d
y involved the use of the 3
σ
criteri
on to filter the origi
n
al
data. Takin
g
into accou
n
t the sam
p
le da
ta with
the ori
g
inal dime
nsi
on of 2, the actual 3
σ
filteri
n
g
wa
s ba
sed
o
n
the dista
n
ce between m
easure
d
va
lu
e and a
c
tual
value as
cri
t
erion, u
s
ed
to
determi
ne wh
ether the dat
a wa
s in a re
aso
nabl
e ran
ge.
S
u
cc
es
siv
e
3
σ
filtering algorithm is as follows:
1) Cal
c
ul
ate the col
o
r devi
a
tion of t
he original color
co
ordin
a
tes d
a
ta
∆
x
i
,
∆
y
i
yi
yi
i
xi
xi
i
p
t
y
p
t
x
,
(1)
Whe
r
e,
p
xi
, p
yi
are
ch
rom
a
ticity coo
r
di
nat
es of th
e
sam
p
le me
asure
m
ents, a
nd
t
xi
, t
yi
are
the chrom
a
ticity co
ordi
na
tes of the
a
c
tual va
lu
e
of sam
p
le
s.
In the follo
wi
ng formula, t
h
e
meanin
g
s of these symbol
s are the same
;
2) Cal
c
ul
ate
the raw dat
a pair re
ga
rding t
he col
o
r co
ordinate
s
in the ch
romaticity
diagram
∆
e
i
2
2
i
i
i
y
x
e
(2)
3) Calculate
the mean di
stance
E(
∆
e)
and the me
a
n
squ
a
re esti
mate
e
ˆ
. MSE is
based on the
actual
stand
a
r
d deviation t
o
estimate
N
i
i
e
N
i
i
e
e
N
e
N
e
E
1
2
1
)
(
1
ˆ
1
)
(
(3a,
b)
4) If
e
i
e
e
ˆ
3
, remov
e
No.
i
s
a
mple;
5) If a sample
is remove
d, go ba
ck to 3),
otherwi
se th
e algorith
m
e
nds.
c. Lea
st Mea
n
Squared Te
st Erro
rs Alg
o
r
ithm
In the RBF kernel
ba
sed
SVR, two pa
rameters na
m
ed the pe
nalt
y
paramete
r
C and th
e
kernel pa
ram
e
ter
γ
sho
u
ld
be determi
n
ed first. Different
values of
these two p
a
ram
e
ters (C,
γ
)
lead to different re
sults of
SVR predi
ct
ion. To
find the be
st para
m
eter
s, the experim
ent d
a
ta
coul
d be divid
ed into two in
depe
ndent
se
ts, one for trai
ning, and the
other for valid
ating.
Thus, the L
e
a
s
t Mean Squ
a
red T
e
st Errors al
go
rithm (LMSTE) i
s
u
s
ed in thi
s
pa
per.
Obje
ctive fun
c
tion that received re
peat
ed trai
ni
ng fo
r optimi
z
ation
wa
s the lea
s
t mean
squ
a
re
d test error, i.e.
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. 10, Octobe
r 2013 : 553
0 –
5538
5533
min
test
N
i
i
i
test
test
a
t
N
mse
1
2
)
(
1
(4)
W
h
er
e
a
i
i
s
t
he p
r
edi
ctive
value of th
e
sample;
t
i
is the a
c
tual
val
ue of th
e
sa
mple;
N
test
is the numb
e
r of test sampl
e
s, 16.7%
of the total s
a
mple in this
s
t
udy.
