TELKOM
NIKA
, Vol. 13, No. 4, Dece
mb
er 201
5, pp. 1319
~1
329
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i4.1899
1319
Re
cei
v
ed Au
gust 26, 20
15
; Revi
sed O
c
t
ober 2
5
, 201
5; Acce
pted
No
vem
ber 1
3
,
2015
A Neighbor-finding Algorithm Involving the Application
of SNAM in Binary-Image Representation
Jie He
1
, Hui Guo
1
, Defa Hu*
2
1
School of Infor
m
ation a
nd El
e
c
tronic Eng
i
ne
erin
g,
W
u
zhou
Univers
i
t
y
, W
u
zhou 5
4
3
002,
Guang
xi, Chin
a
2
School of Co
mputer an
d Informatio
n
Engi
n
eeri
ng,
Hun
an
Univers
i
t
y
of Commerce, Ch
a
ngsh
a
41
020
5,
Hun
an, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: hdf666
@1
63.
com
A
b
st
r
a
ct
In view
of the low
executio
n
efficiency a
n
d
poor
practic
a
bility of the ex
isting n
e
ig
hb
or
-findi
ng
meth
od,
a fast
ne
igh
bor-fi
ndi
ng
alg
o
rith
m is
put forw
ard
o
n
the
b
a
sis
of
Squar
e N
on-sy
mmetry
an
d A
n
ti-
packi
ng M
o
d
e
l
(SNAM) for b
i
n
a
ry-i
mag
e
. F
i
rs
t of al
l, the
i
m
p
r
oved
min
o
r-di
ago
nal
sca
nni
n
g
w
a
y is
ap
pli
e
d
to strength
en
SNAM
’
s
a
dapt
abil
i
ty to vari
o
u
s textur
es, th
us red
u
cin
g
th
e total n
u
m
b
e
r
of nod
es aft
e
r
codi
ng; then th
e storag
e struc
t
ures
for its su
b-patterns
are
standar
di
z
e
d
a
nd a gr
id arr
a
y
is used to r
e
co
ver
the sp
atial-
pos
ition r
e
lati
ons
h
i
ps a
m
on
g su
b-patterns,
s
o
as to furth
e
r
reduc
e th
e c
o
mpl
e
xity of t
he
nei
ghb
or-fin
din
g
al
gorith
m
. Experi
m
ental result
sh
ow
s that this
method
’
s
ex
ecu
t
ion effici
ency
i
s
signific
antly h
i
g
her than th
at of the classic Li
n
ear Quad T
r
ee
(LQT
)-based n
e
ig
hbor-fi
ndi
ng
meth
od.
Ke
y
w
ords
: Ne
igh
bor-F
in
din
g
;
SNAM for Binary-Ima
ge;
Min
o
r-Dia
go
nal Sc
ann
ing Mo
de;
Grid Array
Copy
right
©
2015 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
As the basi
s
of a variety of image operatio
ns
su
ch a
s
the calcul
ation of images’
geomet
ric p
r
opertie
s
, the
labeling
of con
n
e
c
ted d
o
main
s, ima
ges’ e
dge
d
e
tection, et
c. [1],
neigh
bor-findi
ng algo
rithm
can di
re
ctly affect t
he execution effici
e
n
cy
of these
operation
s
. The
expre
ssive
method
s a
d
opted i
n
dig
i
tal image
a
nd thei
r a
d
j
a
ce
nt definiti
ons de
cide
the
perfo
rman
ce
and spa
c
e-ti
me com
p
lexity of neighbor
sea
r
ching al
g
o
rithm. The o
r
iginal n
e
ighb
or-
finding al
go
rithm is execut
ed in th
e two
-
dime
nsi
onal
array of imag
e, however,
due to th
e la
rge
stora
ge
spa
c
e the two
-
di
mensi
onal
array occu
pi
e
s
and the
wide
