Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
7, N
o
. 3
,
Ju
n
e
201
7, p
p
. 1
651
~166
0
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v7
i
3.p
p16
51-
166
0
1
651
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Shape based Image Retrieval
usi
n
g L
o
wer Ord
e
r Zernike
Mom
e
nts
G
.
Su
cha
r
it
ha,
Ra
nj
an
K.
Sen
a
pa
t
i
Department o
f
Electronics
and C
o
mmunication,
K L University
,
India
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 9, 2016
Rev
i
sed
O
c
t 28
, 20
16
Accepted Nov 12, 2016
Shape is one of the significant
featur
es of Content Based Imag
e Retrieval
(CBIR). This paper proposes a strong and
successful shape featur
e, which
is
based on
a set o
f
orthogonal co
mplex mo
ments of images know
n as Zernike
mome
nt
s.
For s
h
a
p
e
cl
a
ssi
fic
a
tion Z
e
rni
k
e
mome
nt
(Z
M) i
s
the
domi
n
a
n
t
solution. Th
e radial poly
nomial
of Ze
rnike moment produces the number of
concen
tric circles based on the order.
As the
order increases number of
circ
les wil
l
in
cr
eases, du
e to
thi
s
the lo
ca
l infor
m
ation of
an im
age wi
ll b
e
ignored. In this
paper, we
introd
uced
a nov
el m
e
thod for
radial poly
nomial
where lo
cal
inf
o
rm
ation of an
im
age giv
e
n im
portanc
e. W
e
s
u
cce
eded
to
extra
c
t th
e loc
a
l fe
atures
and
s
h
ape fea
t
ures
at ver
y
a
lo
w order of
pol
y
nom
ia
l com
p
ared to th
e sta
t
e of trad
ition
a
l
ZM.The propo
sed m
e
thod
gives an adv
a
ntage of a
lower
order,
le
ss c
o
mpl
e
x,
a
nd lower
dimension
featur
e ve
ctor.F
or m
o
re s
i
m
ilar im
ages
we find that s
i
m
p
le
Euclid
ia
n
distance approximately
zero. Pr
oposed
method tested on a MP
EG-7 CE-1
shape database, Coil-100 data
b
a
ses. Exper
i
ments dem
onstrated that it is
outperforming in identif
y
i
ng the shape of
an object in th
e im
age
and reduc
ed
the r
e
tri
e
ving
ti
m
e
and
com
p
lex
i
t
y
of
c
a
lcu
l
at
ion
s
.
Keyword:
CBIR
Eu
clid
ian d
i
stan
ce
GF
D
LZM
ZM
Copyright ©
201
7 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
G
.
Su
ch
a
r
ith
a,
Depa
rt
em
ent
of El
ect
r
oni
cs
a
n
d
C
o
m
m
uni
cat
i
on E
n
gi
nee
r
i
n
g
,
KL Uni
v
er
sity
,
Gree
n
Fi
el
ds,
Vad
d
es
waram
,
G
unt
ur
(
D
i
s
t
)
52
2
5
0
2
,
A
n
dra
Pra
d
es
h,
I
ndi
a
.
Em
a
il: su
ch
arith
asu
@
g
m
ai
l.co
m
1.
INTRODUCTION
The p
r
ocess o
f
im
age ret
r
i
e
val
depe
nds
on
v
a
ri
o
u
s
im
age features. T
h
e fe
atures re
present the im
age
m
o
re significa
nt. Features i
n
clude c
o
lor,
te
xture, s
h
ape
,
s
h
adows, etc.
In
all features s
h
ape of a
n
obje
c
t gives
a po
w
e
r
f
u
l
clue in
id
en
tif
ying
th
e obj
ect [1]. So
, an ef
fect
ive and e
fficie
n
t s
h
ape
desc
ri
ptor is
require
d
.
The
sha
p
e de
scri
pt
ors
are
di
vi
ded
i
n
t
o
t
w
o cat
e
g
ori
e
s,
co
nt
o
u
r
base
d an
d
re
gi
on
base
d
[2]
.
C
ont
ou
r
based
sha
p
e
descri
pt
o
r
gi
ve
s t
h
e bo
u
nda
ry
i
n
fo
rm
at
i
on of an o
b
j
ect
. He
re i
t
i
gno
res t
h
e i
n
t
e
ri
or i
n
fo
r
m
at
i
on of t
h
e s
h
ape
.
The algorithm
s
use
d
for this
are F
ourier
descriptors, Elongation, Area,
Curvature sca
l
e space etc [3]. The
r
e
g
i
o
n
b
a
sed
descr
i
p
t
or
s
m
a
k
e
u
s
e o
f
bo
undar
i
es
and
in
ter
i
o
r
r
e
g
i
on
s o
f
t
h
e
sh
ap
e.
In
r
e
g
i
on
b
a
sed
m
e
th
od
s,
t
h
e i
n
f
o
rm
at
i
on capt
u
re
d fr
o
m
bot
h b
o
u
n
d
a
r
i
e
s and i
n
t
e
ri
o
r
regi
on
of s
h
a
p
e. M
o
m
e
nt
s are t
h
e com
m
onl
y
used
approaches
for sha
p
e i
d
en
tificatio
n
.