Thus, the alg
o
rithm can be
modified as f
o
llows:
1) Use of succe
ssive 3
σ
filter to pre
p
ro
cess the origi
n
al data;
2) Data after pretreatment
are divid
ed i
n
to
training samples
set, tes
t
samples
s
e
t and
predi
ction
sa
mples
set, the ratio is: 0.5:
0.167:0.33
3;
3) Data normaliz
ed to [-1, 1];
4) Set the training
param
eters,
i
n
cl
udi
ng the p
enal
ty paramete
r
C
an
d the
kernel
para
m
eter
γ
with the
rang
e
C
mi
n
,
C
ma
x
,
γ
mi
n
,
γ
max
and the g
r
owth
steps
C
step
,
γ
ste
p
, the initial v
a
lue
of the training
param
eters (
C
,
γ
)=
(
C
mi
n
,
γ
mi
n
);
5) Use (
C
,
γ
) and traini
ng sample
s set to
perform the trainin
g
of the SVR;
6) The te
st sample is u
s
e
d
for this trai
ned
SVR to o
b
tain the pre
d
icted valu
e, cal
c
ulate
its
ms
e
test
;
7) If
ms
e
test
is
lower tha
n
the previou
s
sa
ved value, then save thi
s
traine
d SVR model;
8) (
C
,
γ
) =
(
C
+
C
step
,
γ
+
γ
st
ep
);
9) If (
C
,
γ
)
≤
(
C
ma
x
,
γ
ma
x
), go back to 5),
otherwise the
training en
ds.
4. Experimental Re
sults
and An
aly
s
is
a. Experimen
tal Data and
Comp
ared M
e
thod
s
Experimental
data includ
e
d
240 gr
oup
s, where the
Successive 3
σ
Filter wa
s use
d
to
pro
c
e
ss the
raw d
a
ta. Two thirds
were
taken as tra
i
ning sa
mple
s and an
oth
e
r one third as
predi
cted
sa
mples to te
st the va
rio
u
s fitting
m
e
thod
s in
te
rms of thei
r gen
erali
z
ati
o
n
perfo
rman
ce.
To illustrate t
he calibration perform
a
nce
of SVR, the comparativ
e experiment
s were
also
carried
out on seve
ral algorithm
s that are co
mmonly use
d
in color cali
bration, in
clu
d
ing
polynomial
re
gre
ssi
on[15], BP neural net
work an
d rel
e
vance ve
ctor
machi
ne[16].
1) Polynomial
regressio
n
Takin
g
into a
c
count that the actu
al col
o
r
imagi
ng a
nd display is inco
rpo
r
ated
into a
nonlin
ear
system, as sho
w
n in Fig
u
re 1,
P
and
T
a
r
e subje
c
t to a non
-line
a
r f
unctio
n
,
so t
he
experim
ents i
n
this
pap
er
introdu
ce
d a
quad
rati
c pol
ynomial for compa
r
ative e
x
perime
n
ts,
a
s
expre
s
sed in
the followin
g
form.
T
y
x
y
x
y
x
y
x
y
y
y
x
x
x
y
x
P
P
P
P
P
P
P
b
b
P
b
b
b
b
b
b
A
A
2
2
0
0
5
2
1
5
2
1
...
...
(5a,
b)
2) BP neural netwo
rk
(BP)
BP neural ne
twork is
wide
ly used. It is a pr
oven fa
ct
that three-la
yer BP network
ca
n
approximate
any complex
function. In
th
is p
ape
r,
thre
e-laye
r BP n
eural
net
work wa
s al
so
u
s
ed
in com
parative experim
ent
s. As far a
s
the BP net
wo
rk of three lay
e
rs, the hi
dde
n node
s ne
ed
to
be ela
b
o
r
ate
d
. In ord
e
r to
reflect th
e pe
rforma
nce of
BP netwo
rk i
n
this
ca
se, t
he hid
den
no
des
received a
re
peated traini
ng u
s
ing the
BP network
of
a variabl
e
stru
cture to test the mini
mum
sampl
e
MSE
,
aiming to
determi
ne th
e be
st hidd
en no
de
s[17
]. Furtherm
o
re, Leven
be
rg
-
Marq
uardt (L
M) ba
ck-p
rop
agation
with early stop
pin
g
method wa
s appli
ed to p
r
event overfitting.
The main p
a
r
amete
r
s a
r
e:
the transfe
r func
tion of hi
dden laye
r is hyperboli
c
tange
nt
sigmoi
d tra
n
sfer fun
c
tion
(
tansi
g
), a
nd th
e output i
s
li
n
ear t
r
an
sfer functio
n
(
purel
in
). Th
e trai
ni
ng
function i
s
L
M
back-pro
p
a
gation.