sea
r
ch sco
p
e involved in
the
pixel-pixel tra
v
ersal, the n
e
ighb
or-findin
g
algor
ith
m
b
a
se
d on pixel
array ha
s a
n
unsatisfa
ctory
efficien
cy. The widely use
d
Method
s su
ch as
q
uadtree [2], linear quadtree [3] can redu
ce b
a
si
c
image
rep
r
e
s
entatio
n uni
ts, save th
e
storage
sp
ace
and
en
able the
ra
p
i
d “bl
o
ck-blo
ck”
executio
n of
image o
p
e
r
ation. Lite
ra
ture [4
-6] separately pu
ts forward
neigh
bor-findi
ng
algorith
m
s
ba
sed
on the
q
uadtre
e an
d l
i
near
qua
dtre
e rep
r
e
s
e
n
tations,
whi
c
h h
a
ve sig
n
ifican
tly
improve
d
the
efficiency of
some ima
g
e
pro
c
e
s
sing
operations [
7
-9]. Ho
weve
r, becau
se the
neigh
bor
rela
tionshi
p is n
o
t a one-to
-o
ne rel
a
tion
sh
ip, this kin
d
of method cannot be
ea
sily
perfo
rmed i
n
the actual
image o
pera
t
ion. T
herefo
r
e,
as ne
w and
mo
re si
mplified
ima
g
e
expre
ssive m
e
thod
s emerge co
nt
inuou
sly, people a
r
e still see
k
in
g for highe
r-e
fficient neigh
bor
sea
r
ching m
e
thods.
The metho
d
of non-symm
etry and anti
-
packin
g
imag
e rep
r
e
s
entat
ion achieves optimal
asymmet
r
ic i
m
age
segm
e
n
tation so
as to obtain a
h
i
gher
efficien
cy of rep
r
e
s
e
n
tation than t
hat
of the quadt
ree metho
d
[10], and de
rives a
se
ries
of high-efficient
image p
r
o
c
e
ssi
ng alg
o
rith
ms
[11-14]. Lite
rature [15] p
r
opo
se
s a bi
n
a
ry im
ag
e
re
pre
s
entatio
n method whi
c
h
uses sq
ua
re,
isolate
d
poi
nt, line segme
n
t
as the
ba
sic rep
r
e
s
entati
on unit
s
in th
e NAM m
e
th
od. With
reg
u
l
ar
sha
pe an
d si
mple structu
r
e, these ba
si
c re
pre
s
e
n
tation units
can
serve a
s
ex
celle
nt basi
s
for
further devel
o
p
ing
other im
age
pro
c
e
s
si
ng al
gorith
m
s. Ho
wever,
th
ere
rem
a
in
so
me defi
c
ien
c
i
e
s
with this met
hod, restri
cti
ng its
su
ppo
rtive ab
ility for othe
r ima
g
e
processing
pro
c
e
dures:
Its
raste
r
scanni
ng mea
n
s i
s
pron
e to produ
cing
m
o
re
su
b-schem
es when performing reverse
arrang
ement
in image
s
with rich ma
ssive text
ures; th
e se
parate st
andal
one storage stru
cture
of
the three sub
-
sche
me
s also increa
se
s the algo
ri
thm’
s sp
ace-time
compl
e
xity. Besid
e
s, altho
ugh
the coordinat
es
of the
sub
-
schem
e
s
hav
e bee
n
re
corded, the
r
e i
s
a la
ck
of de
scription
abo
ut the
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No
. 4, Decem
b
e
r
2015 : 131
9 – 1329
1320
relation
of sp
atial po
sition
among th
em,
whi
c
h typica
lly entails trav
ersal ove
r
all
stora
ge q
ueu
es
in the derivati
v
e algorithm.
