Co
m
pu
ter Sci
ence a
nd Inf
or
mat
i
on
Tec
h
no
lo
gies
Vo
l.
1
, No
.
3
,
Novem
ber
2020
, p
p.
12
6
~
1
3
4
IS
S
N:
27
22
-
3221
,
DOI: 10
.11
591
/
csi
t.v
1i
3
.p
12
6
-
134
126
Journ
al h
om
e
page
: htt
p:
//
ia
esprime
.com/i
ndex.
php/csit
An opti
mized
rubb
er
sh
eet m
odel fo
r norm
alizati
on phas
e of
IRIS rec
og
niti
on
Selvam
uthuk
uma
r
an
.
S
1
,
R
amk
u
mar
.T
2
, Sha
nt
h
ar
ajah
SP
3
1
Facul
t
y
of
Com
pute
r
Appl
ic
a
ti
o
ns,
AV
C
Coll
eg
e
of
Engi
n
ee
ring
,
Indi
a
2,3
School
of
In
fo
rm
at
ion
T
ec
hno
l
og
y
& Engi
ne
ering,
VIT
Univer
s
ity
,
India
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
J
a
n
23
, 2
0
2
0
Re
vised
Ma
y
2
7
, 2
0
2
0
Accepte
d
J
un
1
6,
20
2
0
Iris
re
cogni
t
ion
is
a
prom
ising
b
iometri
c
au
the
nt
ic
a
ti
on
appr
oa
ch
and
it
is
a
ver
y
ac
t
ive
top
ic
in
both
r
ese
arc
h
and
r
ea
l
isti
c
applications
b
ecause
the
patter
n
of
the
hum
an
ir
i
s
diffe
rs
from
p
erson
to
p
erson,
eve
n
be
twee
n
t
wins.
In
th
is
pape
r,
an
opt
imize
d
iri
s
norm
a
li
z
at
ion
m
et
hod
for
the
conve
rs
ion
o
f
segm
ent
e
d
image
int
o
nor
m
al
iz
ed
form
has
bee
n
p
ropose
d.
Th
e
ex
isti
ng
m
et
hods
are
conve
rt
ing
the
Cart
esi
an
coor
d
ina
t
es
of
the
s
egmente
d
imag
e
in
to
po
la
r
coor
dinates.
To
get
m
ore
a
cc
ur
acy
,
th
e
p
roposed
m
et
hod
is
using
an
opt
imize
d
rubbe
r
sh
ee
t
m
odel
w
hic
h
con
ver
ts
the
pol
ar
coor
d
inates
into
spheri
cal
coor
dinates
fol
l
owed
b
y
lo
calized
histogr
am
eq
ual
i
za
t
ion.
The
expe
riment
al
result
show
s
th
e
proposed
m
et
h
od
score
s
an
en
cour
agi
ng
per
for
m
anc
e
wi
th
respe
ct t
o
accurac
y
.
Ke
yw
or
d
s
:
Bi
om
e
tric
s
Histo
gr
am
equal
iz
at
ion
IRIS
norm
al
iz
a
ti
on
IRIS
rec
ogniti
on
Spherical
c
oor
din
at
es
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Selvam
uth
ukum
aran
.S
,
Faculty
of Com
pu
te
r
A
pp
li
c
at
ion
s,
AV
C C
ollege
of Enginee
rin
g, I
ndia
.
Em
a
il
:
s
m
ks
m
k@gm
ai
l.co
m
1.
INTROD
U
CTION
The
progressi
ve
di
gital
so
ci
et
y
de
m
and
s
s
ecur
e
i
den
ti
fic
at
ion
te
ch
niqu
es
for
the
de
ve
lop
m
ent
of
bio
m
et
ric
syst
em
in
div
e
rse
fi
el
ds
[
1].
T
he
iri
s
bio
m
et
ric
syst
e
m
s
are
bec
om
ing
c
omm
on
ly
im
ple
m
ented
as
one
of
the
best
way
s
to
ce
rtai
nly
i
den
ti
fy
pe
ople
[2
]
.
T
he
iris
is
an
outwa
rd
ly
a
nd
c
olour
f
ul
organ
cl
os
e
the
pupil
of
the
ey
e
[
3].
Fi
gure
1
s
how
n
t
he
str
uctur
e
of
the
ey
e,
w
hic
h
dem
on
strat
es
the
e
xact
posit
ion
of
t
he
iris
and
it
s
su
r
rou
nd
i
ng
th
ing
s
.
T
he
pro
pe
rty
of
t
he
iris
gu
a
ra
ntees
th
at
even
e
qual
twins
ha
ve
unc
orrelat
ed
iris
de
ta
il
s
.
Th
us
,
t
he
e
xclu
sivit
y
of
eve
ry
iris,
incl
ud
i
ng
the
c
ouple
poss
essed
by
si
ng
le
ind
i
vidual,
pa
r
al
le
ls
the
excl
usi
vity
of
eve
ry
fin
ge
rprint
regar
dless
of
w
hethe
r
there
is
a
c
om
m
on
ge
no
m
e
[
4,
5].
Th
e
iris
in
vo
l
ve
s
of
s
ever
al
irregular
sm
al
l
blo
c
ks
sim
il
ar
to
fr
ec
kles
,
stri
pes,
f
urr
ow
s
,
c
oro
nas
,
et
c
.
In
add
it
io
n,
the
te
xture
div
isi
ons
in
th
e
iris
are
ar
bitrar
y
.
Th
e
se
parat
e
m
erit
s
of
t
he
iris
ca
us
e
it
s
high
c
onsist
en
cy
for
in
div
id
ua
l
identific
at
io
n
[6
]
.
Hen
ce
the
m
et
hod
of
iris
i
de
ntific
at
ion
bec
om
es
an
excit
ing
resea
rc
h
point
in
c
urren
t
y
ears
[7
]
.