In
gene
ral, the
m
o
m
e
nts are qua
ntitative va
lues that
desc
ribe a distribution,
raisi
ng the c
o
m
pone
nts
to
d
i
fferen
t
powers [4
].Th
e
defin
itio
n of t
h
e reg
u
l
ar m
o
m
e
n
t
or
g
e
o
m
etric
m
o
m
e
n
t
is
,
∞
∞
Whe
r
e
,
i
s
a
rea
l
fu
nct
i
o
n,
p
&
q a
r
e
or
der
o
f
a
p
o
l
y
nom
i
a
l
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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088
-87
08
I
J
ECE
Vo
l. 7
,
N
o
. 3
,
Jun
e
201
7
:
1
651
–
166
0
1
652
Ho
we
ver
,
ge
o
m
et
ri
c
m
o
m
e
nt
s co
nt
ai
n
hi
ghl
y
re
d
u
n
d
a
n
t
i
n
fo
rm
ati
on.
As t
h
e
or
de
r i
n
crea
ses
co
m
p
u
t
atio
n
a
l co
m
p
lex
ity in
c
r
eases. It do
esn
'
t h
a
v
e
an
y desired
ro
tatio
nal in
v
a
rian
ce, tran
slation
and
scale
i
nva
ri
ant
.
I
n
t
h
e ge
om
et
ri
c m
o
m
e
nt
s t
h
e
bas
i
s f
unct
i
o
n
is
n
o
t
or
thog
on
al
. Th
e r
e
con
s
tructio
n
of
im
ag
e
wi
t
h
t
h
ese m
o
m
e
nt
s wo
ul
d
i
n
v
o
l
v
e
red
u
nda
nt
i
n
fo
rm
at
i
on am
ong al
l
t
h
e m
o
m
e
nts an
d p
r
od
uc
e hi
g
h
co
m
p
u
t
atio
n
a
l co
m
p
lex
ity.
A.
K
hot
a
n
za
d
and
M
.
R
.
Tea
g
ue et
.al
.
[
5
]
,
[6
]
,
i
n
t
r
od
uce
d
a
t
w
o
di
m
e
nsi
o
n
a
l
ort
h
o
g
onal
m
o
m
e
nt
s i
.
e
Zerni
k
e m
o
m
e
nts, which are
inva
riant to
i
m
ag
e tran
slation
,
o
r
ien
t
ation
and
si
ze. It has been observe
d
that the
m
a
gni
t
ude
of
ZM
w
oul
d
n
o
t
chan
ge
f
o
r
any
r
o
t
a
t
i
on
an
d s
cal
i
ng
of
a
n
i
m
age.
Due
t
o
t
h
ese p
r
o
p
e
r
t
i
e
s
of
ZM
,
i
t
out
pe
rf
o
r
m
s
t
h
an m
a
ny
ot
h
e
r
descri
pt
or
s,
suc
h
as
Ge
om
et
ri
c, Le
gen
d
re
an
d Ps
eu
d
o
Z
e
rni
k
e m
o
m
e
nt
s [
7
]
,
[8]
.
Nu
gr
o
ho a
nd Ti
a
n
et
.al
[9
], [1
0
]
prov
ed th
at, th
e ro
tari
o
n
a
l inv
a
rian
t p
r
op
erty g
i
v
e
s
th
e do
m
i
n
a
n
t
resu
lts
com
p
are to
other s
h
ape
de
scri
ptors.
Ho
we
ver
,
di
re
ct
com
put
at
i
o
n
of
t
h
ese m
o
m
e
nt
s i
n
hi
g
h
e
r
or
der
i
s
ve
ry
e
xpe
nsi
v
e. T
h
e
r
e i
s
a g
r
eat
need t
o
lim
i
t their use at higher
orders. T
h
e cause be
h
i
nd is n
o
t
on
ly a co
m
p
u
t
atio
n
a
l co
m
p
lex
ity, b
u
t also
h
i
gh
ly sen
s
itive to
n
o
i
se
[11
]
, [12
]
. Th
e
p
e
rfo
rm
an
ce of th
e syste
m
m
a
y d
i
min
i
sh
if th
e ord
e
r an
d m
o
m
e
n
t
are
ch
osen pr
op
er
ly.
In
t
h
i
s
pa
per
we ha
ve not
o
n
l
y
t
r
i
e
d
t
o
re
d
u
ce
t
h
e or
der
,
but
al
so
t
r
i
e
d
t
o
red
u
ce
t
h
e di
m
e
nsi
ons
of
the feature
vec
t
or.
Ge
nerally the order
of t
h
e
Zerni
k
e po
lyno
m
i
a
l
d
ecid
e
s th
e No
.of con
c
en
tric circles.
As th
e
polynom
i
al order inc
r
eases
, the No.of ci
rcle
s also increa
se
s. So, the area
cove
re
d by
t
w
o co
nsec
ut
i
v
e
ci
rcl
e
s
will b
e
m
i
n
i
m
i
zed
. If th
is area is
m
i
n
i
mized
, th
e sh
ap
e wi
t
h
in
terior informatio
n
o
f
an
ob
j
ect is no
t possib
l
e,
and
wi
t
h
m
o
r
e
num
ber
of
m
o
m
e
nt
s t
h
ere
i
s
a hi
g
h
si
m
i
l
a
r i
n
fo
rm
at
i
o
n w
h
i
c
h i
s
n
o
t
m
u
ch use
f
ul
whi
l
e
ret
r
i
e
vi
n
g
.