Since the efficien
cy of neighbo
r se
arch
ing
algo
rithm
depend
s directly on the relative
positio
nal
rel
a
tion b
e
twe
e
n
an
d q
uantit
y of ba
sic re
pre
s
entative
units,
solutio
n
s to
the
ab
ove
probl
em
s are
the key to
high-efficient
neigh
bor
se
arching
on S
N
AM. The
a
u
thor
begin
s
by
utilizing the
structu
r
al cha
r
acteri
stic
of squar
e to incl
ude sub-scan
ning alo
ng th
e back-diag
o
nal
dire
ction in raster
scanni
n
g
and en
han
ce the ad
apt
ability of reverse arran
g
e
m
ent to massive
textures; an
d then uses a
same data
structure to
re
cord three different
sub
-
sch
e
mes
so that
the
stora
ge and
operating mo
de can
be
u
n
iforme
d
a
c
ross different
sub
-
sch
e
me
s; next the a
u
t
hor
con
s
tru
c
t
s
gri
d
matrix, an
interme
d
iate
stru
ctur
e, to
resto
r
e th
e p
o
sition
al rel
a
tion am
ong th
e
sub
-
sch
e
me
s and redu
ce t
he sea
r
chin
g
range for ne
ighbo
r. Thro
u
gh the above
measu
r
e
s
, the
neigh
bor
sea
r
chin
g is imple
m
ented on th
e result of SNAM codin
g
, and com
p
a
r
ed
experim
entall
y
with the LQT
-
based nei
ghb
or se
archi
ng
method to
de
monst
r
ate the
efficacy of this wo
rk.
2. SNAM fo
r Binar
y
-Image and Its Op
timization
2.1. Square NAM
-Bas
ed Repr
esen
ta
tion Metho
d
o
f
Binary
Ima
g
e
The imag
e e
x
pressive me
thod of tran
sform dom
ain
usually ha
s highe
r com
p
re
ssi
on
ratio than me
thods of sp
atial domain [1
6], but t
he latter can reserve the image’s origi
nal local
textural
cha
r
acteri
stics an
d po
sition
al relation
m
o
re
effectively. SNAM for bi
nary-im
age
i
s
a
nond
estructiv
e
re
presentat
ion meth
od,
whi
c
h
i
s
based o
n
the
sp
ace
dom
ain
and
uses three
types of su
b-patte
rn
s - squ
a
re, lin
e se
gment
and i
s
olated
point - a
s
the ba
sic i
m
age
rep
r
e
s
entatio
n unit. Its proce
s
s is
as
follows:
sq
ua
re, line
se
g
m
ent an
d isolated p
o
ints at
different scales
a
r
e extracted
in
a ra
ster sc
an mo
d
e
from a
pa
cked
bina
ry image th
rou
g
h
the
anti-pa
cking
algorith
m
, an
d corre
s
p
ond
ing paramet
e
r
s of the
s
e sub-p
a
ttern
s a
r
e re
co
rde
d
and
store
d
, thus f
o
rmin
g the re
pre
s
entat
io
n of the given binary imag
e.
Figure 1
sho
w
s the
re
sult
of a
n
ti-pa
cking, codin
g
and
sto
r
ing
a bin
a
ry i
m
a
ge
with
SNAM. Figu
re 1(a) i
s
the
given ori
g
inal
bina
ry imag
e
T
with
a
size of 2
n
×2
n
(
n
=3). Fi
gu
re 1
(
b
)
sho
w
s the re
sult of SNAM
anti-pa
cki
ng
in t
he rast
er scan mo
de. Six square su
b-pattern
s (s
1
, s
2
,
s
3
, s
4
, s
5
and
s
6
), two line segm
ents
(
l
1
and
l
2
) an
d two isolated p
o
ints (
p
1
an
d
p
2
) are extra
c
ted
from the
ori
g
i
nal ima
ge. Fi
gure
1
(
c) i
s
t
he rep
r
esent
ation of
T
by
usi
ng the
a
bove-m
ention
e
d
sub
-
pat
t
e
rn
s.
