TELKOM
NIKA
, Vol. 11, No. 7, July 201
3, pp. 3641 ~ 3647
e-ISSN: 2087
-278X
3641
Re
cei
v
ed
Jan
uary 22, 201
3
;
Revi
sed Ap
ril 6, 2013; Accepte
d
April 1
8
, 2013
A Gravitational Edge Detection for Multispectral Imag
es
Gen
y
un Sun*, Zhenjie Wang
Coll
eg
e of Geo
-resourc
e
s and
Information,
Chin
a Un
iversit
y
of Petrol
eum
(East Chin
a), Qingd
ao Sh
an
don
g, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: gen
yu
nsu
n
@
163.com
A
b
st
r
a
ct
Gravitation
a
l e
dge
detectio
n
i
s
one of the
ne
w
edge d
e
tecti
on al
gor
it
h
m
s that is bas
ed o
n
the la
w
of gravity. T
h
is
alg
o
rith
m ass
u
mes t
hat e
a
c
h
i
m
ag
e p
i
xel
i
s
a cel
e
stial
bo
dy w
i
th a mass
repres
ented
b
y
its
graysca
le int
e
nsity and th
eir
interactio
ns a
r
e base
d
on
t
he New
t
oni
an
law
s
of gravity. In this article
,
a
mu
ltisp
e
ctral v
e
rsio
n of the
algor
ith
m
is
introduc
ed.
T
he metho
d
us
es grav
itati
ona
l techn
i
q
u
e
s in
combi
natio
n w
i
th metric tens
or to det
ect e
dges
of
multis
pectral
i
m
ag
es
incl
udi
ng c
o
l
our i
m
ages. T
o
eval
uate th
e
perfor
m
a
n
ces
of the pro
p
o
sed
alg
o
ri
th
m, sever
a
l
e
x
peri
m
e
n
ts ar
e perfor
m
ed.
T
he
exper
imenta
l
results confir
m t
he efficie
n
cy of
the mu
ltispectr
al grav
it
ation
a
l edg
e
detecti
on
.
Ke
y
w
ords
: ed
ge detecti
on, i
m
a
ge pr
ocessi
ng, gravity, seg
m
e
n
tatio
n
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Edge d
e
tecti
on is the
pro
c
e
s
s of lo
cali
zing
pixel int
ensity tra
n
siti
ons. T
he
su
cce
s
s of
edge d
e
tecti
on provides
a good b
a
si
s for the per
f
o
rma
n
ce of highe
r level image p
r
o
c
e
s
sing
tasks, such a
s
obj
ect
reco
gnition, targ
et tracking,
and
segm
entatio
n. Over
the y
ears, the ta
sk of
detectin
g
e
d
ges in
gray valued
ima
ges is very
well
kno
w
n
,
and
ha
s
been
tho
r
ou
ghly
s
t
udied [1-3].
Neverth
e
le
ss,
these m
e
tho
d
s
have to
e
x
tend to
colo
r, multispe
ctral an
d hyp
e
rspe
ctal
image
s. In re
cently, the d
e
v
elopment
of sen
s
o
r
s
makes m
u
ltispect
ral images usual obj
ect
s
for
analysi
s
. On
e of the most importa
nt tools fo
r worki
ng with
multispe
ctral
images i
s
edge
detectio
n
[3-4
]. However, a
s
long a
s
the task of
dete
c
ting edg
es i
n
gray value
d
image
s is very
well kno
w
n, the sam
e
pro
b
lem for mult
ispe
ctral im
a
ges i
s
mu
ch l
e
ss well d
e
fined [3]. Although
some m
e
tho
d
s for m
u
ltib
and ed
ge det
ection h
a
ve b
een p
r
opo
se
d, most of them are
only valid
unde
r ce
rtain
condition
s, o
r
are only u
s
e
d
for three ba
nd colo
ur ima
ges [5]. The popul
ar meth
od
is applyin
g
the Lapla
c
e of
Gau
ssi
an (L
OG) filter
to
all cha
nnel
s, then the re
su
lts are
summ
ed
and thre
sh
old
i
ng take
s pla
c
e on this ima
ge [5]. While
DiZen
z
o [6] shows that the ways of finding
edge
s by co
mbining the
output of differen
c
e o
per
a
t
ors in ea
ch
comp
one
nt does n
o
t actu
ally
coo
perate
with on
e a
nothe
r. He
con
s
ide
r
ed
the m
u
lti-dimen
s
ion
s
a
s
a
vecto
r
fiel
d an
d fou
nd t
h
e
tens
or gradient [7]. In ref [8], W.