It is notewort
h
y that beca
u
se th
e initia
l we
ig
ht matrix for each training
se
ssio
n wa
s
based on ran
dom
valu
es, a
si
ngle
traini
ng
in
a parti
cular network stru
cture
m
a
y
not
b
e
a
b
le
t
o
get the
re
sult
s that truly reflect the
pe
rforman
c
e
of
t
he stru
cture. This pap
er was de
signe
d to
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)
5534
perfo
rm the trainin
g
for 20
times in ea
ch netwo
rk structure, wh
ere the best p
e
r
forma
n
ce (i.
e
.,
minimum
MSE) was u
s
ed
to exp
r
e
s
s
the pe
rfor
ma
nce
of the
n
e
twork struct
ure.
Using
th
is
strategy
and,
ultimately, the b
e
st
stru
cture
of
the
netwo
rk was 2*2*
2. Thi
s
pap
er
had
the
experim
ental
results of the
BP network that we
re all d
e
rived in this
netwo
rk
stru
cture.
3) Rel
e
van
c
e
Vector Ma
chi
ne (RVM
)
In regressio
n
analysi
s
, RVM can get
a vector
mat
r
ix that is sp
arser tha
n
the SVR.
Mean
while, it also ha
s mo
re flexible fea
t
ures i
n
cl
udin
g
the definitio
n of the ke
rn
el function a
n
d
the probabilit
y of output. In
recent
years, the research
activities
hav
e become increasingly active
on the
RVM.
So, this pa
p
e
r
also
involv
ed the
u
s
e
of the Sp
arse
Bayesian
Mo
deling
algo
rit
h
m
(version 2.0
)
(availa
ble
from http://www.r
eleva
n
c
eve
c
tor.
com
)
provid
ed
by Tipping
for
comp
arative experim
ents, whe
r
e
the ke
rnel
fun
c
ti
on
wa
s
con
s
i
s
te
nt with
Ga
ussian
kernel, a
n
d
its
mai
n
p
a
ra
meter ba
sis width (b
w)
al
so su
bje
c
t
to
the
optimiza
t
ion st
rategy
simila
r to
tha
t
in
se
ction 3. Th
e final para
m
eters o
b
taine
d
are:
[
bw
x
bw
y
]
T
= [2.82 19.5]
T
(6)
b. Experimen
t Contents
1) SVR traini
ng
In this paper, Least Mean
Squared T
e
st Errors algorithm descri
bed in
section III was
employed
to
obtain the
tra
i
ning p
a
ra
me
ters
of SVR (
C
,
γ
). With t
he help of LI
BSVM[18],SV
R
algorith
m
wa
s pro
g
ramme
d unde
r Matla
b
R20
09a.
The
trai
ning para
m
eter (
C,
γ
) and
ms
e
on
th
e
p
a
ram
e
ter sp
ace co
nsi
s
tin
g
of
test
sampl
e
s
are
as
sho
w
n i
n
Figure 2. Le
a
s
t Mea
n
Sq
u
a
red
Te
st Errors algo
rithm
looked to g
e
t the
para
m
eter p
a
ir
(
C,
γ
) to minimize
ms
e
test
. In this ca
se, SVR
wa
s obtain
e
d as the
opt
ima
l
para
m
eters:
[
C
x
γ
x
]
T
= [12
8
0.0625]
T
a
nd [
C
y
γ
y
]
T
=
[32 0.125]
T
(7a,
b)
Figure 2. SVR mse va
riati
on with different para
m
ete
r
s (C,
γ
)
In Figu
re
2,
SVR ha
s
12
0 traini
ng
sa
mples,
and
40 te
st sam
p
les,
with
ms
e
to
be
cal
c
ulate
d
on
the test
sam
p
le. Subscript
x
an
d
y
den
o
t
e the CIE 19
31 chro
matici
ty coordinate
s
x
and
y
. The
Lea
st Mean
Squared Te
st Errors algo
rithm (LMST
E
) wa
s empl
oyed to sea
r
ch
para
m
eters (C,
γ
) in the parameter spac
e to minimize
ms
e
.