I
n t
h
e pr
op
ose
d
m
e
t
h
o
d
t
h
e aspec
t
s are t
a
ken i
n
t
o
co
nsi
d
e
r
at
i
o
n:
or
der a
nd
di
m
e
nsi
ons
of fe
at
ure
vector.
The
rem
a
i
nder
o
f
t
h
e
pa
per
i
s
o
r
ga
ni
zed
as
fol
l
o
ws.
Sect
i
o
n
2 i
n
t
r
o
d
u
ces
ZM
s, Sect
i
o
n
3
descri
bes
Im
age
m
a
ppi
ng an
d t
r
ans
f
o
r
m
di
at
ance, t
h
e pro
p
o
se
d m
e
t
h
o
d
i
s
i
n
Sect
i
on 4, e
xpe
r
i
m
e
nt
al
resul
t
s
and
co
m
p
ariso
n
are presen
ted
in Sectio
n
5
.
Fi
n
a
ll
y, in
Section
6co
n
c
l
u
sion
are
o
u
tlin
ed
.
2.
Z
E
RNIKE M
O
ME
NTS
Co
m
p
lex
Zern
i
k
e m
o
m
e
n
t
s c
o
n
s
titu
te a set
o
f
orthog
on
al b
a
sis fun
c
tion
s
m
a
p
p
e
d
ov
er
a u
n
it circle.
Th
e
ortho
gon
al p
r
op
erty
o
f
ZM's su
its b
e
t
t
er fo
r sh
ap
e reco
gn
itio
n sche
m
e
s. Th
is
pro
p
e
rty shows t
h
at th
e
cont
ribution
of each m
o
m
e
n
t
is inde
pe
nde
n
t and unique. Due t
o
this
pr
operty the redund
ancy has
been
reduce
d as m
i
nim
u
m
as com
p
ared to t
h
e
geometric
m
o
m
e
nts.
M
a
t
h
em
at
i
cally
, Zerni
k
e
basi
s fu
nct
i
on i
s
d
e
fi
ne
d wi
t
h
an
or
der
n
and
rep
e
titio
n
m
ov
er
C={(
n
,
m
)
| 0
≤
n
≤
∞
,
|m
|
≤
n
,
|n-m
|=e
v
en
}.
,
,
(
1
)
w
h
er
e
,
.∗
(
2
)
and
∑
1
!
!
|
|
!
|
|
!
|
|
/
(
3
)
Whe
r
e
n
is a
po
sitiv
e in
teg
e
r
represen
tin
g the o
r
d
e
r
o
f
t
h
e rad
i
al po
lyn
o
m
i
a
l an
d
m
is no
.o
f
rep
e
titio
n
s
.
Where
f (x, y
)
is a function
of an i
m
age with
th
e size o
f
NxN.
Fo
r
d
i
g
ital imag
es th
e in
teg
r
als in
Equ
a
tion
1
are
repl
ace
d by
su
m
m
a
t
i
ons.
∑∑
,
.∗
,
(
4
)
3.
IM
AGE
M
A
PPIN
G AND
TR
AN
SFORM
D
I
STA
N
C
E
Th
e
ortho
gon
ality an
d
co
m
p
leten
e
ss
o
f
Zern
ik
e po
l
yno
m
i
als allo
w u
s
to
represen
t an
y
sq
u
a
re im
ag
e
fu
nct
i
o
n i
n
t
o
t
h
e
uni
t
di
sk
[
8
]
l
i
k
e as s
h
ow
n
i
n
Fi
g
u
r
e
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
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S
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:
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8-8
7
0
8
S
hap
e b
a
sed
Im
ag
e Retrieva
l
u
s
i
n
g L
o
wer
Orde
r Zer
n
ike
Moments (
G. S
u
charitha
)
1
653
Fig
u
re
1
.
Tran
sform
i
n
g
th
e imag
e in
t
o
u
n
it ci
rcle
The tra
n
s
f
ormed
distance
a
n
d the
phase a
ngle
at
a
pi
xe
l
(x,y
) are
de
s
i
gne
d i
n
su
ch
way
t
o
i
n
sert
t
h
e
im
age into t
h
e
unit
disk. T
h
e
equations
are
(
5
)
1
21
12
(
6
)
To
m
a
p
th
e
d
i
gital i
m
ag
e in
to
th
e circle,
first
th
e im
ag
e h
a
s to
co
nv
ert i
n
to
a squ
a
re im
age i.e NXN, whe
r
e
N
is ev
en
.
As a m
a
tter of
fact, if t
h
e im
a
g
e size is
odd (i.e N), the
cent
e
r of t
h
e im
age is
,
,
at
t
h
i
s
poi
nt
from
the above
equations
0
an
d
t
h
e
pha
se a
ngl
e
.
Th
e
way to
reso
lv
e t
h
is pro
b
le
m
is to
select th
e i
m
ag
e size is squ
a
re as
well as ev
en
matrix
. Th
e
im
age not
ha
v
e
any
cent
e
r a
nd
n
o
re
du
n
d
a
n
cy
.T
hi
s t
r
ans
f
orm
di
st
ance g
e
nerat
e
s
o
m
e
conce
n
t
r
i
c
ci
rcl
e
s fo
r
an
y k
i
nd
o
f
NX
N
m
a
tr
ix
. H
e
r
e
w
e
ar
e br
ing
i
ng
th
e r
i
ng areas, which
de
notes the
im
ag
e tran
sfo
r
m
e
d
in
to
th
e
ci
rcl
e
i
n
p
o
l
a
r
co
or
di
nat
e
sy
st
em
as sh
ow
n i
n
Fi
gu
re
2.
