TELKOM
NIKA
, Vol. 11, No. 5, May 2013, pp. 2822 ~ 2829
ISSN: 2302-4
046
2822
Re
cei
v
ed
Jan
uary 12, 201
3
;
Revi
sed Ma
rch 2
1
, 2013;
Acce
pted Ma
rch 3
0
, 2013
Edge Steganography for Binary Image
Hong
xia Wa
ng*
1
, Gouxi Chen
2
, Meng
Zhang
2
Shan
xi W
a
ter T
e
chnical Prof
essio
nal C
o
ll
eg
e,
T
a
i
y
uan, 0
3
002
4, Chi
na
Schoo
l of Com
puter Scie
nce
and T
e
chno
log
y
, North
U
n
iver
sit
y
of Chi
na, T
a
i
y
u
an 0
300
51
, China
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
w
a
ng
h
x
s
x
t
y
@16
3
.c
om, cheng
ou
xic
g
x@
1
63.com, zhan
la
ng
x0
@gma
il.c
o
m
A
b
st
r
a
ct
In ord
e
r to
i
m
p
r
ove th
e ste
g
a
nogr
aph
ic r
obu
stness of
the
al
gorith
m
in
b
i
na
ry i
m
a
ges, s
u
p
pose
a
n
new
stegan
og
raph
ic met
hod
w
h
ich deals
w
i
th t
he edge of the bin
a
ry image
usi
ng mathe
m
ati
c
a
l
mor
p
h
o
lo
gy a
nd co
mbin
es
F
5
enco
d
i
n
g metho
d
to
embe
dd
ed i
n
formatio
n
. Margi
nal
i
z
a
t
io
n
an
d
reconstructi
on
on bi
nary i
m
age
by dil
a
tio
n
a
nd er
osi
o
n
op
eratio
ns, a
nd ta
g b
l
ocks
that ca
n e
m
b
e
d
infor
m
ati
on
to. F
i
nally e
m
b
ed secret
infor
m
ation us
in
g F
5
al
gorith
m
. T
h
ro
u
gh ex
peri
m
ent
s and
ana
lysis
it
comes out the
stegano
gra
phi
c robustness o
f
the algor
ith
m
can be en
han
ced, and h
a
ve
a smal
l chan
g
e
s
on the carri
er i
m
a
ge q
ual
ity after embed
di
ng
infor
m
ati
on, an
d also h
a
s a go
od e
m
b
e
d
d
in
g capac
ity.
Ke
y
w
ords
:
stegan
ogra
phy, mathe
m
atic
al mo
rpho
logy, bi
nar
y ima
ge, F
5
al
gorith
m
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Esse
ntially th
e bina
ry ima
ge is bla
c
k-a
nd-white im
a
ge which e
a
c
h
pixel only
one
bit,
and it h
a
s
si
mple
stora
g
e
and
com
p
a
c
t stru
cture.
It is
widely u
s
ed in th
e fiel
d of informati
o
n
hiding. Prece
n
t Stegano
graphi
c alg
o
rith
m ba
sed
on binary
im
age
can
be sum
m
ari
z
ed as bl
ock
embed
ding
method,
m
o
d
i
fied
tours e
m
bedd
ed me
thod, bo
unda
ry modifie
d
method, the
half-
tone ima
ge
method,
cha
r
acter di
spla
cement m
e
tho
d
an
d fre
que
ncy d
o
main
e
m
beddi
ng m
e
thod
[1-3].
Do
cume
nt [4
] divide text steg
ano
gra
phy to
sem
antic
steg
an
ogra
phy a
n
d
format
stega
nog
rap
h
y
, further m
o
re, it divide t
e
xt st
egan
og
raphy to
sem
antem
e, syntax
and sp
ace.