H. Baker
con
s
ide
r
t
he p
r
oble
m
i
n
feature spa
c
e, he
uses
LOG
filter in combi
nation with di
stan
ce mea
s
ure
s
, su
ch a
s
the Euclidea
n distan
ce, to
detect edg
es of
hyperspe
c
tral
images. Th
e method is simply and
effective, howeve
r
it will misse
s so
me
importa
nt ed
ges. Simila
rly, Kang [9] defines an
obje
c
tive function
to detect ed
ges of g
r
ay-l
evel
image
s a
nd
extend it to color im
age. T
h
is al
go
rithm
can
elimin
ate dou
ble
edg
es,
spe
ckl
es
to
some
extent,
but it will
get t
h
icker ed
ge f
o
r n
a
ture ima
ges.
Cum
ani
[4] sug
g
e
s
ts t
he exten
s
io
n
of
pro
c
ed
ures
b
a
se
d on th
e
seco
nd-order
derivatives of
the imag
es f
unc
tio
n
s. T
h
i
s
op
erator i
s
one
of the funda
mental works in m
u
ltisp
e
ctral
edg
e
detectio
n
. Th
e multi-dim
e
nsio
nal g
r
adi
ent
method i
s
al
so extende
d b
y
Sylvain Roussea
u
[
10]. In re
cently, althoug
h there
prop
osed
so
me
new e
dge d
e
tection fo
r multispe
ctral image
s [11-
1
2
], it is still
a chall
eng
e for multisp
e
ctral
image
s edg
e detectio
n
.
Re
cently, we have pro
p
o
s
e
d
a new meth
od for edg
e detection (GE
D
) ba
se
d on the law
of universal
gravity [13].
Even if the original
ve
rsi
o
n of GED wa
s improved b
y
C. Lopez [
14]
based o
n
the
triangul
ar
no
rms, it suffer
the two
p
r
obl
ems a
s
m
enti
oned
above.
The go
al of this
pape
r i
s
to fi
nd ways to
o
v
erco
me the
probl
em
s a
s
sociate
d
with
the g
r
avitation
a
l metho
d
an
d
extend it to
multispe
ctral
image
s. The
basi
c
id
ea of
the propo
se
d metho
d
co
me from th
at, for
each com
pon
ent the spatia
l information
sho
u
ld be in
v
o
lved. In this way, we tune
the param
eters
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
A Gravitatio
n
a
l Edge Dete
ction for Multi
s
pe
ctral Im
ag
es (Gen
yun S
un)
3642
to achieve th
e best po
ssib
le edge d
e
tector for
every
comp
one
nt, and then utilize the detecto
r to
get edge
ma
gnitude of e
a
c
h
comp
one
n
t. Then co
nsi
der
the m
u
ltispe
ctral im
ag
es a
s
a ve
ctor
field to fuse t
he re
sult
s co
mbined
with
metric te
nsor [6, 10]. The improve
d
me
thod ca
n offe
rs
different ma
sks acco
rdi
n
g
to different
comp
one
nts
and ove
r
com
e
the la
rge
kernel
proble
m
s.
Experiment
s indicate that the app
roa
c
h
i
s
effective for multispe
ctral
images.