The
fi
rst
ste
p
in
iris reco
gnit
ion
is
the
proce
ss
of
ca
pturin
g
the
im
age
of
a
n
ey
e [8
]
. Dur
i
ng
sta
ge
of
the
i
m
age
acq
uisit
i
on,
a
ca
m
era
is
us
e
d
to
rec
ord
iris
te
xtures
.
T
he
ca
pt
ur
e
d
im
age
is
furthe
r
pr
ocess
ed
f
or
the
l
ocali
zat
ion
sta
ge
,
wh
e
re
the
locat
io
n
of
the
iris
is
car
ried
ou
t,
f
ollo
we
d
by
the
se
gm
e
ntati
on
phase.
I
n
se
gm
entat
ion
,
irise
s
a
re
sepa
rate
d
from
the
ey
e
[6]
.
Ne
xt
t
o
t
his,
a
no
rm
alizat
io
n
of
th
e
iris
im
age
is
done
us
i
ng
var
i
ou
s
no
is
e
rem
ov
al
te
c
hniq
ues
,
and
t
he
im
ages
are
st
or
e
d
in
t
he
bi
nar
y
f
or
m
at
[
9].
The
pro
cess
of
th
e
i
ris
rec
ogniti
on
syst
e
m
con
ti
nues
wit
h
the
featu
re
e
xtr
act
ion
sta
ge,
w
her
e
the
e
xtract
ion
s
of
va
rio
us
featur
e
s
of
irise
s
are
id
entifi
ed
[10].
I
n
ver
i
ficat
ion
process
,
m
at
ching
will
be
do
ne
w
her
e
the
ac
qu
i
red
im
age
is
com
par
e
d
with
the
im
ages
store
d
in
the
dat
abase
[11].
A
ty
pical
iris rec
ogniti
on syst
e
m
w
hich
include
s a
bove
stages is
sho
w
n
in
the
Fig
ur
e
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
Com
pu
t.
Sci.
I
nf. Tec
hnol.
An o
ptimized
r
ubber
sh
eet
m
odel
for
nor
ma
li
za
ti
on
phas
e
of
I
R
IS reco
gnit
ion
… (
Selva
mu
t
hu
k
umar
an.
S
)
127
Figure
1. Str
uc
ture of
an
ey
e
Figure
2.
IRIS
r
ecognit
ion s
yst
e
m
In
the
phase
of
norm
al
iz
a
ti
on
,
segm
ented
i
ris
im
age
has
been
pr
e
par
e
d
f
or
the
feat
ure
ext
racti
on
process
.
Th
ou
g
h,
seve
ral
of
al
go
rit
hm
s
[1
,
5,
11
]
are
a
vaila
ble
f
or
th
e
norm
al
iz
a
ti
on
phase
of
th
e
Ir
is
recog
niti
on
,
D
aughm
an’
s
[
12]
an
d
Wilde
’s
[13]
al
go
rithm
s
are
si
gn
i
ficant.
T
o
c
om
pen
sat
e
the
di
ff
e
re
nces
i
n
the
m
agn
it
ud
e
of
the
pupil
,
D
aughm
an
[
12
]
pro
po
se
d
a
r
ub
ber
sh
eet
m
od
e
l
for
norm
al
iz
a
t
ion
.
I
n
t
his
way
,
so
m
e
of
the
irise
s
sti
ll
m
ay
be
seal
e
d
by
ey
el
ids
or
ey
el
ashes
,
e
ve
n
w
hen
the
in
ne
r
a
nd
ou
te
r
boun
dar
ie
s
of
t
he
iris
are
reac
hed
.
W
il
des’
syst
em
is
a
pate
nt
of
t
he
iris
rec
ogniti
on
syst
em
wh
ic
h
e
m
plo
ye
s
the
gradie
nt
-
ba
sed
Hou
gh
trans
form
to
cho
ose
the
t
wo
ci
rcu
la
r
bo
undar
i
es
of
an
i
ris.
It
has
big
c
om
pu
ta
ti
on
al
cha
r
ge
,
since
it
exam
inat
es
a
m
on
g
al
l
of
th
e
possi
ble
ca
ndidate
s.
Be
si
des
,
the
al
gorithm
’s
accu
racy
si
gnific
antly
deteri
or
at
es
w
hile
de
al
ing
with
the
noisy
data.
T
he
a
bove
tw
o
norm
alizat
ion
te
ch
niques
tra
nsfo
rm
Ca
rtesi
an
co
or
din
at
es
in
to
pola
r
coor
din
at
es
f
or
u
n
-
wr
a
ppin
g
the
iris
te
xtur
e
int
o
a
fixe
d
siz
e
rectan
gula
r
blo
c
k.
I
n
pola
r
co
ordi
nates
,
t
he
distance
an
d
a
ngular
po
sit
io
n
ha
ve
ext
rem
ely
aff
ect
e
d
i
ris
i
m
ages
with
re
sp
ect
t
o
t
he
ca
m
era
.
Additi
onal
ly
,
il
lu
m
inati
on
ha
s
a
direct
in
flue
nce
on
t
he
pu
pil
siz
e
and
s
ourc
es
non
-
li
near
di
sti
nctions
of
t
he
iris
patte
rn
s
[14]
.
More
ov
e
r,
the
pupil
bo
unda
r
y
and
li
m
bu
s
bounda
ry
are
us
ua
ll
y
two
no
n
-
c
oncentric
c
on
t
ours.
T
he
non
-
co
nce
ntric
co
ndit
ion
le
a
ds
to
di
ff
e
ren
t
ch
oices
of
re
fer
e
nce
points
f
or
tra
nsfo
rm
ing
an
iris
int
o
pola
r
coor
din
at
es,
w
hich
is
no
t
s
ui
ta
ble
for
iris
i
m
ages
with
m
or
e
no
ise
.
H
ence,
it
is
ne
cessary
to
a
dopt
an
op
ti
m
iz
ation
te
chn
i
qu
e
for
t
ra
ns
f
or
m
ing
t
he
iris
im
age
to
c
om
pen
sat
e
the
se
va
riat
ions.