Do
cume
nt [5-8] propo
sed
a serie
s
of al
gorithm
s fo
r t
e
xt format m
o
ving mai
n
ly
inclu
de li
ne
shift
and
character shift. According to the image
connectivity and smoot
hness requi
rements,
document [9]
embed
ded
se
cret i
n
to blo
c
k. The
se
cu
rit
y
of the abov
e metho
d
s
are not g
ood
a
nd
anti-po
or offe
nsive.
This pa
pe
r p
r
opo
se a n
e
w
steg
ano
graphy algo
rith
m that combi
nes the math
ematical
morp
holo
g
y with b
ound
ary modificatio
n
s, a
nd u
s
e
F5 codin
g
al
gorithm. T
h
ro
ugh
experim
ental
demon
stratio
n
, this algorit
hm has
stro
n
g
robu
stne
ss, highly stega
nographi
c safety.
This p
ape
r i
s
organi
ze
d
as follo
ws. In se
ction
2, prep
ro
ce
ss
cover i
m
ag
e
s
u
s
ing
mathemati
c
al
morph
o
logy
and blo
ck l
abelin
g.
Section 3 de
scri
bes the e
m
b
eddin
g
co
urse.
Section 4 is t
he implem
ent
of this algorit
hm. Sect
ion
5 is the analy
s
is of the exp
e
rime
nt results.
Finally is the conclusion.
2. Pretrea
t
men
t
of The
Carr
ier Image
2.1. The Basi
c Principle of Math
ematic
al Morpholo
g
y
Mathemati
c
al
morp
holo
g
y prod
uced in
1
964,
was
pro
posed by
Dr.
J. Serra a
nd t
eacher
Mather Wi
ng
of Pari
s S
c
hool
of Mine
s. Math
emati
c
al m
o
rphol
o
g
y ba
sed
on
the
rigo
rou
s
mathemati
c
al
theory an
d
geomet
ry, focu
se
s on
the
geomet
ry and rel
a
tion
sh
ip of the ima
ge
.From th
e p
e
rspe
ctive of
set
theo
ry,
mathemat
i
c
al
morphol
ogy
co
ntain
s
th
e comp
utatio
nal
method
s that
cha
nge from
one a
ggrega
te to anothe
r. The pu
rp
ose
of the ch
ang
e is to find th
e
spe
c
ific
geo
metry of ori
g
inal a
ggreg
at
e, and the
aggregate
being
ch
ang
ed contain t
h
e
informatio
n. The chan
ge i
s
a
c
hieved
b
y
a feat
ure a
s
semble
nam
ed structu
r
al
element
s. Th
e
basi
c
id
ea i
s
that use
a
structural el
eme
n
t to ex
plore
an ima
ge, fin
d
out the
app
rop
r
iate
site t
o
put stru
ctural element, and
mark the site
s,
to obtain the informatio
n of the image.
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2822 – 282
9
2823
Suppo
se
X
i
s
im
age
ag
g
r
egate,
B
is structu
r
al
el
ements a
ggregate, m
a
the
m
atical
morp
holo
g
y mean
s
B
do
th
e
c
o
rr
es
p
ond
in
g
op
er
a
t
ion
s
to
X
. In fa
ct, structu
r
al
element i
s
al
so
a
image a
g
g
r
e
gate. De
sig
n
a ori
g
in for
every structu
r
al ele
m
ent, i
t
is the reference poi
nt of the
stru
ctural el
ement a
nd
mathem
ati
c
al
morphol
ogy. Here a
r
e
several b
a
si
c o
peration
s
of
mathemati
c
al
morph
o
logy.