(a) An 8
×
8 bi
nary imag
e
T
(b)
Th
e SNA
M
anti-pa
ckin
g
T
={
s
1,
s
2,
s
3,
s
4,
s
5,
s
6,
l
1
,
l
2,
p
1,
p
2
}
(c
)
T
he result
of of
T
Figure 1. The
process of a
n
ti-pa
cki
ng a
binary ima
ge
with SNAM
Acco
rdi
ng to
SNAM, the it
ems nee
d to
be recorded
are: fo
r
squ
a
re, the
coo
r
di
nates
sp
of the upp
er
left vertex (i.e., the
startin
g
point)
and
the sid
e
leng
th
side
; for line segment, the
c
o
or
d
i
na
te
s
p
1
of the starti
ng poi
nt and
the co
ordi
nat
es
p
2
of the
end p
o
int; for isolate
d
poin
t,
only the coordinate
s
of th
e vertex. The
stora
ge
st
r
u
c
t
u
r
es
for
a
ll
s
u
b-
p
a
tter
n
s
a
r
e
as
s
h
ow
n in
Figure 2.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Neighb
or-finding Algo
rith
m
Involving the
Applicatio
n of SNAM in Binary-im
ag
e …
(Defa Hu
)
1321
sp
side
p
1
p
2
i_ p
(a) squ
a
re
(b)
lin
e
(c) isol
ated p
o
int
Figure 2. The
process of a
n
ti-pa
cki
ng a
binary ima
ge
with SNAM
SNAM can al
so b
r
in
g som
e
problem
s f
o
r ima
ge p
r
o
c
e
ssi
ng. Lite
rature [1
7] not
es that
the ra
ster
scan mod
e
ha
s a good p
e
rf
orma
nce towa
rd ima
g
e
s
with unobviou
s
blocky features,
but sho
w
s lo
w efficien
cy towa
rd ima
g
e
s
with obvio
u
s
blo
cky featu
r
es. In ad
ditio
n
, the diversit
y o
f
SNAM’s sto
r
a
ge stru
ctures for
th
ree type
s of
sub
-
p
a
tterns an
d its ori
g
inal a
n
ti-p
acking
algo
rith
m
lead to the
e
m
erg
e
n
c
e of
both ho
rizont
al and ve
rt
ica
l
line segme
n
t
s in the
codi
ng re
sult, furt
her
increa
sing th
e compl
e
xity
of sub
s
eq
uen
t image pro
c
e
ssi
ng.
2.2. Optimization of the
Scanning M
ode
Ra
ster sca
n
is ch
ara
c
te
rized by the line-by
-li
ne ho
ri
zontal
scan, and a combi
nation of
raste
r
scan a
nd blo
ck
sca
n
will produ
ce a strong
er
adapta
b
ility to image
s wit
h
blocky texture.
The ho
rizont
al dire
ction i
s
still the mai
n
scanni
ng di
rectio
n, but
whe
n
unm
arked bla
ck
poin
t
is
detecte
d, the
stru
ctu
r
al
ch
ara
c
teri
stics
of sq
uare a
r
e
used
and
de
terminin
g the
pixel value
s
of
pixels on th
e mino
r-di
a
g
onal i
s
re
garded a
s
the
core alg
o
rith
m - thu
s
th
e mino
r-di
a
g
onal
scanni
ng mo
de is fo
rme
d
. Its prin
cipl
e i
s
sho
w
n in
Fi
gure
3. The
r
e
i
n, Figure 3
(
a
)
is th
e dia
g
ram
of the minor-diago
nal sca
nning di
re
ctio
n, whe
r
e t
he
dotted line in
dicate
s that a
fter these p
o
i
n
ts
form a
squa
re, they need
n’t go thro
ug
h hori
z
o
n
ta
l scan
any more. Figure 3(b) sho
w
s the seria
l
numbe
rs of al
l pixels in the
minor-dia
gon
al sc
anni
ng p
r
ocess. Thi
s
mode n
o
t onl
y has a st
ron
ger
adapta
b
ility,
but only lowers th
e com
p
lexity of
SNAM by onl
y produ
cing
hori
z
ontal li
ne
segm
ents.