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Vol. 11, No
. 10, Octobe
r 2013 : 553
0 –
5538
5535
In the n
eural
network trai
ning, the
im
medi
ately fixed trai
ning
sample
s a
nd
netwo
rk
results
will
al
so have
the different pre
d
i
ction mod
e
ls be
cau
s
e
of
different i
n
itia
l wei
ghts of t
he
netwo
rk, an
d the rand
omn
e
ss of their training may
le
ad to the network to be co
nverge
nt to local
optimum. As for the SVR training pa
rameters, so l
ong as the t
r
ainin
g
sam
p
les and traini
n
g
remai
n
the
same, the sa
me predi
ction
model i
s
al
ways obtain
e
d
,
with
the converg
e
n
c
e result
alway
s
bei
ng
the glob
al mi
nimum. Thi
s
i
s
an
other
obv
ious fe
ature
o
f
SVR that is
better tha
n
the
neural network.
2) Perfo
r
man
c
e Evaluation
This expe
rim
ent al
so
we
nt to the
comp
arison
on
several
othe
r
cali
bration
meth
ods that
were mentio
n
ed in se
ction
IV. They presented the
cali
bration
re
sult
s on the colo
r calibration, as
sho
w
n in Ta
b
l
e 1.
Table 1. Perf
orma
nce of different calib
ra
tion method
s
Performa
nce
Uncali
b
rate
d
Qua
d
r
a
tic
pol
y
n
o
m
ial
BP RVM
SVR
SSE
t
0.14275
0.02699
0.02894
0.02902
0.02734
SSE
p
0.03662
0.00762
0.00945
0.00764
0.00637
RM
SE
t
0.02987
0.01299
0.01345
0.01347
0.01307
RM
SE
p
0.02240
0.01022
0.01138
0.01023
0.00934
R
2
t
0.90855
0.98271
0.98146
0.98141
0.98248
R
2
p
0.88695
0.97647
0.97083
0.97641
0.98034
M
EAN(
∆
d
p
)
0.02094
0.00808
0.00958
0.00803
0.00663
std
p
0.00800
0.00629
0.00618
0.00638
0.00662
r
t
**
0.98998
0.99157
0.99111
0.99093
0.99146
r
p
**
0.98989
0.99064
0.98946
0.98981
0.99167
M
AX(
∆
d
t
)
0.05961
0.06308
0.06469
0.06481
0.06327
M
AX(
∆
d
p
)
0.05329
0.04526
0.04410
0.04279
0.04534
*NG
p
0 1
6
5
1
*
NG
indicated th
e number of
samples w
i
th gre
a
ter
∆
d
than uncalibr
a
ted.
**
r
was defined a
s
Pearson produ
ct-mom
ent corr
elation coefficient[19].
In Table 1, all evaluation in
dicato
rs
we
re
calculated o
n
distan
ce e
r
ror vecto
r
s
∆
d
i
.
2
2
)
(
)
(
yi
yi
xi
xi
i
a
t
a
t
d
(8)
In this study
, the output variable
wa
s two, includi
ng ch
rom
a
ticity coordin
a
tes
x,
y
.
Therefore, th
e error
cal
c
u
l
ation nee
ds
to cover th
e
errors in b
o
th dire
ction
s
.
a
xi
is
x
for the
predi
cted val
ue of the
sa
mple,
a
yi
, th
e c
o
or
d
i
na
te
y
; Lik
e
wise,
t
xi
, t
yi
indicate
x, y
for the
actual
value of the sample.
The subs
cr
ipt
t
and
p
ide
n
tified the cal
c
ulation on
16
0 trainin
g
sa
mples
or 7
3
predi
ction
sampl
e
s. A
s
see
n
from
th
e Tabl
e 1, alt
houg
h
the SV
R did
have th
e be
st corre
c
tion pe
rforma
nce
for the traini
ng sam
p
le, it had the best value for
the indicato
rs of all the pre
d
icting
sampl
e
s,
esp
e
ci
ally
r
p
and
NG
p
(
NG
, the Numb
er of sa
mple
s with G
r
eat
er
∆
d
th
an
un
c
a
lib
r
a
t
ed
.)