-
dilation—th
e operator of dil
a
tion is
,
X
is dilated by
B
is
X
B
, it is defined as:
^
X
X
B
=
x
[(
B
)
]
A
(1)
In formula (1):
B
is the ma
ppi
ng of
B
, it is d
e
fined a
s
:
,
Bx
x
b
b
B
(2)
()
X
B
mean
s shift
mappin
g
of
B
for
x
bits, it is defined a
s
:
()
,
X
M
yy
a
x
a
M
(3)
In formul
a (3): the proces
s
of the dil
a
tion
that
B
to
X
i
s
that: map th
e center pixel
of
B
at
first, then shi
ft the mappin
g
of
B
for
x
,
the interse
c
tion of
X
and
B
is not em
p
t
y set. In other
words, the
ag
greg
ate of th
e dilation of
B
to
X
is that, the agg
re
gate
of t
he site of
the ce
nter pix
e
l
of
B
, when there is at lea
s
t one nonzero el
ement
s interse
c
t betwe
en the mappi
ng of
B
and
X
.
That is, formu
l
a (1)
can b
e
written a
s
:
[(
)
]
X
X
Bx
B
X
X
(4)
Formul
a
(4)
can
help
u
s
to und
ersta
nd the
dilati
on op
eration
s
by the
co
nce
p
t o
f
convol
ution. If as
B
the te
mplate of co
nvolution,
dilation mean
s do the mappi
ng of
B
about the
cente
r
pixel, and then mov
e
the mappin
g
contin
uou
sl
y on
X
.
-
Erode
-- the o
perato
r
of ero
de is
,
X
is eroded by
B
is
X
B
, it is defined as:
()
x
X
Bx
B
X
(5)
Formul
a (5
) e
x
plain that the result of
B
erod
e
X
is the aggregate
of all the
x
, in whic
h the
B
that tran
sla
t
ion
x
i
s
still
in
X
.In other
words, th
e ag
greg
ate that
B
erod
e
X
is the ag
gregate
of
the origin
al p
o
sition of
B
when
B
is com
p
letely included in
X
.
2.2. Choice
of Struc
t
ur
al Elements
The tre
a
tmen
t that mathe
m
atical m
o
rp
hology to
im
a
ge is
ba
sed
on the
con
c
e
p
t that fill
place the
st
ructural
eleme
n
ts, choo
se
of struct
u
r
al
element
s a
n
d
the info
rmati
on of t
he im
a
g
e
has clo
s
e rel
a
tionship,
we
can co
mplet
e
different
im
age a
nalysi
s
throug
h con
s
tructio
n
differe
nt
stru
ctural co
mplete, and o
b
tain different
experime
n
tal
result
s.
Tran
slatio
n the stru
ctu
r
al el
ements
S
for
x
get
S
x
,if
S
x
and
X
intersec
t is
not empty ,we
record the p
o
i
nt
x
, the a
g
g
r
egate
that b
e
ing
comp
osed by
x
that
meet the a
b
o
v
e con
d
ition
s
is
calle
d the re
sult that
S
dilate
X
. The formula is :
X=
x
x
SS
x
(6)
The re
sult of dilation is to l
a
rge
r
the targ
et, as figure 1
sho
w
s:
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TELKOM
NIKA
ISSN:
2302-4
046
Edge Stegan
ogra
p
h
y
for Binary Im
age (Hon
gxi
a
Wa
n
g
)
2824
X
S
X
S
Figure 1. Dila
tion example
The method
of the dilation is that, compare the ori
g
in
al point of
S
and the point of
X
one
by one, if
on
e poi
nt of
S
fall within the sc
ope of
X
,
then th
e p
o
i
n
t that corre
s
po
ndin
g
to t
he
origin
al point
of
S
being the image; im
age to the ri
ght is t
he re
sult of being d
ilated. It can be
see
n
, it co
ntain all th
e ra
nge of
X
, like
X
bei
ng dil
a
ted a l
ap. A
nd if the
orig
inal poi
nt of t
he
stru
ctural ele
m
ents differe
nt, the result
s of the dilation are differen
t
.
2.3. To Achi
ev
e the Math
ematical Mor
pholog
y
Alg
o
rithm
We can se
e from the abov
e descri
p
tion,
if dila
ted by the stru
ctu
r
al
element
s, the object
image will dil
a
te a lap .Then if we let th
e image that being dilate
d minus the o
r
i
g
inal image,
can
get the e
dge
of the ima
g
e
. In bina
ry i
m
age, th
e
e
dge of th
e o
b
ject a
ppe
ar as th
e form
of
mutation of
gray valu
e.