Let
o
be t
h
e
cent
e
r
of a
n
ob
ject
a
n
d
R
be t
h
e
in
crem
en
tal rad
i
u
s
leng
th. Using
th
e Equ
a
tio
ns (5),
(6
) ri
n
g
s were co
n
s
tru
c
ted
fro
m
th
e cen
ter to
th
e
b
oun
d
a
ry of an
obj
ect. Th
e area with
i
n
th
e
first ring
co
nstitu
tes th
e first
ring
area an
d
t
h
e area
b
e
tween
first
and sec
o
nd is a second ring a
r
ea. Th
e
hum
an o
b
ser
v
at
i
o
n r
e
sul
t
s
, t
h
e pi
xe
l
va
lues in a particular ring area are
ap
pro
x
i
m
a
tel
y
eq
u
a
l,
b
u
t
th
e
p
i
x
e
l v
a
lues lin
early in
cr
ease from
the center to the
out
war
d
ri
n
g
.
The out
e
r
m
o
st
ring pixel val
u
es are greater than
or equ
a
l to
u
n
ity. Th
e in
n
e
rm
o
s
t rin
g
, i.e at th
e
cen
ter p
i
x
e
l valu
e is
co
m
p
letely zer
o
.
With
t
h
is
ρ
,
th
e lower ord
e
r Zern
ik
e m
o
m
e
n
t
s are in
cap
a
ble to gi
ve t
h
e s
h
ape
of a
n
obje
ct.
Fi
gu
re 2.
R
i
ng
areas
To
ov
er
co
m
e
t
h
is pr
ob
lem
,
t
h
e tr
ansform
distance for a NXN m
a
trix
is d
e
sign
ed
in
such
way th
at
,
the pi
xel
values are
cust
om
ized in
their re
spective
rings. Ass
u
m
e
that
there a
r
e C
num
ber of rings
and R
denotes t
h
e
distance bet
w
ee
n
two a
d
jacent
ri
ngs
.
The tra
n
s
f
orm
distance
ρ
m
a
tr
ix
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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J
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l. 7
,
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o
. 3
,
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e
201
7
:
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–
166
0
1
654
Quer
y
Inte
r
p
olation fo
r siz
e
LZ
M
Radial Pol
y
no
mial
Select
ion & Ext
r
action of
Z
M
calcu
l
at
ed
with
th
e
p
r
op
os
ed
modified
ρ
Extracted mag
n
itudes of LZ
M
1
2
.
.
.
.
1
(7
)
Th
e no
rm
alize
d
fun
c
tion
,
for
a ring a
r
ea ca
n
be
defi
ned as
1
2
.
.
1
.
.
.
.
0
1
(8
)
For t
h
e or
de
rs
sho
w
n i
n
Ta
b
l
e 1, t
h
e radi
al
pol
y
n
o
m
i
a
l
c
a
lculated using above
trans
f
orm
distance
method.
The
practical observations cle
a
red t
h
at, the
num
b
er of circl
e
s for a
n
y NXN
m
a
trix
are 10
fo
r th
e
p
o
l
y
n
o
m
ia
l
o
r
d
e
r lessth
a
n
o
r
equ
a
l to
5
.
Fr
o
m
th
e above calcu
latio
n
s
th
e inn
e
r
m
o
s
t an
d ou
ter
m
o
s
t cir
c
le p
i
x
e
l
v
a
lues ar
e
1
a
nd
0
resp
ectiv
ely, so
th
e
p
i
x
e
l v
a
lu
es abov
e th
e ou
te
rm
ost circle are zero
.
Usi
ng the
Eq
uations
(2
),
(3
) a
n
d
(4) th
e rad
i
al po
lyn
o
m
ial, an
d Zern
ik
e m
o
m
e
n
t
s were calcu
l
a
ted
fo
r th
e
orders sh
own
i
n
Tab
l
e1
.
4.
PROP
OSE
D
LZ
W
The
pr
op
oses
d
bl
oc
k
di
agr
a
m
sho
w
n i
n
F
i
gu
re 3
wi
t
h
vari
ous
st
eps i
n
v
o
l
v
e
d
i
n
cal
cul
a
t
i
ng t
h
e
feature
vector. The
entire
da
tabase as
well
as the
que
r
y
im
age has t
o
resize in
order
to get
a s
qua
re size
matrix
. Sin
c
e,
to
calcu
late Zern
i
k
e m
o
m
e
n
t
s th
e im
ag
e sh
ould i
n
s
qua
re s
i
ze. Here we
followe
d a
prac
tice of
resi
zi
ng
(i
.e
i
n
t
e
rp
ol
at
i
o
n
)
bas
e
d on
t
h
e di
m
e
nsi
o
ns of
i
m
ages.
Fi
gu
re
3.
B
l
oc
k
di
ag
ram
of p
r
o
p
o
sed
m
e
t
hod
For que
r
y im
age a
nd t
h
e
database im
ages LZMs ar
e calc
u
lated.