I
n
t
his
pap
e
r,
w
e
ha
ve
pro
po
se
d
a
n
optim
iz
ed
norm
al
iz
at
ion
t
echni
qu
e
based
on
rubb
e
r
s
heet
m
od
el
wh
ic
h
conve
rts
Ca
rtesi
an
coor
din
at
es
i
nt
o
s
pherical
c
oor
din
at
es
i
nst
ead
of
po
la
r
co
ordi
nates
and
perform
local
iz
ed
histogram
equ
al
iz
at
io
n
f
or
furthe
r
acc
ur
acy
.
The
res
t
of
the
pa
per
has
been
org
anized
as
f
ollow
s;
in
sec
ti
on
2,
th
e
i
m
pr
ovise
d
m
od
el
for
iris
norm
al
iz
ation
ha
s
bee
n
il
lustr
at
ed
with
the
inclusive
ste
ps.
The
e
xp
e
rim
ental
inv
est
igati
ons
of
t
he
pro
po
se
d
work
with
th
e
help
of
CA
S
IA
databa
se
[
15]
is
ex
plaine
d
in
sect
io
n
3,
wh
e
re
con
cl
ud
i
ng r
e
m
ark
s a
nd f
eat
ur
e
r
es
ea
rch di
recti
on
s
are
sum
m
arized in
se
ct
ion
4.
2.
AN OPTI
MIZ
ED RUBB
ER
SHEE
T M
ODE
L FOR
IR
I
S
N
O
R
MA
LIZ
ATIO
N
The
norm
al
iz
ation
sta
ge
ai
m
s
to
gain
in
var
ia
nce
t
o
siz
e,
pos
it
ion
a
nd
pupil
dilat
at
ion
i
n
t
he
se
gm
ented
iris
re
gion.
Mo
st
of
t
he
m
et
ho
ds
us
e
Da
ughm
an’
s
[12]
rub
ber
s
heet
m
odel
co
ns
ide
rs
t
he
possi
bili
ty
of
pu
pil
dilat
ion
a
nd
th
e
ap
pear
a
nce
of
di
ff
e
ren
t
siz
e
s
in
diff
e
re
nt
im
ages.
F
or
thi
s
pur
pose,
t
he
coor
din
at
e
syst
e
m
is
al
te
red
by
un
-
wr
a
ppin
g
the
ir
is
and
pl
otti
ng
al
l
the
po
i
nts
w
it
hin
the
e
dg
e
of
the
ir
is
i
nto
t
he
ir
pola
r
c
oor
din
at
es
.
The
Ca
rtesi
an
to
pola
r
tra
ns
f
or
m
at
ion
is
defi
ned
f
or
the
co
ntinuo
us
f
or
m
of
im
ages.
H
oweve
r,
in
t
he
di
screte
form
,
the
tra
nsfo
rm
ation
e
nc
ounte
rs
pro
blem
s
in
w
hich
the
po
la
r
sam
ples
do
no
t
entirel
y
m
at
ch
the
Ca
r
te
sia
n
sam
ple
s
wh
ic
h
resu
lt
s
in
exce
s
sive
i
nter
po
la
ti
on
a
nd
i
n
s
om
e
cases
loss
of
i
nfor
m
at
ion
w
ould
be
t
he
res
ult.
T
he
pro
po
se
d
m
et
ho
d
is
the
im
pr
ovise
d
m
et
ho
d
of
Da
ughm
an’s
r
ubbe
r
s
heet
m
od
el
and
it
im
pr
ov
es
t
he
ac
cur
acy
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2722
-
3221
Com
pu
t. Sci.
I
nf. Tec
hnol.
,
V
ol.
1
, N
o.
3, N
ov
em
ber
20
20:
12
6
–
134
128
by
ad
vocat
in
g
a
two
-
ste
p
pr
oc
ess.
At
First,
th
e
co
ordinate
syst
e
m
of
th
e
I
ris
re
gion
is
c
onve
rted
from
Ca
rtesi
an
into
the
s
ph
e
ric
al
.
T
hen,
the
re
m
app
in
g
proce
ss
is
do
ne
f
or
t
he
norm
al
iz
at
i
on.
Locali
ze
d
hi
stog
ram
eq
ual
iz
at
ion
is
ap
plied
on
the
i
ris
reg
i
on
f
or
f
ur
t
her
nor
m
al
iz
ation
.
Th
e
va
rio
us
inclu
sive
sta
ges
of
t
he
pro
posed
w
ork
a
r
e
il
lustrate
d
in
th
e
Fig
ur
e
3.
Figure
3.
Flo
wc
har
t
of pr
opos
e
d work
2.1.
Conv
ersi
on o
f
ca
r
tesian co
or
dina
tes
in
to s
pheric
al c
oor
dinates
In
the
s
pherica
l
coo
r
dina
te
syst
e
m
,
the
po
sit
ion
of
a
po
i
nt
is
sp
eci
fied
by
three
co
ordi
nates;
(
,
,
)
wh
e
re
‘
’
is
t
he
ra
dial
distanc
e
f
r
om
a
fixe
d
or
i
gin
,
‘
’
is
the
el
evati
on
a
ng
l
e
of
that
point
from
a
pla
ne,
a
nd
‘
’
is
the
azi
m
ut
h
a
ng
le
of
it
s
ort
hogo
nal
pro
je
ct
ion
on
that
plane
from
a
fixed
directi
on.
The
el
e
vation
ang
le
is
of
te
n
re
pl
a
ced
by
the
i
nc
li
nation
a
ng
l
e
m
easur
ed
from
the
azim
uth
;
the
directi
on
pe
rpen
dicu
la
r
to
the
ref
e
re
nce
pl
ane.
Th
e
ra
dial
distance
is
al
so
nam
ed
the
rad
iu
s
or
ra
di
al
coo
r
din
at
e
and
t
he
incli
na
ti
on
is
nam
ed
as
cola
ti
tud
e.
T
he
co
ordinate
c
onve
rsion
is
re
pr
es
ented
in
Fig
ure
4.