. T
h
is
sho
w
s that the SVR had th
e optimum ge
nerali
z
atio
n a
b
ility.
Among the e
x
perime
n
tal result
s, the q
uadrat
ic p
o
lynomial a
nd t
he pe
rform
a
n
c
e of BP
netwo
rk a
r
e
simila
r to
re
sults o
b
taine
d
by Liu
et
al[20]. Ho
weve
r, this d
o
e
s
n
o
t sh
ow that
the
neural n
e
two
r
k ha
s
a p
e
rf
orma
nce that
is
wo
rse
th
a
n
that of
the
quad
ratic pol
ynomial, only
to
find that in thi
s
ca
se, a
s
fe
w a
s
1
60
sa
mples were
u
s
ed
for t
r
ainin
g
, leadin
g
to i
s
n
o
t fully ne
ura
l
netwo
rk l
earn
i
ng and th
e d
e
clin
e of
its g
eneralization
ability. This al
so
sho
w
s th
a
t
in the ca
se
o
f
small sampl
e
s, SVR, base
d
on statisti
cal learni
ng th
eory, has b
e
tter gene
rali
za
tion ability. RVM
failed to
sh
o
w
g
ood
pe
rfo
r
man
c
e
in thi
s
ca
se, in
spi
t
e of the
use
of Ga
ussia
n
ke
rnel
same
as
SVR,
whi
c
h use
d
a sp
arser relevan
c
e
vector, re
su
l
t
ing in the
d
e
crea
sed
abil
i
ty of the exact
approa
ch
an
d thu
s
un
de
rfitting appe
ared. The
r
efo
r
e
,
there i
s
a
n
eed to fin
d
a
suita
b
le
ke
rnel
function fo
r
improvin
g th
e perfo
rma
n
c
e of
RVM. Quad
ratic
polynomial
d
i
splaye
d a g
ood
perfo
rman
ce
in this ca
se,
mainly attribu
t
ed to
a high degree of lin
ear
correlatio
n of the origi
nal
sampl
e
(
r
t
=0
.98998,
r
p
=0
.98989
), and
the se
co
nd
polynom
ial
further im
p
r
oved its li
n
ear
correl
ation co
efficient.
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Colo
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ion Model in I
m
aging De
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rt Vector
Reg
r
e
s
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ang B
o
)
5536
Figure 3
sh
ows the
pre
d
iction
erro
r of va
rio
u
s method
s
in
CIE
193
1 ch
romati
city
diagram,
whi
c
h i
n
cl
ude
s t
he
size of fo
recast
erro
rs and
their di
rectio
ns in t
he
chromati
city
diagram. Th
e
si
ze
of forecast e
r
rors
ca
n be
mo
re
cl
early see
n
in
figure 4.
In
Fi
gure
s
3
a
nd 4,
it
is clea
r
th
at no co
rre
ction
of
alm
o
st all
sa
mple
s
are
larg
er than
the
co
rre
ction
brought
by t
he
different
co
rrection
meth
o
d
s,
with o
n
ly
a few valu
e
s
that a
r
e
only
rel
a
tively sm
all (th
e
spe
c
if
ic
numbe
r we
re
given by
NG
p
in
Table
1. Thi
s
sho
w
s that th
e va
riou
s
co
rre
cti
on met
hod
s
can
redu
ce
the e
r
rors of the
origi
nal me
asurements,
wh
er
e the ave
r
ag
e erro
r corre
c
ted by SVR
is
the smalle
st, with the be
st overall pe
rformance.
In Figure
3, the absci
ssa and verti
c
al coo
r
din
a
te
s are, re
spe
c
tively, the measured
values of
ch
romaticity
coo
r
dinate
s
x, y
for p
r
edi
ction
sa
mple
s. Ve
ctor diag
ram
stand
s fo
r th
e
differen
c
e
bet
wee
n
predi
cted an
d a
c
tua
l
values fo
r
a
variety of m
e
thod
s. In order to
be
cle
a
rly
displ
a
yed on
the map, the length of the ve
ctor h
a
s u
n
d
e
rgo
ne the a
u
tomatic
scali
ng.