Whe
n
the
st
ructu
r
al
elem
ents at
flat area
s (the same
g
r
ay
va
lue),
becau
se the differen
c
e of the value is bi
g, t
he value of output image that being chang
ed is lo
wer
than the origi
nal image. S
o
if we let the dilat
ed ima
ge minu
s the
original im
a
ge, can g
e
t the
edge of the o
r
iginal im
age
[10].
Expresse
d the thought by morp
holo
g
ica
l
operatio
ns i
s
that:
()
()
C
XB
X
X
X
B
(7)
This a
r
ticle
choo
se
s 3×3 structu
r
al elem
ents for the e
x
perime
n
tal.
Figure 2 is th
e re
sult of bi
nary ima
ge b
e
ing
simulati
on in math
e
m
atical m
o
rp
hology. In
whi
c
h, the ori
g
inal imag
e Figure 2
(
a
)
is the im
age that
owne
d by the sen
der a
n
d
receive
r
,bei
ng
use
d
to com
pare t
he im
age
s when
got by the re
ceive
r
Bein
g dilated
wit
h
3×3 st
ru
ctural
element
s, an
d bein
g
mi
su
sed,
we
ca
n
get the
edg
e imag
e Fig
u
re
2(c) that
ca
n be
u
s
e
d
in
st
ega
nog
rap
h
i
c re
sea
r
ch.
(a) O
r
igin
al bi
nary imag
e
(b) Ima
ge bei
ng dilated
(c) Edge ima
g
e
Figure 2. Extract ed
ge ba
sed on bin
a
ry image
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02-4
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TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2822 – 282
9
2825
2.4. Restore
Cov
e
r b
y
Image Parti
t
ion
And Identi
f
y
ing
After extract the edg
e of the origin
al ima
ge,
we shoul
d also tre
a
t it through the
method
of image
pa
rtition and i
d
e
n
tifying .Divide the e
dge
i
m
age fig
u
re
2(c) into
3
×
3
image
mod
u
l
e
,
12
2
,
,
...,
t
F
FF
a total of 2t.
Provide
i
F
(i
=1,
3
,5…2t-1
)
is the identification modul
e
,
then
j
F
is th
e aggregate
o
f
module that the inform
atio
n can b
e
emb
edde
d.
In
i
F
,
p
r
ovide
the mo
dule t
h
at avera
ge
pi
xel is b
e
twe
e
n
0.3 a
nd
0.7
is
F
u
ui
(F
F
)
,then
the mo
dule
that
F
u
co
rrespondi
ng
F
u
+1
(
u+1
j
FF
) is the i
m
a
ge m
odul
e th
at ca
n
be
e
m
bedd
ed
into informati
on. Comp
ose
the module t
hat can b
e
e
m
bedd
ed int
o
new ima
g
e
T
,
T
is the real
image that ca
n be embe
dd
ed inform
atio
n.
3. Information
Hiding Algor
ithm B
ase
d on Math
ema
t
ical Morpho
log
y
3.1. Introduc
e the Embed
d
ing Algorithm
In this paper,
the embeddi
ng informatio
n is t
he matri
x
coding tech
nology. Matri
x
coding
techn
o
logy was propo
se
d by Ron Cran
dall in 199
8. The emb
eddi
ng rate imp
r
o
v
ed greatly si
nce
F5 steg
anog
raphy introd
uce the techn
o
l
ogy.