(a)
Dire
ction f
o
r mino
r-diag
onal sca
n
(b) Pixel se
qu
ence in mino
r-diag
onal
sca
n
Figure 3. Prin
ciple of mino
r-diag
onal
sca
n
The spe
c
ific
pro
c
ed
ure of the SNAM a
l
gorithm b
a
sed on min
o
r-diago
nal sca
n
(Mino
r
Diag
onal
-SNAM, or MD-S
NAM) is
as fo
llows:
Input:
a bi
nary image
T
with a s
i
ze of
n
×
n.
Outpu
t
:
V_s
—the set of
squa
re sub
-
patterns,
V_l
—the set of
line segm
e
n
t sub-
patterns
,
V_p
—the set of isolated poi
nt sub-p
a
ttern
s.
Step 1
Sea
r
ch fo
r the
un
marked
point
with
ze
ro pix
e
l value
by st
arting f
r
om th
e pixel
f
i
rst
see
n
wh
en
a
c
ce
ssi
ng
T
in
this ci
rcle, and
u
s
e t
he fou
nd
pixel a
s
the
up
p
e
r ve
rtex of t
he
squ
a
re
sub-p
a
ttern, then
reco
rd it
s coo
r
dinate
s
(
sp
_x
,
sp_
y
), a
nd i
n
itialize th
e
side len
g
th of t
he
s
q
ua
r
e
s
u
b-
pa
tte
r
n
w
i
th
side
.
Step 2
Se
arch for u
n
ma
rked pixel
s
on
the ba
ck
dia
gonal
of the
squ
a
re
with
side
-
l
on
g
side
s, and ju
dge whethe
r their pixel valu
es are 0:
if they are not 0, swit
ch to Step 1.
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930
TELKOM
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Vol. 13, No
. 4, Decem
b
e
r
2015 : 131
9 – 1329
1322
Step 3
Make
side
=
s
ide
+
1,
and
contin
u
e
to pe
rform
Step 2 until
no mo
re
squ
a
re
su
b-
pattern forms; store the fo
und squa
re in
V_s
, and ma
rk all the pixe
ls cove
red
by the squa
re
with
side
-lon
g sid
e
s.
Step 4
Rotate Steps 1
~
3
until no ne
w square
su
b-pa
tterns
can be
extracted o
u
t.
Step 5
S
earch for the
un
marked
point
with
zero pi
xel value by
starting
from
the pixel
first se
en wh
en acce
ssing
T
in this circle
, and re
cord its co
ordi
nate
s
(
l
_
x
1
,
l_y
1
).
Step 6
Ju
dg
e wh
ethe
r th
e value of th
e neig
hbo
rin
g
pixel at the
hori
z
o
n
tal ri
ght sid
e
of
the point
(
l
_
x
1
, l_y
2
) i
s
ze
ro: if it is, cont
inue the
sea
r
ch to
wa
rd th
e
hori
z
o
n
tal ri
g
h
t sid
e
until t
h
e
line segm
ent
stop
s enl
argi
ng, t
hen re
co
rd
the
line se
gment’s
rig
h
t endp
oint’s co
ordin
a
tes
(
l
_
x
2
,
l_y
2
), a
nd
sto
r
e the
line i
n
V_l
, and the
n
mark all
the
pixels that it
covers; if it is not zero, go
to
Step 5.
Step 7
Rota
te Step 5 a
nd Step 6 u
n
til no ne
w l
i
ne segme
n
t sub
-
patte
rn
s can
be
extracted o
u
t.
Step 8
S
earch for the
un
marked
point
with
zero pi
xel value by
starting
from
the pixel
first seen
wh
en a
c
cessin
g
T
in this ci
rcl
e
, and
re
cord
its coordinat
es
(
p
_
x
,
p_
y
); then sto
r
e it
in
V_p
and ma
rk this poi
nt.
Step 9
Rotate Step 9 until no ne
w isol
ated-p
o
int su
b-pattern
can b
e
extracted o
u
t.
Step 10
Output
V_s
,
V_l
and
V_p
.