The
re
st of th
e pa
per is organi
zed
as th
e fo
llo
wing: t
he la
w of
uni
versal
g
r
avity is
brie
fl
y
reviewed in
Section 2. T
hen, the alg
o
rithm of
the
propo
se
d e
dge dete
c
tor is pre
s
ente
d
in
se
ction 3. Fu
rtherm
o
re, a
pplication
s
of the pr
e
s
e
n
ted algo
rithm
are given i
n
Section 4.
The
perfo
rman
ce
is illustrate
d using a
numbe
r of real image
s.
Both noise
free and n
o
isy
contami
nated
image
s a
r
e
use
d
for th
e experi
m
ent
s. Finally, concl
u
si
on
s a
r
e p
r
e
s
ente
d
in
Section 5.
2. The Grav
it
ational Edge Detection
In this se
ction
,
we introd
uce a brief
revie
w
of gravitational ed
ge d
e
te
ction [14]. A
s
state
d
by Newto
n
in
the Law of Universal G
r
avity [
15], anybody attract
s
ever
y othe
r body by a force
proportional to the product
of thei
r masses as illustrated in Figure 1:
r
2
m
f
f
1
m
Figure 1. Ne
wton'
s law of
universal g
r
a
v
itation
More
con
c
retely, the force
is given by:
3
2
1
2
2
1
12
r
r
m
Gm
r
r
m
Gm
f
(1)
whe
r
e
12
f
is the force on o
b
j
ect 1 due to obje
c
t 2, G is the gravitational con
s
tant,
1
m
and
2
m
are the
masse
s
of th
e obje
c
ts 1 a
nd 2,
r
is the
vector
con
n
e
c
ting the p
o
si
tions of the
mass
.
To con
s
tru
c
t
an ed
ge
dete
c
tor, eve
r
y pi
xel is a
s
sume
d to be
an
ob
ject, which
ha
s
some
relation
shi
p
with other pixel
s
within its n
e
i
ghbo
rh
o
od th
roug
h gravitational force
s
. For ea
ch pixe
l,
the mag
n
itud
e an
d the
direction
of the
vector of
the
sum
of all th
e
gravitation
a
l
force
s
the pix
e
l
exerts o
n
its
neigh
borhoo
d
,
conveys the
vitally
important inform
ation abo
ut an
edge
stru
ctu
r
e.
Now considering that the
nei
ghborhood of a pixel
(i,
j)
will be restricted to a
wind
ow, the
resulting force assigned to it will be:
)
,
(
)
,
(
&
)
,
(
,
;
,
,
j
i
l
k
l
k
y
F
x
F
f
f
y
x
l
k
j
i
j
i
(2)
whe
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
e-ISSN:
2087
-27
8
X
TELKOM
NIKA
Vol. 11, No
. 7, July 2013
: 3641 – 364
7
3643
2
,
,
,
;
,
r
r
m
Gm
f
l
k
j
i
l
k
j
i
(3)
)
,
(
)
,
(
&
)
,
(
)
,
(
)
,
(
&
)
,
(
,
;
,
,
;
,
j
i
l
k
l
k
f
F
j
i
l
k
l
k
f
F
y
l
k
j
i
y
x
l
k
j
i
x
(4)
3
2
1
,
;
,
3
2
1
,
;
,
)
(
)
(
r
j
l
m
Gm
f
r
i
k
m
Gm
f
x
l
k
j
i
x
l
k
j
i
(5)
Eq. (3-5)
co
mpri
se
s the
core of th
e
method,
in
th
e sense that
it provide
s
t
he way of
obtainin
g
pix
e
l (i, j
)
e
dge
intensity,
x
F
and
y
F
，
with th
e di
rectio
n of
x a
nd y
re
spe
c
ti
vely for
every pixel in the image [13
]. Finally, the
edge ma
gnitu
de ca
n be co
mputed a
s
follows:
)
arctan(
)
(
)
(
2
2
y
x
y
x
F
F
F
F
F
(6)
The pri
n
ci
ple
of gravitation
a
l method ca
n be implem
e
n
ted as follo
ws:
1) F
o
r ea
ch ima
ge
p
o
int
)
,
(
j
i
g
, we
co
nsid
er an
m×n
nei
ghb
orho
od
with
pixels
)
,
(
)
,
(
&
)
,
(
j
i
l
k
l
k
. For each p
o
int, the gravitationa
l
force of the
point exert
s
on
its neigh
bori
n
g pixels which is co
mpute
d
usin
g Eq. (2);
2) Get the ed
ge stre
ngth with Eq. (6).