Figure 3. Sca
l
ed error ve
ctors o
n
predi
ction sam
p
le
s
In Figure
4, the ab
sci
ssa i
s
the num
be
r of
predi
ction
sampl
e
s, an
d in this stu
d
y
, th
e
numbe
r
of predictive sam
p
les
i
s
73. V
e
rtical
axis i
s
the di
stan
ce
betwe
en th
e
mea
s
ured
a
n
d
predi
cted
val
ues in
the
CIE 19
31
chrom
a
tici
ty
coordi
nate
s
. The error curve sh
ows
the
gene
rali
zatio
n
ability of th
ese five m
e
th
ods, the
mea
n
erro
r an
d t
he sta
nda
rd
deviation
can
be
see
n
in T
abl
e 1. In the fi
gure, fo
ur
kin
d
s of d
a
ta o
b
tained
by the sa
mple
s
were
clo
s
e
r
to
the
actual valu
e than the un
co
rrecte
d data.
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 10, Octobe
r 2013 : 553
0 –
5538
5537
Figure 4. Cali
bration e
r
rors of different method
s
5. Conclusio
n
These above
results may l
ead to the followin
g
co
nclu
sion
s:
1) Su
cce
ssive 3
σ
Filter al
gorithm
can
b
e
use
d
to eli
m
inate the la
rger e
r
rors fou
nd in the
measurement
data, and
also
able to
improve th
e gen
erali
z
at
ion capa
bility of corre
c
tion
algorith
m
;
2) The L
e
a
s
t Mean Squa
red Test Errors
algo
rithm can be u
s
ed t
o
optimize th
e SVR
para
m
eters, while redu
cin
g
the
amount
of fitting and over fitting;
3)
Com
pared
with
other m
e
thod
s in
col
o
r
co
rre
ction,
the SVR met
hod
pre
s
e
n
te
d a m
o
re
accurate p
r
e
d
iction
of un
kno
w
n
sam
p
l
e
s, that is
,
chrom
a
ticity coordi
nate
s
of
its proje
c
tions
sho
w
e
d
the more a
c
curate estimation
on
the actu
al chromati
city coordi
nate
s
.
Thro
ugh the
prop
osed dyn
a
mic ove
r
mo
dulation
meth
od, a quick d
y
namic torqu
e
cont
rol
can be a
c
hi
eved by sel
e
cting a voltage vecto
r
that prod
uces the large
s
t tangential flux
comp
one
nt. The p
r
op
ose
d
method i
s
ca
pable
of obtai
ning the
faste
s
t dynami
c
to
rque
control f
o
r
any ope
rating
conditio
n
s i
n
cludi
ng the fi
eld we
ak
enin
g
regi
on with
six-ste
p
mod
e
. The propo
sed
dynamic
ove
r
modulatio
n re
sulted
in a si
mple
hy
ster
e
s
is-ba
s
e
d
structure a
s
ori
g
inally DT
C.
O
n
ly
minor modifi
cation
is nee
ded
and
no
SVM and
he
nce
voltage
referen
c
e
a
r
e
req
u
ired to
be
gene
rated.
M
o
st of
the
m
a
in
com
pone
nts of
t
he
b
a
si
c
DT
C hy
stere
s
i
s
-ba
s
e
d
st
ru
cture
a
r
e
retained.
Ackn
o
w
l
e
dg
ments
This work was supp
orted
by the Chu
nhui
Plan sp
onsore
d
by Ministry of Education
(Grant Z2
00
8-1
-
63
019
) a
nd the
sci
en
tific and
te
ch
nologi
cal re
search proj
ect
by
Cho
ngqi
ng
Munici
pal Ed
ucatio
n Co
m
m
issi
on (Gra
nt KJ091
409
). Thanks for
the postd
oct
o
ral resea
r
ch
in
depa
rtment o
f
optics an
d p
hotoni
cs
of National Central University.
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TELKOM
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ISSN:
2302-4
046
Colo
r Cali
brat
ion Model in I
m
aging De
vice Control usi
ng Suppo
rt Vector
Reg
r
e
s
sion (Y
ang B
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)
5538
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