D
uri
ng
c
o
-
ordi
nate
c
onve
rsion
,
the
ce
ntre
of
th
e
pupil
is
co
ns
i
der
e
d
as
locat
i
on
point
an
d
t
he
ra
dial
vect
or
ci
rcle
has
bee
n
consi
der
e
d
in
t
he
Ir
is
reg
i
on.
T
he
c
oor
din
at
e
c
onve
rsion
is
pe
rform
ed
to
obta
in
the
in
var
ia
nce
of
iris
siz
e,
po
sit
ion
a
nd
di
fferen
t
degrees
of
pupil
dilat
ion.
It
pro
duces
t
he
iris
re
gions
,
wh
ic
h
have
th
e
sam
e
con
sta
nt
dim
ensions,
with
the
intenti
on
th
at
two
im
ages
of
the
sam
e
iris
sho
uld
ha
ve
char
act
e
risti
c
f
eat
ur
es
unde
r
diff
e
re
nt
co
ndit
ion
s
at
the
sam
e
sp
at
ia
l
place.
T
he
propose
d
te
c
hniq
ue
is
use
f
ul
in
br
i
ng
i
ng
iris
im
ages
i
nto
a
sta
ndar
d
fixe
d
res
ol
ution,
wh
ic
h
sim
plifie
s
the
featu
re
extracti
on
proc
ess.
I
n
the
a
dj
us
te
d
r
ubbe
r
s
h
eet
m
od
el
,
th
e
centre
of
t
he
pupil
is
us
e
d
as
the
r
efere
nce
point
;
an
d
the
ra
di
al
and
azi
m
u
th
ve
ct
ors
c
ross
the
iris
re
gion.
The
s
pherical
coor
din
at
es,
(
,
,
)
of
a
po
i
nt
can
be
obta
ined
from
it
s
Ca
rtesi
an
coor
din
at
es,
(
,
,
)
by
the foll
owin
g
e
qu
at
io
n
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
Com
pu
t.
Sci.
I
nf. Tec
hnol.
An o
ptimized
r
ubber
sh
eet
m
odel
for
nor
ma
li
za
ti
on
phas
e
of
I
R
IS reco
gnit
ion
… (
Selva
mu
t
hu
k
umar
an.
S
)
129
Figure
4
Co
ordi
nate co
nversi
on
=
√
2
+
2
+
2
(
1)
=
(
,
)
(2)
=
|
√
2
+
2
|
(
3)
Wh
e
re
(
,
)
is a
va
r
ia
nt of th
e
arct
ang
e
nt
functi
on that
r
et
urns
t
he
a
ng
le
fro
m
the
-
axis
to
t
he
vecto
r
(
,
)
in
the
fu
ll
ra
ng
e
(
−
,
)
.
The
form
ulas
assume
that
the
two
syst
em
s
hav
e
the
or
i
gin
,
t
he
n
the
sp
he
rical
ref
e
r
ence
pla
ne
is
the
Ca
rtesi
an
′
−
′
plan
‘
’
is
the
incli
natio
n
fro
m
the
′
′
directi
on
a
nd
the
azim
uth
an
gles
are
m
easur
ed
us
in
g
t
he
c
oor
din
at
es.
Af
te
r
conve
rting
the
dat
a
points
of
the
iris
reg
i
on
int
o
sp
he
rical
co
or
din
at
es,
rem
app
in
g
has
been
done
t
o
re
scal
e
the
po
i
nts
on
t
he
a
ng
le
a
rou
nd
the
in
ner
a
nd
oute
r
bounda
ries.
T
he
rem
app
in
g
of
t
he
iris
r
egi
on
from
′
(
,
,
)
′
,
the
Ca
rtesi
an
c
oord
i
nates
to
t
he
norm
al
ise
d
sp
he
ric
al
r
e
pre
sentat
ion can
be m
od
el
le
d
as i
n
the
foll
owin
g eq
uation.
(
(
,
,
)
,
(
,
,
)
,
(
,
,
)
)
=
(
,
,
)
(4)
Wh
e
re
′
(
,
,
)
′
is
the
iris
re
gion
i
m
age,
‘
(x,y,z)
’
are
the
ori
gi
nal
Ca
rtesi
an
coor
din
at
es,
a
nd
‘(
,
,
)
′
are
the
co
rres
pondin
g
norm
al
iz
ed
spherical
coor
din
at
es.
It
al
so
re
pr
ese
nts
the
co
ordinates
of
the
pupil
and iris
bounda
ries alo
ng the
‘θ’ d
irect
io
n a
nd furnis
hed in
the
fo
ll
owin
g equ
at
io
ns.
(
,
,
)
=
(
,
,
)
(5)
=
(
,
)
+
(
(
,
)
-
(
,
)
)
1
(6
)
=
(
,
)
+
(
(
,
)
-
(
,
)
)
1
(
7)
=
(
,
)
+
(
(
,
)
-
(
,
)
)
1
(
8)
wh
e
re θ
=
2
,
Her
e
′
′
is
the
′
×
′
norm
al
iz
ed
i
m
age
and
′
(
,
)
,
(
,
)
,
(
,
)
′
an
d
′
(
,
)
,
(
,
)
,
(
,
)
′
are
the
c
oor
din
at
es
of
th
e
in
ner
a
nd
ou
t
er
boun
dar
y
points.
′
′
is
t
he
i
nc
li
nation
from
the
‘Z’
directi
on
i
n
the
ori
gin
al
im
age,
‘
’.
This
proces
s
en
ds
with
the
norm
al
ise
d
Ir
is
i
m
age,
w
hich
i
s
furthe
r
f
orwa
rded
for hist
ogra
m
eq
ualiz
at
ion
w
it
h
t
h
e
view of
g
et
ti
ng
bette
r
acc
ur
acy
.
2.2.