Theo
retically, gravitational
method bel
o
ngs to
the
cl
ass of soft computing
alg
o
rithm
s
[16]. Sun et al. [13] gave a co
mpa
r
ative
study betwee
n
the me
thod
and a small
numbe
r of we
ll-
kno
w
n edg
e detectio
n
alg
o
rithm
s
.
The results su
gge
st
that this
a
ppro
a
ch
which is i
n
spire
d
by
the law of gra
v
ity has merit in the field of edge dete
c
ti
on
3. Multispectral Gr
av
itational Method
Although tra
d
i
tional ope
rat
o
rs
are ve
ry efficient, their efficiency i
s
not well pre
s
erve
d
once they a
r
e su
bje
c
ted t
o
the an
alysi
s
multi
s
pe
ctral image
s. E
a
rly ap
pro
a
ches to
dete
c
t
i
ng
discontin
uities in multi
s
pe
ctral ima
g
e
s
attempted to
combi
ne the
respon
se of
edge d
e
tect
ors
applie
d sepa
rately to ea
ch
of the imag
e
com
pon
ent. While th
ese
method
s
suffered
from
so
me
probl
em
s a
ccordin
g to
abo
ve analy
s
is. I
n
this pa
per,
we
wo
uld
ch
oose a
metri
c
ten
s
o
r
on t
he
feature
sp
ace
com
puting t
he g
r
adie
n
t a
s
de
scri
bed
b
y
[6] and furt
her
used in [
10] su
mma
rized
as
follows
:
An m-band
i
m
age
is ind
e
ed b
e
rep
r
e
s
ented
by fun
c
tion
m
R
R
f
2
:
that m
aps a
point
)
,
(
y
x
p
in the image pla
ne to an m-ve
cto
r
))
,
(
),...,
,
(
(
1
y
x
f
y
x
f
f
m
, obviously, for
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
e-ISSN:
2087
-278X
A Gravitatio
n
a
l Edge Dete
ction for Multi
s
pe
ctral Im
ag
es (Gen
yun S
un)
3644
a colo
r imag
e, m=3. Let
)
,...,
(
1
1
x
f
x
f
f
m
and
)
,...,
(
1
2
y
f
y
f
f
m
. A tensor T is then
introdu
ce
d:
)
(
)
(
2
2
2
1
2
1
2
1
H
F
F
K
f
f
f
f
f
f
T
(7)
The eige
nval
ues of T are given by:
2
2
4
)
(
2
F
H
K
H
K
(8)
and the eig
e
n
v
ectors are:
)
sin
,
(cos
(9)
W
h
er
e
2
)
2
arctan(
2
1
H
K
F
(10
)
The
eige
nvectors of m
a
trix
T p
r
ovide
the
di
rectio
n
of
maximal
a
n
d
minimal ch
an
ges
at a
given point P
=
(x, y) in the
image, an
d the ei
ge
nvalu
e
s a
r
e the
co
rre
sp
ondi
ng rates of chan
ge.
is
calle
d the
dire
ction
of m
a
ximal chang
e and
the maximal rate
of
cha
nge. Simi
larly,
and
are the
dire
ction of
minimal chan
ge and th
e
m
i
nimal rate
of chan
ge, re
spectively. For
mono
ch
romat
i
c ima
g
e
s
,
is
co
rre
sp
on
ding to th
e g
r
adie
n
t. The
eigenvalu
e
s
ca
n be
extended to l
o
cate e
dge p
o
int of color i
m
age.
Based
on the abov
e equatio
n, we propo
se
d
a
multispe
ctral image ed
ge d
e
tection. The
gradi
ent is e
s
timated as fol
l
ows:
)
(
g
(11
)
Whe
r
e
is eigen value
s
of matrix T in eq
uation (3.6
).