The t
r
a
n
sform
distanc
e
, the
radial
pol
y
n
o
m
i
al
p
l
ays a m
a
in
ro
le in ex
t
r
actin
g th
e sh
ap
e f
eat
u
r
es. Th
e ord
e
r
o
f
th
e
p
o
l
ynomial d
ecid
e
s
t
h
e num
ber o
f
no
n zer
o ci
rcl
e
s and i
t
s
area. As t
h
i
s
or
de
r
goes on increasi
n
g, the num
ber of concent
r
ic circles
also inc
r
eases. As a
comm
om
though
t tha
t
, if the
num
b
er of circles
increase
s
of a
give
n s
p
ace, t
h
e are
a
co
v
e
red
b
y
each
ring
(i.e
area
b
e
tween
two
co
n
c
en
tric
ci
rcles)
will redu
ce.
I
n
or
d
e
r
t
o
an
alyze th
e eff
ect
of
o
r
d
e
r
s
, th
e mo
m
e
n
t
s ar
e d
i
vid
e
d
i
n
to
t
w
o gr
oup
s.
Th
e two gr
oup
s ar
e
Gr
ou
p
1:
3
5
|
|
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
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8
S
hap
e b
a
sed
Im
ag
e Retrieva
l
u
s
i
n
g L
o
wer
Orde
r Zer
n
ike
Moments (
G. S
u
charitha
)
1
655
G
r
o
up2
:
6
1
5
|
|
(
1
0
)
The feat
ure
ve
ct
or co
nsi
s
t
s
o
f
o
n
l
y
m
a
gni
t
ude
s o
f
Zer
n
i
k
e
m
o
m
e
nt
s. The si
m
p
l
e
m
e
tri
c
s use
d
t
o
fi
nd t
h
e
si
m
ilar i
m
ag
es fro
m
th
e d
a
tab
a
se are Eu
clid
ian
,
Manh
attan
d
i
stan
ce.
If
all th
e m
o
m
e
n
t
s
o
f
th
e im
age
f(x,y
)
wi
t
h
an or
der
n
are kno
wn
, it is p
r
oved
th
at recon
s
t
r
u
c
tion
of
an i
m
age is possible. The rec
onst
r
ucte
d
fu
nct
i
o
n ca
n
b
e
f
o
rm
ed as f
o
l
l
ows:
,
∑∑
,
(
1
1
)
Table1.
List
o
f
Low
e
r Ord
e
r
Zer
n
i
k
e M
o
m
e
n
t
s for
Gro
up1
Order
Zernike
m
o
m
e
nts
Di
m
e
nsionality of
the specified order
0 Z
0,0
1
1 Z
1,1
, Z
1,-
1
2
2 Z
2,0
, Z
2,2
, Z
2,-
2
3
3 Z
3,1
, Z
3,-
1
, Z
3,3
, Z
3,-
3
4
4 Z
4,0
, Z
4,2
,
Z
4,-
2
, Z
4,
4
, Z
4,-
4
5
5 Z
5,1
, Z
5,-
1
, Z
5,3
, Z
5,
-3
, Z
5,5
,Z
5,-
5
6
4.
1.
Feat
ure
E
x
tr
a
c
ti
on
Fro
m
th
e p
r
eced
ing
,
we ob
tain
ed
scale inv
a
rian
t,
ro
tation
a
l in
v
a
rian
t an
d tran
slation
a
l i
n
v
a
rian
t
ZM
feat
ure
s
.
Ho
we
ver
,
f
r
om
t
h
e t
a
bl
e1
the
number
of m
o
m
e
nts calculated for
group1 is
21. But all these features
are not re
quire
d
for
sha
p
e iden
t
i
f
i
cat
i
on. T
h
e
val
u
es of
and
are c
o
ns
tant for all norm
a
lized and
bina
ry im
ages, they are
not i
n
cluded
as
image
features. T
h
e e
x
perim
e
nts’
resu
lts show
th
at
ZMs, with
t
h
e
m
a
x o
r
de
r
up
t
o
fi
ve,
co
ul
d
h
a
ve a
su
ffi
ci
ent
l
y
go
od
i
m
age rep
r
ese
n
t
a
t
i
on
po
we
r.
4.
2.
Query
M
a
tchi
ng
Feature
vect
or for query
image is
re
prese
n
ted as
,
,
,….
is ob
tain
ed after the
feature
ext
r
action. Sim
i
larly, each
im
age in the
data
bas
e
is represe
n
t
e
d with
their own feature
vectors
,
,
,….
,
1
,
2
,
3
…
|
|
. T
h
e aim
is
to retrie
ve the possible
bes
t
im
ages that
resem
b
l
e
t
h
e query
i
m
age. Thi
s
i
n
vol
ves se
l
ect
i
on o
f
som
e
t
op m
a
t
c
hed im
ages by
m
e
asuri
ng t
h
e di
s
t
ance
bet
w
ee
n que
ry
and
dat
a
base
i
m
ages.
Eu
clid
ian
d
i
stan
ce is u
s
ed
as
a si
m
i
larity
me
tric. To
find
the si
m
i
larity o
n
l
y th
e
m
a
g
n
itu
de o
f
LZMs
are con
s
id
ered
. Th
e d
i
stan
ce metric resu
lts will b
e
u
s
ed
in retriev
i
ng
th
e
i
m
ag
es fro
m
th
e d
a
tab
a
se
b
y
so
rti
ng
and ra
nking. T
h
e E
u
clidian di
stance
m
easure
d
usi
n
g fol
l
o
wi
ng
f
o
rm
ul
a.
∑
/
(
7
)
Whe
r
e
n
i
s
t
h
e
l
e
ngt
h
of
feat
u
r
e vect
o
r
,
N
i
s
t
h
e
num
ber
of
i
m
ages i
n
t
h
e
d
a
t
a
base.