Localiz
ed hist
og
r
am
equ
alizati
on
The
no
rm
alize
d
im
age,
res
ultant of
th
e p
r
evi
ou
s
phase
m
ay
ha
ve
lo
w
inte
ns
it
y
co
ntrast
a
nd
im
pr
oper
br
i
gh
t
ness
due
to
the
posit
ion
of
the
li
ght
s
ou
rces
a
nd
ot
her
issues.
I
n
su
c
h
s
it
uations
,
to
ac
hieve
m
or
e
acc
ur
at
e
resu
lt
s,
histogr
a
m
equ
al
iz
at
io
n
has
been
c
hose
n.
This
m
eth
od
is
a
c
on
t
ra
st
en
ha
ncem
ent
te
chn
i
que
with
t
he
obj
ect
ive
to
obta
in
a
ne
w
e
nh
anced
iris
im
a
ge
with
a
unif
or
m
histo
gr
am
.
It
distrib
utes
the
histo
gr
am
of
the
pix
el
le
vels
in
a
un
if
orm
m
ann
er
without
an
y
loss.
It
has
be
en
im
ple
m
ented
f
or
im
pr
oving
t
he
look
of
a
no
isy
i
m
age b
y am
pl
ifie
s the g
l
ob
al
co
nt
rast of the
iris i
m
age.
Th
e h
ist
ogram
, ‘
[
]
’ c
on
ta
in
s p
i
xels
w
it
h
the
value
,
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2722
-
3221
Com
pu
t. Sci.
I
nf. Tec
hnol.
,
V
ol.
1
, N
o.
3, N
ov
em
ber
20
20:
12
6
–
134
130
′
′
.
T
he
c
um
ulativ
e
densi
ty
fun
ct
ion
of
the
his
togram
‘
[
]
’
co
nt
ai
ns
the
num
ber
of
pix
el
s
wit
h
the
val
ue,
′
′
or less i
s
giv
e
n by the
f
ollowi
ng
e
quat
io
n.
(
[
]
)
=
[
0
]
+
[
1
]
+
[
2
]
+
⋯
+
[
]
(9)
It
shou
l
d
be
ap
plied
to
eac
h
pi
xel
in
the
Ir
is
i
m
age
and
rep
l
ace
the
existi
ng
val
ue
with
th
e
cal
culat
ed
value.
T
he
hi
stogram
of
a
dig
it
al
i
m
age
in
the
range
of
[
0
,
−
1
]
is
a
discr
et
e
functi
on
a
s
giv
e
n
i
n
the foll
owin
g
e
qu
at
io
n.
(
)
=
(
10)
Wh
e
re
‘
’
is
th
e
k
th
gray
le
vel
,
is
th
e
nu
m
ber
of
pix
el
i
n
t
he
im
age
with
th
at
gr
am
le
ve
l,
‘n’
is
t
he
total
n
um
ber
of
pix
el
s in
the
im
age,
an
d k =
0,1,2,…
,K
-
1.
(
)
Gives
the
pro
ba
bili
ty
o
f occu
r
ren
ce
level
,
.
Con
si
der the
f
ollow
i
ng sam
ple o
ri
gin
al
e
ntire ey
e s
how
n
i
n
the
foll
owin
g
Fig
ur
e
5.
Figure
5. O
rigi
nal im
age b
ef
ore local
iz
ed
h
is
togram
eq
ualiz
at
ion
The c
ontrast
of
the
i
ris
im
age
is
am
plifie
d
,
m
ai
nly
w
hen
the
us
e
d
data
of
t
he
iris
im
age
is
r
epr
ese
nted
by
near
c
ontra
st
val
ues.
T
he
intensit
y
w
ould
be
bette
r
s
pr
ead
on
the
hist
ogram
,
thr
ough
t
hi
s
fine
-
tu
ni
ng
.
It
changes
the
a
r
eas
of
lo
we
r
c
on
t
rast
t
o
rise
a
higher
c
on
tr
ast
with
out
dis
tressi
ng
t
he
ov
erall
preci
sio
n
of
the
i
rises.
T
he
feat
ur
e
of
interest
in
t
he
im
age
m
a
y
require
e
nr
ic
hm
ent
local
ly
.
Histo
gr
am
equal
iz
at
ion
reac
h
e
s
thi
s
by
ef
fici
ently
sp
rea
ding
out
the
m
os
t
fr
e
qu
ent
inte
ns
it
y
va
lues.
By
us
i
ng
t
his
m
et
ho
d,
the
histo
gram
of
t
he
resu
lt
ant im
age is as
flat
as po
ssible. T
he res
ultant hist
ogra
m
eq
ualiz
ed
im
age is sho
wn in th
e
Fig
ure
6.
Figure
6.
Im
age af
te
r
t
he
l
oca
li
zed
histo
gra
m
eq
ualiz
at
ion
It
c
on
sist
s
of
a
pp
ly
in
g
local
iz
ed
histo
gram
equ
al
iz
at
io
n
i
ndepende
ntly
to
c
aptu
re
t
he
iris
r
egio
n
in
the
ey
e
i
m
age
since
m
os
t
s
m
al
l
reg
io
ns
are
very
sel
f
-
sim
il
ar.
If
the
im
age
is
m
ade
up
of
di
screte
re
gions,
m
os
t
sm
a
ll
reg
ion
s
li
e
entirel
y
withi
n
one
or
the
oth
er
re
gion.
T
hi
s
m
e
tho
d
at
tempts
to
e
qual
iz
e
the
num
ber
of
pix
el
s
wh
ic
h
te
nd
to
f
la
tt
en
and
raise
an
im
age’
s
histogram
.
Ver
ti
cal
equ
al
iz
at
ion
us
es
on
ly
a
sin
gle
colum
n
of
pix
el
s
into
t
he e
qu
al
i
zat
ion
process
,
w
her
eas
horizon
ta
l
e
qual
iz
at
i
on
use
s
a
sin
gle
r
ow
of
pix
el
s
. It
m
od
ifie
s
th
e
pixe
l
Evaluation Warning : The document was created with Spire.PDF for Python.
Com
pu
t.
Sci.
I
nf. Tec
hnol.