(1) A
c
cordi
n
g to what m
entione
d abo
ve, the entire algo
rithm for ed
ge dete
c
tion of
multispe
ctral image
s ca
n b
e
impleme
n
te
d as follo
ws:
(2)
For ea
ch imag
e poi
nt
)
,
(
j
i
g
, we
con
s
ider
an m
×
n neig
hbo
rh
ood
with
pixels
)
,
(
)
,
(
&
)
,
(
j
i
l
k
l
k
.
(3)
Use e
quat
ion (2
) to
co
mpute the
gravitational force of the
poin
t
)
,
(
j
i
g
exerts o
n
its
neigh
bori
ng p
i
xels for ea
ch
multispe
ctral
image co
mp
onent.
(4)
Comp
ute the magnitu
de
of gradient u
s
ing e
quatio
n
(11)
(5) Set an ap
prop
riate thre
shol
d to prod
uce a
n
edg
e map.
4. Results a
nd Discu
ssi
on
The prim
ary
goal of this
pape
r is to e
x
tend
the gravitational m
e
thod to mult
ispe
ctral
image
s.
In
t
h
is se
ction we de
scribe
the
re
su
lt
s o
f
our
experi
m
ents. Both
colo
r ima
g
e
s
and
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7
3645
remote
se
nsi
ng imag
es
are used. The
colo
r Le
na i
m
age
(Figu
r
e
2(a
)) h
a
s
so
me ch
allen
g
i
n
g
feature
s
fo
r
edge
dete
c
to
rs. F
o
r in
sta
n
ce,
sh
ado
ws o
n
the
face an
d bl
urry ba
ckgro
und
are
difficult to pro
c
e
ss. T
he mu
ltispe
ctral im
age (Fig
u
r
e 3
(
a)) is
a com
p
lex scen
e which
co
nsi
s
ts
of
31 sp
ectral b
and
s [17].
We have
selected the
CVVEFM and Kang
operators proposed in
recently fo
r
comp
ari
s
o
n
s
with 3×3 ke
rn
el size
sin
c
e they prod
uce better re
sult
s [9, 18]. In
ord
e
r to sho
w
th
e
sup
e
rio
r
ity of the propo
se
d method,
a
simple
edg
e dete
c
tion
scheme
is
a
dopted,
whi
c
h is
comp
osed of
gradie
n
t est
i
mation and
threshol
di
ng.
Smoothing
and po
stprocessing meth
ods
(e.g. no
maxi
ma supp
re
ssion, thinnin
g
)
are
not u
s
e
d
in this secti
on. Fo
r
simpl
i
city, this pa
p
e
r
utilizes fixed threshol
d [19].
Figure 2. Shows col
o
r L
ena ima
ge a
nd gradi
ent
i
m
age
s
with 3×3 ke
rnel size.
All
gradi
ent ima
g
e
s
are
no
rma
lized
with
re
spect to th
eir
maximum val
ues and
thre
shol
ded
at le
ve
l
0.1. Figure 2
(
b)
sh
ows th
at t
he propo
sed
metho
d
detect
s
the
e
dge
s corre
c
tly. Howeve
r,
the
conventional
method
and CVVEFM
me
thod cannot extract smooth
ed
ges
(e.g.
,
vertical
sm
ooth
line on th
e le
ft side of the
image
) a
s
shown in Fi
gu
re 2
(
d
)
an
d (e), re
sp
ective
ly. Figure 2.
(c)
sho
w
s that smooth ed
ge
s at lowe
r rig
h
t
corn
er
se
e
m
to vanish
and
cann
ot d
e
tect the ed
g
e
in
the hat.
Next we will consi
d
e
r
the multispe
ctral
image whi
c
h is big
ger t
han thre
e ba
nds (Figu
r
e
3(a)). Fi
gure
3(c) i
s
the result of
CVVEFM me
thod applied
on the band 1, band 3 and
band 4
sin
c
e it is use
f
ul for three-b
and imag
es o
n
ly.