Figure 3. Embeddi
ng mod
u
le that F5 hidden info
rmat
ion
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Edge Stegan
ogra
p
h
y
for Binary Im
age (Hon
gxi
a
Wa
n
g
)
2826
Embeddi
ng
efficien
cy is the bits that
eac
h im
age
can be im
p
r
oved for th
e se
cret
informatio
n. In the usual
LSB stega
nography
, the averag
e rate that cha
nge LSB when
embed
ded
1
bit informatio
n is 1/2.Th
at is, every
chan
ging
can o
n
ly embed
2 bit i
n
formatio
n. But
in the
F3
ste
gano
gra
phy
and
F4
steg
a
nography,
be
cau
s
e
it may
appe
ar invali
d em
bed
ded,
the
rate of the embeddi
ng mi
ght be low. T
he purpo
se o
f
the matrix coding is to e
m
bed mo
re secret
informatio
n when imp
r
ove l
e
ss bits.
F5
ste
gan
ography system obtai
n
s
em
be
dding
se
cret i
n
formatio
n m
odule
and
extractio
n
module, p
r
og
ram flow
cha
r
t shows a
s
Fi
gure 3 a
nd Fi
gure 4.
The propo
rtio
n of F5 steg
a
nographi
c alg
o
rith
m can a
c
hieve even m
o
re tha
n
13%
of the
size of
JPEG file. F5
st
egan
ography
embe
d the
informatio
n i
n
to wh
ole im
age, an
d em
bed
informatio
n n
o
t throug
h L
SB repla
c
em
ent algo
ri
thm
but matrix codi
ng, it ca
n embe
d large
numbe
r of informatio
n wh
en ch
ang
e little bit. Co
mp
ared
with oth
e
r ste
gano
graphi
c system
, it
indee
d ha
s b
e
tter rob
u
stn
e
ss [11].
Figure 4. Hid
den informati
on by F5
4. Algorithm Implementa
tion
4.1 Load Information
Let bina
ry image figu
re 2
(
a) (256
×25
6
) that
come
s
from the sy
stem as th
e e
x
ample,
embed
which
the bi
nary i
m
age
Figu
re
5(b
)
(50
×
50
),
tran
sform Fi
gure
2
(
a) int
o
ed
ge im
ag
e
Figure 2
(
c) th
roug
h m
a
the
m
atical
morp
hology
and
i
m
age
pa
rtition an
d id
entifying, then
em
bed
the se
cret in
formation Fig
u
re 5
(
b) into
t
he edge image, com
p
lie
s the whol
e pro
c
e
ss in th
is
algorith
m
, the result a
s
Fig
u
re 5
(
c) sh
ows:
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TELKOM
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Vol. 11, No
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9
2827
(a) O
r
igin
al c
o
v
e
r imag
e
(b) Se
cret image
(c) Stego ima
g
e
Figure 5. Embeddi
ng process
4.2. Restore
the Ste
go Image
At first, treat
ment the
bin
a
ry ima
ge Fi
gure
2
(a
) in
dilation, l
e
t the bi
nary i
m
age th
at
being dilate
d Figure 2 (b)
munu
s the st
ego edgy
im
age, then get
the transmit stego ima
ge.
As
Figure 6 sh
o
w
s:
(a) the ima
g
e
that be dilate
(b)
stego e
d
g
e
image
(c) steg
o origi
nal bina
ry image
Figure 6. Pro
c
e
ss of the bi
nary imag
e re
store
5. Analy
s
is the experiment
results
5.1. Analy
s
is
the Hiding
Capa
cit
y
On the b
a
si
s
of the sel
e
cti
on of the
cov
e
r ,
half of an
image
will be
use
d
to emb
e
d
se
cret
informatio
n ,but when e
m
bed se
cret in
formation
through F5 al
g
o
rithm in bin
a
ry image, in
a
n
image size
mn
,
the upp
er lim
it of the bits
that can
hi
de
whe
n
at mo
st modify on
e pixel is
2
lo
g
(
1
)
mn
.Then, in this
article, in the
context of en
sure the se
cu
rity incre
a
se by exponenti
a
l ,if
the size of the image is
M
N
, stegan
ographi
c capa
city will be
2
lo
g
(
0
.
5
1
)
MN
.