An o
ptimized
r
ubber
sh
eet
m
odel
for
nor
ma
li
za
ti
on
phas
e
of
I
R
IS reco
gnit
ion
… (
Selva
mu
t
hu
k
umar
an.
S
)
131
intensit
ie
s
for
a
bette
r
ap
pe
aran
ce
of
t
he
Ir
ise
s.
T
he
pro
posed
m
et
ho
d
im
pr
oves
t
he
vis
ual
ap
pe
aran
c
e
[16] of a
n
im
a
ge.
3.
E
X
PERI
MEN
TAL STU
D
Y
To
ac
hieve
a
s
iz
e
-
inv
a
riant
s
a
m
pling
of
t
he
vali
d
iris
pi
xe
l
po
i
nts,
we
ha
ve
a
pp
li
ed
th
e
optim
iz
ed
rub
ber
s
heet
m
od
el
t
o
m
ap
the
sam
pled
iris
pi
xels
f
r
om
the
Ca
rtesi
an
c
oor
din
at
es
int
o
the
norm
al
iz
ed
sp
he
rical
coor
din
at
es.
T
o
ef
fecti
vely
im
ple
m
ent
ou
r
pro
po
sal
,
t
he
iris
i
m
age
database
CA
SIA
Database
Ver
s
ion
3.0
(CASIA
-
I
risV
3)
release
d
by
t
he
Ce
nt
re
f
or
Bi
om
e
tric
s
and
S
ecur
it
y
Re
sear
ch
of
Nati
onal
Lab
or
at
ory
of
Patt
er
n
Re
cogniti
on,
Chinese
Acade
m
y
of
Scie
nce
s
has
bee
n
us
e
d
[
15
]
.
T
he
pupil
is
s
m
al
le
r
i
n
the
im
age;
ho
we
ve
r,
the
norm
al
isa
t
ion
process
ca
n
abl
e
to
resc
al
e
the
iris
re
gion,
s
o
that
i
t
has
a
co
ns
ta
nt
dim
ension
.
In
our
exp
e
rim
ental
st
ud
y,
the
recta
ngula
r
r
ep
rese
ntati
on
is
c
onstr
uc
te
d
f
r
om
12
,
000
data
points
in
the
iris
re
gion.
The
rem
app
ing
is
done
usi
ng
the
spherical
coor
din
at
es.
T
he
I
ris
show
n
in
Fig
ure
7
is
the
seg
m
ented
i
m
age o
f
S
1046R0
4.
Figure
7. Se
gme
nted Iris
im
ag
e of S
1046R0
4
Af
te
r
t
he
su
cce
ssfu
l
c
onve
rsion
of
t
he
Ca
rtes
ia
n
c
oor
din
at
e
into
the
s
ph
e
rical
co
ordinate
syst
e
m
,
the
norm
al
ise
d
Ir
is
is sho
wn in t
he
foll
ow
i
ng f
ig
ur
e
.
Com
par
in
g
the
r
es
ults f
r
om
the
belo
w Fi
gure
8
a
nd
Fi
gure
9,
it
has
been
ob
s
erv
e
d
t
hat
the
distrib
ution
is
sh
ifte
d
to
ward
s
the
highe
r
va
lues,
w
hile
the
peak
at
the
m
i
nim
u
m
intensit
y
rem
ain
s
after
t
he
loc
al
iz
ed
histo
gr
a
m
equ
al
isa
ti
on.
It
rec
ov
e
re
d
s
om
e
of
th
e
ap
pa
ren
tl
y
lost
co
ntrast
in
an
im
age,
by
re
m
app
in
g
the
bri
ghtness
values
in
s
uc
h
a
way
as
to
eq
ualiz
e,
or
m
or
e
even
ly
distri
bu
te
it
s
br
i
gh
t
ness valu
es. T
he hist
ogr
a
m
o
f
t
he norm
al
ise
d
iris
of
Figure
8
is s
how
n
in
Fig
ure
10.
The u
nwrappe
d
fla
t
iris
has
a
lo
w
c
on
t
rast.
This
iris
is
e
nhance
d
by
ap
plyi
ng
loca
li
zed
hist
ogra
m
equ
al
iz
at
ion.
T
he
res
ultant
i
m
age
is
sh
ow
n
in
t
he
fo
ll
owin
g
fig
ure.
T
he
histo
gra
m
of
the
norm
al
ise
d
iris
of
Fi
gure
9
afte
r
the
local
iz
ed
hist
ogra
m
equ
al
iz
at
io
n
is
sh
ow
n
in
Fi
gur
e
11.
Figure
8. N
orm
al
iz
ed
IRIS
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2722
-
3221
Com
pu
t. Sci.
I
nf. Tec
hnol.
,
V
ol.
1
, N
o.
3, N
ov
em
ber
20
20:
12
6
–
134
132
Figure
9. N
orm
al
iz
ed
IRIS
a
fter
histo
gr
am
eq
ualiz
at
io
n
Figure
10
.
Histogram
o
f norm
al
iz
ed
IRI
S af
t
er c
onversi
on i
nto
spherical
c
oor
din
at
es
Figure
11
.
Histogram
o
f
the
nor
m
al
iz
ed
IRIS afte
r
a
pply
ing
the locali
zed
h
i
stogram
eq
ualiz
at
ion
By
com
par
ing
the
Histo
gra
m
s
(
Figu
re
10
and
Fig
ur
e
11)
,
it
has
been
obser
ved
that
the
inten
sit
y
var
ia
ti
ons
are
equ
al
ly
norm
a
li
sed
a
fter
t
he
local
iz
ed
histogram
equ
al
is
at
ion
.
Als
o
ou
tpu
t
of
t
he
pr
opos
e
d
m
et
ho
d
f
or
s
om
e
of
the
CA
S
IA
im
ages
are
sh
ow
n
i
n
t
he
T
able
1,
A
s
a
re
s
ult,
no
ise
s
in
th
e
flat
reg
i
ons
a
nd
rin
g
artefact
s at the
edg
e
s ar
e
no
rm
al
ise
d,
a
nd no
w
the
irises a
re
r
ea
dy for f
ur
t
he
r processi
ng.