Figure 3(d) and (b) sh
ows the re
sul
t
s of Kang an
d
the pro
p
o
s
ed
method, re
spectively. From the
re
sul
t
s, we
see t
hat, some
e
dge
s could
be
detecte
d in t
he multispe
ctral ima
ge (Fi
gure
3.
2(b)) that wa
s n
o
t deter
mi
ned i
n
the thre
e-b
and
image (Fi
g
u
r
e 3(d
)). In co
ntrast, the ed
ge image of
Kang (Fig
ure 3(d
)) is p
o
o
r
.
(a)
(b)
(c
)
(d)
(e)
Figure 2. Co
mpari
s
o
n
s
with different me
thods fo
r “len
a” imag
e with
3×3 ma
sk
(a) the o
r
igin
al “lena
” imag
e; (b) the ed
g
e
map
by usi
ng the pro
p
o
s
ed me
thod
(c) the re
sult of
the Kang met
hod (d) the
result of CVVEFM method; (e) the
result of conventional method.
(Gradie
n
t images a
r
e thresholde
d at their 10% of their maximum value).
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TELKOM
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e-ISSN:
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A Gravitatio
n
a
l Edge Dete
ction for Multi
s
pe
ctral Im
ag
es (Gen
yun S
un)
3646
(a)
(b)
(c
)
(d)
Figure 3. Co
mpari
s
o
n
s
with different me
thods fo
r multispe
ctral
rem
o
te sen
s
in
g image with 3
×
3
mask (a
) the
origin
al multispce
c
tral im
ag
e; (b
) the ed
g
e
map by usi
ng the pro
p
o
s
ed method
(c)
the result of the CVVEFM
method (d) the resu
lt of Kang method. (Gradi
ent images are
threshold
ed a
t
their 10% of their maximu
m value).
5. Conclusio
n
and Futu
r
e
Rese
arch
In re
ce
nt yea
r
s, va
riou
s
al
gorithm
s fo
r
edge
dete
c
tio
n
have
be
en
develop
ed. G
E
D i
s
a
new al
gorith
m
whe
r
e it is co
nstructe
d based on
the law of Gravity. To the best of our
kno
w
le
dge,
GED alg
o
rith
m has
not ye
t been a
pplie
d to multisp
e
c
tral im
age
p
r
ocessin
g
task up
to date. In this arti
cle, a m
u
ltispe
ctral ve
rs
io
n of GED
has b
een int
r
odu
ced. Fo
r
each co
mpo
n
e
n
t
of input im
ag
e, the GE
D’s output i
s
d
e
t
ermine
d an
d
then, results are
combin
ed to
com
p
u
t
e
gradi
ents in v
e
ctor imag
e. The p
e
rfo
r
ma
nce
of
the
p
r
opo
sed algo
ri
thm
is comp
a
r
ed with
ma
ny
recently developed
methods, including t
he Kang
and CVVEFM detecto
rs. It is
evident from
the
obtaine
d re
sults that the
algorith
m
is
p
r
odu
cin
g
resu
lts co
ntainin
g
most of th
e i
m
porta
nt edg
es
for all images.
Ackn
o
w
l
e
dg
ments
This
study
was
su
ppo
rted
by Chi
n
e
s
e
Natural S
c
ien
c
e F
oun
datio
n Proj
ect
(41
0012
50),
the Fu
ndam
ental
Re
sea
r
ch
Fun
d
s fo
r the
Centra
l Unive
r
sitie
s
of China
(grant
num
be
r:
10CX0
400
8A
) an
d the
project "L
and S
u
rface Mo
del
i
ng an
d Data
Assimil
a
tion
Re
sea
r
ch" (g
rant
numbe
r: 200
9AA1221
04) f
r
om the natio
nal high
-tech prog
ram
(86
3
)
of China
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TELKOM
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Vol. 11, No
. 7, July 2013
: 3641 – 364
7
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