4.3. Experiments
To eval
uat
e
t
h
e over
a
l
l
perf
o
r
m
a
nce of t
h
e pro
p
o
se
d im
age ret
r
i
e
val
m
e
t
h
o
d
base
d o
n
sha
p
e a
n
d
l
o
cal
feat
ure
s
,
t
h
e M
P
EG
-7 C
E
-1
, C
o
i
l
-
10
0
dat
a
bases
a
r
e
used. Som
e
exam
ples form
MPEG-7CE
-1 da
tabase
as show
n in
Fig
u
r
e
4
.
Experiment *1
In t
h
i
s
ex
peri
m
e
nt
, M
P
EG-
7
C
E
-1
dat
a
ba
se [1
3]
used
. Thi
s
dat
a
ba
se con
s
i
s
t
s
of a l
a
rge n
u
m
b
er o
f
bi
na
ry
im
ages of va
ri
ous s
h
a
p
es o
f
di
ffe
re
nt
ob
jec
t
s i
n
vari
o
u
s o
r
i
e
nt
at
i
ons
. Th
ese bi
nary
i
m
ages are p
r
e-cl
a
ssi
fi
e
d
in
to
d
i
f
f
e
r
e
n
t
categ
o
r
i
es, each of
size is
20
an
d to
tal nu
m
b
er
o
f
ob
j
ects ar
e 70
b
y
do
m
a
in
p
r
o
f
ession
als.
Ro
ta
tio
n test:
Th
er
e ar
e 70 g
r
ou
ps of
imag
es
whe
r
e
ea
ch gr
ou
p has 20
si
milar
images with different
ori
e
nt
at
i
ons
. A
l
l
t
h
e 7
0
i
m
ages fr
om
al
l
gro
u
p
s a
r
e
use
d
as
que
ri
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 7
,
N
o
. 3
,
Jun
e
201
7
:
1
651
–
166
0
1
656
No
ise test
:
T
h
e effi
ci
e
n
cy
o
f
t
h
e
descri
pt
o
r
ve
ri
fi
ed
u
n
d
e
r
r
o
t
a
t
i
o
n
,
scal
i
ng,
rec
o
nst
r
uc
t
i
on
wi
t
h
di
f
f
e
r
ent
noi
se a
dde
d i
m
ages. Vari
ou
s l
e
vel
s
of sal
t
& pep
p
er
, Ga
ussi
an
noi
se i
s
used
wi
t
h
va
r
i
ous S
N
R
val
u
es as
sho
w
n i
n
Fi
gu
r
e
7.
Fi
gu
re
4.
Exa
m
pl
es from
MPEG
-7
C
E
-
1
D
a
t
a
base
Fi
gu
re
5.
Sam
p
l
e
im
ages wi
t
h
sal
t
&
pe
ppe
r
n
o
i
s
e
un
der
di
ff
erent
val
u
es
o
f
SNR
Subject test:
This databa
se ha
s 1400 bina
ry images, with
70 subjects and each subject has 20 sim
ilar images
with
all ro
tatio
n
s
and
scaling
i
m
ag
es. Fig6
shows so
m
e
sam
p
l
e
s of t
h
e M
P
EG-
7
dat
a
base.
Al
l
70
sub
j
ect
im
ages use
d
as
queries.
Experiment *2
In t
h
i
s
ex
peri
m
e
nt
C
o
i
l
-
1
0
0
i
m
age dat
a
base i
s
used
[
14]
. C
o
i
l
-
1
00
dat
a
base
havi
ng
1
00
di
f
f
ere
n
t
o
b
ject
s
wi
t
h
each object ha
s 72 similar images with
diffe
rent orientations
. This dat
a
ba
se hel
p
s to verify the rot
a
tional
pr
o
p
ert
y
o
f
t
h
e desc
ri
pt
o
r
i
n
al
l
angl
es
.Al
l
10
0 i
m
ag
es from
various
objects
used
as
queries.Som
e
sam
p
le
s
fr
om
C
o
i
l
-
100
dat
a
base s
h
o
w
n i
n
Fi
g
u
r
e
6 wi
t
h
va
ri
o
u
s
rot
a
t
i
o
ns.
Al
l
t
h
e ab
ove
t
e
st
s per
f
o
r
m
e
d on t
h
es
e
dat
a
bases
al
so
.
Fi
gu
re
6.
Sam
p
l
e
im
ages fr
om
C
o
i
l
-
1
0
0
Dat
a
base
Evaluation Warning : The document was created with Spire.PDF for Python.
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J
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S
hap
e b
a
sed
Im
ag
e Retrieva
l
u
s
i
n
g L
o
wer
Orde
r Zer
n
ike
Moments (
G. S
u
charitha
)
1
657
To e
v
al
uat
e
t
h
e
pr
op
ose
d
d
e
scri
pt
o
r
'
s
pe
r
f
o
r
m
a
nce i
n
r
eal
im
ages, C
o
i
l
-
1
0
0
dat
a
ba
se has
bee
n
chosen. To pre
p
are for
our experim
e
nt
s, the im
ages convert
e
d into gray
scale images and selected six views
of di
f
f
ere
n
t
o
r
i
e
nt
at
i
ons pe
r
o
b
ject
.
The sele
cted object from
the database
can
be c
onsi
d
ered a
s
a c
o
m
b
ination
of
scaling, rota
tion a
n
d subjec
t test database.