5.2. Analy
s
is
the Visual Effe
cts
The chan
ging
level of the cover imag
e t
hat embe
dde
d informatio
n
expre
s
sed b
y
PSNR
[12], table1 shows the
cha
nge of PSNR that same
secret inform
a
t
ion embe
dd
ed into different
cover i
m
age,
all the si
ze
of the cove
rs are
sa
me .A
s we can se
en from th
e table, the
sa
me
se
cret info
rm
ation bein
g
e
m
bedd
ed int
o
different co
ver image th
at have sam
e
size, the PSNR
wa
s in th
e sa
me mag
n
itud
e, doe
s n
o
t a
ppea
r the
si
tu
ation that too
high o
r
too
lo
w. And, if PSNR
more than 32, it will not caused
by the human eye’
s attention.
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TELKOM
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ISSN:
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046
Edge Stegan
ogra
p
h
y
for Binary Im
age (Hon
gxi
a
Wa
n
g
)
2828
Table 1. Emb
edde
d se
crets in different
covers
Co
v
e
r i
m
age
PSNR
Co
v
e
r i
m
age
PSNR
Camerama
n.bm
p
Lena.bmp
Elian.tiff
74.532
81.348
71.238
Papio.bmp
Vegetable.jpg
Donna.bmp
70.983
80.113
72.284
5.3. Analy
s
is
the Rob
u
stn
ess
Steganog
ra
p
h
y requi
re th
e cover im
ag
e not only visual effe
ct is good, steg
a
nographic
cap
a
city a
r
e l
a
rge,
but
also
have
goo
d robu
stne
ss,
so it can
re
si
st
the atta
ck th
at intention
a
ll
y or
unintentio
nall
y
. This article
use several
method
s to
tes
t
the robus
t
ness
of the algorithm [13].
(a) Stego im
a
g
e
(b) Stego im
a
ge that be
irre
gula
r
cute
d
(c) Secret tha
t
extracted fro
m
stego ima
ge
be irregul
ar
cut
e
d
Figure 7. Irre
gular
cut to the stego ima
g
e
(a)origi
nal ste
go image
(b) the
stego i
m
age that ad
ded
noise for 20%
(c) the se
cret informatio
n
Figure 8. Add noise for 2
0
%
to the image
From the
result figures
we ca
n
see that, the algo
rithm has the anti-attack capability to
irre
gula
r
cut a
nd noi
se.
5.4. Anti-Ex
h
austiv
e
To the ima
g
e
that si
ze
m×n, the
nu
mber
of
the
method
s that
ch
o
o
se the
stru
ctural
element
s
wh
en dilatin
g
i
s
01
2
1
()
mn
r
rr
r
r
r
CC
C
C
,and the
nu
mber of the
method
s that
Image
Partition a
nd i
dentifying i
s
(2
)
(
2
)
mn
.So, if the
attacker does not
know the key will
not
get t
h
e
se
cret info
rm
ation by exha
ustive.
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ISSN: 23
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TELKOM
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Vol. 11, No
. 5, May 2013 : 2822 – 282
9
2829
6. Conclusio
n
This pa
per u
s
ed
math
em
atical
morph
o
logy
to
pre
p
ro
ce
ss bi
na
ry imag
e, a
n
d get
the
best suitabl
e cover,
th
en mark
ea
ch bl
ock
whic
h ca
n be e
m
be
dd
ed. The
emb
eddin
g
proce
ss i
s
F5 en
cod
e
method. Thi
s
method ma
ke the extr
act
key more complication, the ca
rri
er im
age
structure more
closely,
and al
so
enhance resi
sting attack
. Fut
u
re
will further improve t
he
algorith
m
.
Ackn
o
w
l
e
dg
ments
This
wo
rk
was
sup
porte
d
by Fore
ca
st
ing Platform
in Shanxi
Province Chi
na (No:
2012
0311
010
-1, 2012
113
3
,
213033
1-1
)
.
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