Evaluation Warning : The document was created with Spire.PDF for Python.
Com
pu
t.
Sci.
I
nf. Tec
hnol.
An o
ptimized
r
ubber
sh
eet
m
odel
for
nor
ma
li
za
ti
on
phas
e
of
I
R
IS reco
gnit
ion
… (
Selva
mu
t
hu
k
umar
an.
S
)
133
Table
1
.
Re
s
ult o
f
the
prop
os
e
d
m
et
ho
d f
or
s
om
e o
f
the
CA
SI
A
im
ages
S.No
CASIA
I
m
ag
e
1
S1
0
1
3
L02
2
S1
0
2
2
L04
3
S3
0
4
1
L04
4
S3
3
1
2
R
0
2
The
pr
opos
e
d
s
egm
entat
ion
m
et
hod
norm
al
ized
the
iris
re
gion
i
n
65
8
im
ages
ou
t
of
67
0
im
ages,
wh
ic
h
corres
ponds
to
a
su
ccess
rate
of
98%.
T
he
s
uccess
rate
of
t
he
pro
pose
d
m
et
hod
is
com
par
ed
with
th
os
e
of
the
pr
e
vious
m
et
ho
ds
Daug
hm
an’
s
R
ubber
s
he
et
m
od
el
a
n
d
W
il
d’
s
Im
age
reg
ist
rati
on.
T
he
s
uccess
rat
e
of
the
diff
e
re
nt nor
m
al
iz
at
ion
m
et
h
od
s
is
s
how
n
i
n
Ta
ble
2.
Table
2
.
Su
cce
ss r
at
e
of the
norm
al
iz
ation
m
et
hods
No
r
m
aliz
atio
n
M
et
h
o
d
No
of
ir
ises
(
o
u
t of
67
0
)
Su
ccess R
ate per
ce
n
tag
e
Op
ti
m
ized
rub
b
er
sh
eet
m
o
d
el us
in
g
sp
h
erica
l coo
rdin
ates
658
98
Ru
b
b
er
sh
eet
m
o
d
el
638
95
W
ild
’s
I
m
ag
e
r
eg
is
tration
597
89
Table
2
s
hows
the
stre
ngth
of
t
he
pro
pose
d
m
et
ho
d
w
hic
h
w
orks
bette
r
tha
n
the
e
xisti
ng
m
et
ho
ds
since
98%
of
accu
racy
f
or
the
i
rises
a
nd
t
he
gr
a
phic
al
represe
ntati
on
of
c
om
pari
so
n
is
al
s
o
pro
vid
e
d
in the
Fig
ur
e
12.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2722
-
3221
Com
pu
t. Sci.
I
nf. Tec
hnol.
,
V
ol.
1
, N
o.
3, N
ov
em
ber
20
20:
12
6
–
134
134
Figure
12. Res
ul
ts of
va
rio
us
norm
al
iz
ation
m
et
hods
4.
CONCL
US
I
O
N
In
a
progressi
ve
ly
dig
it
al
s
oci
et
y,
the
r
ole
pl
ay
ed
by
t
he
iri
s
r
eco
gnit
ion
s
yst
e
m
is
a
vital
one.
T
he
tren
ds
an
d
trai
t
s
m
ade
in
secur
it
y
-
base
d
te
ch
no
l
og
ie
s
dem
a
nd
va
rio
us
ne
w
al
gorithm
s
fo
r
qual
it
y
i
m
a
ges.
I
n
this
pa
per
,
a
n
op
ti
m
iz
ation
te
chn
i
qu
e
f
or
th
e
norm
al
iz
a
ti
on
phase
has
be
en
im
ple
m
ente
d
w
hich
perf
orm
s
the
conve
rsion
of
the
Ca
rtesi
a
n
c
oor
din
at
es
i
nto
spherical
c
oor
din
at
es
a
nd
use
s
local
iz
ed
hi
stogram
equ
al
iz
at
ion.
The
re
su
lt
s
obt
ai
ned
rev
eal
th
e
exact
norm
alizat
ion
of
irise
s
for
the
no
isy
i
m
ages.
As
a
fu
t
ur
e
work,
w
e
pu
t
forth
ce
rtai
n
im
pr
ov
em
ents
in
noise
rem
oval
m
et
ho
ds
,
Ir
i
s
reg
i
on
resize
m
et
ho
ds
t
ow
a
rd
s
t
he
bette
r
f
eat
ur
e
extracti
on
of
ir
is im
ages,
REFERE
NCE
S
[1]
N.
Mojt
aba,
G
.
Sedighe
h
.
“
IRIS
re
cogni
t
ion
b
ase
d
on
using
ridg
el
e
t
and
cur
ve
le
t
tr
ansform
.
”
In
ter
nati
onal
Journa
l
of
Signal P
roc
essing,
Image
Pro
ce
ss
ing
and
Pat
t
ern
Recogni
t
ion
.
vol.
4
,
no.
2
,
pp.
7
-
18
,
2011
.
[2]
R.
M.
Da
Cost
a,
A.
Gonza
g
a
.
“
D
y
namic
f
eatur
es
for
Iris
re
cog
nit
ion.
”
I
EE
E
Tr
ansacti
ons
on
Syste
ms
,
Man
a
nd
Cybe
rnet
ic
s
.
vol.
42
,
no.
4,
pp.
10
72
-
1082,
2012
.
[3]
A.D.
R
ahul
kar
,
R.
S.
Hol
ambe
.
“
Half
-
Iris
f
eature
ext
ra
ct
ion
and
r
e
cogni
ti
on
using
a
n
ew
cl
ass
of
b
i
orthogona
l
Tr
iplet
H
alf
-
band
filter
bank
and
f
le
xib
l
e
k
-
out
-
of
-
n:
A
Pos
tc
la
ss
ifi
er
.