Figure
9 a
n
d T
a
ble 2 shows t
h
e c
o
m
p
arison
and precision,
recall
calculations.
In all experiments, each im
a
g
e in the
database is
use
d
a
s
the query image. For eac
h query, t
h
e
algorithm
collects a set of
sim
ilar images from
the dat
a
base
,
,,….
with
t
h
e sh
ortest imag
e
m
a
t
c
hi
ng
di
st
ance com
put
e
d
usi
n
g E
quat
i
o
n
(
7
)
.
T
h
e pe
r
f
o
r
m
a
nce of t
h
e pr
o
pose
d
m
e
t
h
o
d
i
s
m
easured i
n
t
e
rm
s of p
r
eci
s
i
on a
n
d
recal
l
as sh
o
w
n
bel
o
w
.
The precisi
on and
recall defi
ned
as
(
8
)
(
9
)
5.
RESULTS
A n
u
m
b
er
of e
xpe
ri
m
e
nt
s were pe
rf
o
r
m
e
d to a
p
p
r
ai
se t
h
e
per
f
o
r
m
a
nce o
f
t
h
e
pr
o
p
o
s
ed
ZM
, nam
e
d
LZM
(Lo
w
e
r
or
der Ze
r
n
ike
m
o
m
e
nt) with co
rrecte
d
weig
h
t
s in
th
e
tran
sform
distance circles.
These
m
o
m
e
nt
s com
p
ared
t
o
c
o
m
m
o
n
l
y
use
d
ZM
D
wi
t
h
t
h
e
o
r
der
of
1
0
,
an
d
Ge
n
e
ri
c F
o
u
r
i
e
r
De
scri
pt
o
r
(G
FD
)
.
(a)
(b
)
Fi
gu
re
7.
R
e
t
r
i
e
val
pe
rf
o
r
m
a
nce o
f
LZM
a
n
d
ZM
D
10
,
.
(a) Retriev
e
d resu
lts u
s
i
n
g LZM,
(b) Retriev
e
d
resu
lts
usi
n
g ZM
D
10
. The query
im
a
g
e
c
o
rres
ponds
to
top
left of each
row.
Fig
u
re
7
shows th
e
retrieval resu
lts fo
r the propo
sed meth
od
and
ZM
D
in th
e ord
e
r of
ten. For
in
stan
ce, LZM retu
rn
ed
with si
m
i
lar i
m
ag
es with
d
i
fferen
t ro
tating
imag
es also. Fo
Fig
u
re 8
sho
w
s th
e
ret
r
i
e
ve
d
resul
t
s fo
r LZM
an
d
GF
D o
n
C
o
i
l
-1
00
dat
a
base
. Th
e p
r
op
ose
d
m
e
t
hod
ret
u
r
n
ed
t
o
p fi
ve si
m
i
l
a
r
i
m
ag
es in
d
i
fferen
t
o
r
ien
t
ation
s
.
GFD g
a
v
e
a resu
lt with
on
e or two
u
n
m
atch
ed
im
ag
es in
th
e top
fi
v
e
list o
f
im
ages. Fi
g
u
re
9 i
s
gi
vi
ng a
preci
si
o
n
,
reca
l
l
curves
f
o
r
pr
op
ose
d
m
e
t
hod
(LZM
) a
n
d Z
M
D
10
, GF
D
on
Coil-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE
Vo
l. 7
,
N
o
. 3
,
Jun
e
201
7
:
1
651
–
166
0
1
658
10
0
dat
a
ba
se.
Fi
gu
re
1
0
i
s
s
h
o
w
i
n
g
P-R
p
e
rf
orm
a
nce o
f
a p
r
o
p
o
se
d m
e
t
h
o
d
fo
r
vari
ous
S
N
R
val
u
es. T
h
e
g
r
aph
is b
a
sed on
th
e
resu
lts o
f
a no
ise imag
e
q
u
e
ry and its resp
ectiv
e
retriev
e
d
im
ag
es fro
m
th
e o
r
ig
in
al
dat
a
base
. F
r
o
m
t
h
e Tabl
e
2
:
we can
o
b
se
rve t
h
e
perce
n
t
a
ge o
f
preci
si
on
an
d
recal
l
val
u
es
f
o
r
n
u
m
ber of
im
ages per ca
tegory are 20 and
30. The
shown P-R
values a
r
e for single thre
shold for all categories
(ap
p
r
o
xi
m
a
t
e
l
y
0.
09
). F
r
om
t
h
e res
u
l
t
s
i
t
is concl
ude
d t
h
at
, t
h
e
pr
op
o
s
ed m
e
t
hod i
d
ent
i
f
y
i
ng t
h
e s
h
ape
,
includi
ng local
inform
ation
of an im
age.
(a)
(b
)
Fi
gu
re
8.
To
p
f
i
ve ret
r
i
e
ve
d i
m
ages usi
n
g
L
Z
M
an
d
GF
D
on
C
o
i
l
-
10
0
da
t
a
base.
Fi
rst
i
m
age
of
t
h
e eac
h
r
o
w
is query im
age.
Fi
gu
re
9.