”
I
EE
E
Tr
ansacti
o
ns
on
Informati
on
Forensic
s
an
d
Sec
urit
y
.
vol.
7
,
no.
1
,
pp
.
230
-
2
40,
2012
.
[4]
G.
Yang
,
S.
Pa
ng,
Y
.
Yin
,
Y.
Li
,
X.
Li
.
“
SIF
T
b
ase
d
iri
s
re
c
ognit
ion
with
n
orm
al
iz
a
ti
on
an
d
enh
ancem
ent
.
”
Inte
rnational
Jo
urnal
of
Ma
chi
n
e
Learning
and
Cybe
rnet
ic
s
.
vol.
4
,
no.
4
,
pp.
401
-
407,
2012
.
[5]
H.
Proenç
a
.
“
IRIS
Biom
et
ric
s:
i
ndexi
ng
and
ret
r
ie
ving
h
ea
vi
l
y
d
egr
ade
d
data.
”
I
EE
E
Tr
ansacti
o
ns
on
Information
Forensic
s and
S
ec
urit
y
.
vol. 8, n
o.
12
,
pp
.
1975
-
1985,
2013
.
[6]
F.A.
San
tos,
F.
A.
Far
ia
,
L.
A
.
Vill
as
.
“
IRIS
r
e
cogni
ti
on
b
ase
d
on
lo
ca
l
b
ina
r
y
desc
ript
ors.
”
I
E
EE
Latin
Ame
ri
ca
Tr
ansacti
ons
.
vo
l.
13
,
no
.
8
,
pp
.
2
770
–
2775
,
201
5
.
[7]
S.
Selv
amuthukum
ara
n,
S
.
Har
iharan,
T
.
R
amkumar
,
Inve
stig
ation
on
Iris
rec
ogn
it
io
n
s
y
st
em
adop
ti
n
g
cr
y
p
togra
ph
i
c
te
chn
ique
s,
The
Inte
rna
ti
ona
l
Ar
ab
Journal
of
In
f
orm
at
ion
T
ec
hn
olog
y
.
12
(1) (20
15)
1
-
8.
[8]
R.
Him
anshu,
Y.
Anam
ika,
I
ris
r
e
cogni
ti
on
using
c
om
bine
d
support
ve
ct
or
m
ac
hin
e
and
h
amm
ing
dis
ta
nc
e
a
pproa
ch.
Expe
rt
S
y
st
ems
with
Appli
ca
t
ion
s.
41
(2)
(2014) 588
–
593.
[9]
Z.
Peng
,
H.
W
an
g,
J.
W
u,
J.
L
i.
“
An
improved
Da
ugm
an
m
et
hod
f
or
Iris
r
ec
ogn
it
io
n.
”
Wuhan
Uni
v
ersity
Journal
o
f
Natural
Sc
ie
nc
es
.
vol
.
20
,
no
.
3
,
p
p.
229
–
234
,
201
5
.
[10]
[
A.
Bansa
l,
R.
A
gar
wal,
R
.
K.
Sh
arma
.
“
Sta
ti
sti
cal
f
ea
tur
e
ext
r
ac
t
i
on
-
base
d
iri
s
r
ecogniti
on
s
y
st
em.
”
Sadh
ana,
Ind
ia
n
Ac
ademy
of
Scie
nce
s
.
vo
l.
41
,
no.
5
,
pp.
507
-
518,
2016
.
[11]
I.
Ham
ouche
n
e,
S. A
ouat
.
“
Eff
i
cient
appr
oa
ch for
Iris recogn
it
ion
.
”
Signa
l Ima
ge
a
nd
Vi
d
eo
Proce
s
sing
.
vol
.
10
,
no
.
7
,
pp
.
1361
–
136
7
,
2016
.
[12]
J.G.
Daugm
an,
“
How
iri
s
r
ec
ogni
ti
on
works
.”
I
EEE
Tr
ansacti
ons
o
n
Circuits
and
Sy
stems
for
V
ide
o
Technol
ogy
.
vo
l
.
14,
no
.
1
,
pp
.
21
–
30
,
2004
.
[13]
R.
P.
W
il
d
es,
J.C
.
As
m
uth,
G.
L.
Gree
n,
S.C.
Hs
u,
R
.
J.
Kol
czy
nsk
i,
J
.
R.
Matey
,
S
.
E.
McB
ride
.
“
A
m
ac
hine
visio
n
s
y
stem for
I
ris
re
cogni
ti
on
.
”
Mac
hine
Vi
sion a
nd
Appl
ic
a
ti
ons
,
vo
l.
9
,
pp
.
1
–
8,
199
6
.
[14]
H.S.
Ali
,
A.I
.
Is
m
ai
l,
F.A
.
Fara
g
,
F.E
.
Abd
El
-
S
amie
.
“
Speed
ed
up
robust
fe
at
ur
es
for
eff
icient
I
ris
rec
ogn
it
ion
.
”
Signal
Image
an
d
Vi
d
eo Pr
oce
ss
i
ng.
vol
.
10
,
no
.
8
,
pp
.
1385
–
1391
,
2016
.
[15]
CAS
IA
iri
s
image
databa
se
.
Th
e
Nati
on
al
La
bo
rat
or
y
of
Pa
tter
n
Rec
ogni
ti
on
(
NLPR).
Instit
ut
e
of
Aut
omation
,
Ch
ine
se
Ac
ad
emy
of
Sc
ie
nc
es
(
CASIA
-
IrisV1
).
[16]
Y.
Chen
,
J
.
Yan
g,
C
.
W
ang
,
N
.
Li
u
.
“
Multi
m
odal
b
iometrics
re
c
ognit
ion
base
d
o
n
local
fusion
vi
sual
f
ea
tur
es
an
d
var
iational
b
a
y
es
ia
n
ext
reme
lear
ning
m
ac
hin
e.
”
Ex
pert
Syste
ms
wit
h
App
licati
on
s
.
vol. 64, pp.
93
-
103
,
2016
.
Evaluation Warning : The document was created with Spire.PDF for Python.