P-R
per
f
o
r
m
a
nce re
sul
t
s
ba
sed
o
n
usi
n
g,
sep
a
rately, LZM, ZMD,GFD
o
n
th
e C
o
il-100
dat
a
base
Fi
gu
re 1
0
. P-R
pe
rf
orm
a
nce
o
f
pr
op
ose
d
m
e
tho
d
f
o
r
vari
ous
S
N
R
v
a
l
u
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
S
hap
e b
a
sed
Im
ag
e Retrieva
l
u
s
i
n
g L
o
wer
Orde
r Zer
n
ike
Moments (
G. S
u
charitha
)
1
659
Tabl
e 2.
Fo
r t
h
e fi
rst
1
0
cat
eg
ori
e
s
o
f
C
o
l
i
-
1
0
0
dat
a
base
pr
eci
si
on a
n
d re
c
a
l
l
val
u
es
fo
r
fi
rst
n=
2
0
a
n
d
n
=
30
im
ages per cat
egory
Categor
y
n=20
n=30
Precision
(%)
Recall
(%)
Precision (%)
Recall
(%)
1 78.
9
75
62.
06
60
2 90.
9
100
90.
6
96.
6
3 16.
9
45
14.
5
33.
3
4 25.
9
100
27.
5
100
5 22.
2
100
24
100
6 38.
2
65
32.
14
60
7 21.
05
100
21.
8
100
8 40
70
42.
3
73.
3
9 100
95
100
70
10
71.
4
50
91.
6
36.
6
6.
CO
NCL
USI
O
N
In
th
is p
a
p
e
r, we in
trod
u
c
ed
an
efficien
t sh
ape feat
ure descript
or
with less com
p
lexity and
red
u
nda
ncy
.
T
h
e t
r
an
sf
orm
di
st
ance m
a
t
r
i
x
desi
g
n
e
d
i
n
s
u
ch a way
,
i
n
a
ssi
gni
ng t
h
e p
r
ope
r wei
ght
s t
o
t
h
e
resp
ectiv
e circle p
i
x
e
l
v
a
lu
es. Th
e b
a
se functio
n
cal
cul
t
e
d
usi
n
g t
h
i
s
p
r
op
ose
d
fu
nct
i
on
. T
h
r
o
ug
h
t
h
e LZM
we c
a
pt
u
r
e t
h
e m
a
xim
u
m
i
n
form
ati
on a
b
o
u
t
t
h
e i
m
age fo
r a sm
al
l
no.
of
pol
y
n
o
m
i
al
orde
r. Si
nce t
h
e
LZ
W
feat
u
r
e vect
o
r
l
e
n
g
t
h
apr
o
xi
m
a
t
e
l
y
18
,
f
o
r
n=
5.
The resul
t
s
pr
ove
d
t
h
at
, pra
pos
ed
m
e
t
hos i
s
scal
e
i
v
ari
a
nt
an
d r
o
t
a
t
i
onal
i
nva
ri
a
n
t
.
The
pr
o
pos
ed m
e
t
hod pr
o
v
ed i
t
s
effi
ci
e
n
cy
i
n
ret
r
i
e
vi
n
g
t
h
e im
ages fro
m
t
h
e
d
a
tab
a
se, ev
en
f
o
r
a
no
isy qu
er
y im
ag
e.
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IJEC
E
1
660
BIO
G
E
Vo
l.
7
,
N
o
.
G
RA
PH
IES
O
3
,
Jun
e
201
7
O
F AUTH
O
R
G
.
Suc
ha
r
JNTU,
Ind
India, 200
9
experience
India. Her
i
Ranjan K
u
forn NIT,
Engineeri
n
his interes
t
c
o
mpre
ssi
o
:
1
651
– 166
0
R
S
r
itha
rece
ived
i
a, 20
05 and
M
9
. P
r
e
s
entl
y pu
r
and presently
i
nt
ere
s
ted ar
ea
s
u
mar
Se
napat
i
Warangal, Ind
i
g, NIT Rourke
l
t
ed
ar
eas
ar
e I
m
o
n alg
o
rithm
s
,
I
0
B.Tech
degre
e
M
.Tech degree
i
u
rsuing Ph.D
fr
o
working as a
n
s
are
Im
age P
r
o
i
is a pr
ofessor
ia, 200
4. He r
la, Ind
i
a, 2013
.
m
ag
e P
r
oces
s
i
n
I
ma
ge
wa
t
e
rma
r
e
in Electronic
s
i
n Dig
ita
l s
y
st
e
o
m KL Unive
r
n
A
sst.
P
rofe
ss
o
o
cessing, Signa
l
in KL U
n
ivers
i
e
ce
ived his
P
h
.
H
e
h
a
s
m
o
r
e
n
g: Im
ag
e Com
p
r
king
, I
m
age
A
s
and Commu
n
e
m and co
mput
e
sity
, India. Sh
e
o
r in FST, IF
H
l
Processing an
d
i
ty
, India.
He r
e
h
.D degree fro
m
than 12
years
o
p
re
ssion,
VL
S
I
A
na
ly
sis.
ISS
N
:
2
n
ication Engin
e
t
er ele
c
troni
cs
f
e
h
a
s 11
years
H
E Universit
y
,
d
Digital
Elect
r
e
ce
i
v
e
d
hi
s
M.
T
m
Electroni
cs
a
o
f t
each
ing
ex
p
I
im
plem
entati
o
2
088
-87
08
e
ering fro
m
f
rom JNTU,
of teaching
H
y
der
a
ba
d
,
r
onics.
T
ech
degr
ee
a
nd Comm.
p
eri
e
nc
e and
o
n o
f
i
m
a
g
e
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