2.3. Optimization of the
Storag
e Stru
cture
SNAM ha
s d
e
sig
ned
storage st
ru
cture
s
se
pa
ra
tely for three
different type
s of basi
c
rep
r
e
s
entatio
n unit
s
, which, whil
e
can
ensure
comp
act storage, mean
s
the
sa
me
SNAM
-ba
s
e
d
image ope
rati
on
alg
o
rithm need
s
to se
p
a
rately
p
r
o
c
e
ss differe
nt
sub-p
a
ttern
s. Therefore, using
the same
ki
n
d
of
simpl
e
d
a
ta st
ru
cture
to re
co
rd
different
sub-pat
terns i
s
the
key to lo
we
rin
g
the
compl
e
xity of
the sub
s
e
que
nt
image processing al
gorit
hm.
For the three
types of sub
-
patterns -
sq
uar
e, line
seg
m
ent and isol
ated point - i
n
volved
in SNAM, a uniform sto
r
ag
e stru
cture ca
n be define
d
as follo
ws:
x y
Length
Figure 4. The
uniform sto
r
a
ge stru
ctu
r
e for SNAM sub
-
patterns
Therein,
x
re
pre
s
ent
s the absci
ssa of the st
artin
g
p
o
int of the su
b-patte
rn,
y
re
p
r
es
en
ts
its ordi
nate,
and
L
ength
repre
s
e
n
ts th
e su
b-p
a
ttern
’s si
de len
g
th
. In the codi
n
g
, the
Len
gth
of
squ
a
re
and i
s
olate
d
point
is stored a
s
int data, whi
l
e the
Length
of line segm
ent is sto
r
ed
as
st
ring
data.
T
hus the
su
b-p
a
tterns
can
b
e
di
stingui
she
d
by the
Le
ng
th
value
and
data type: if t
he
sub
-
patte
rn is sq
uare, its
Length
must be greater
than 1 and b
e
long to int data; if the sub-
pattern i
s
isol
ated poi
nt, which
ca
n be
regarded
as
a
squ
a
re
with
a sid
e
Le
ngt
h of 1, then i
t
s
Length
mu
st be equ
al to 1 and belon
g to int data; and if the sub-p
a
ttern is line
segm
ent, its sid
e
length (i.e., its length
)
L
eng
th
is al
so g
r
eater tha
n
1
but belon
gs t
o
st
ing
data. In this
way,
a
uniform su
b-pattern set can
be esta
bl
ishe
d
to
r
eal
ize
rapid t
r
a
v
ersal, th
us
providin
g mo
re
effective sup
ports fo
r vario
u
s imag
e ope
ration
s.
3. Neighbor
-Finding Bas
e
d on MD-SNAM
3.1. Definition of Neighbor
The
wo
rd
“ne
i
ghbo
r” i
s
use
d
for
depi
ctin
g the
adja
c
en
t relation
amo
ng ima
ge
are
a
s th
at
image
rep
r
e
s
entation u
n
its co
rre
sp
ond
to, and it
s def
i
n
ition vari
es
depe
nding
on
spe
c
ific ima
g
e
rep
r
e
s
entatio
n method
s. Literature [18] has p
r
e
s
ente
d
the definition of neighbo
r in the quadtree
method, an
d
con
s
id
erin
g
that both SNAM
and
the quadtree rep
r
esent
ation method
exp
r
ess
image source
as the record set of local image bl
o
c
ks, a similar def
inition can b
e
made herein
:
if
there
exist
s
a
t
least
on
e pi
xel in
both
su
b-patte
rn
s th
at ma
ke
s the
two
adj
oin
e
a
ch
othe
r
wit
h
in
the 4-neig
h
b
o
r d
o
main, th
ese
two
su
b-pattern
s a
r
e
neigh
bors. T
he ba
si
c
rep
r
ese
n
tation u
n
i
ts in
SNAM a
r
e
sq
uare, li
ne
se
gment a
nd i
s
olated p
o
int.
Each i
s
ol
ated
point i
s
e
s
se
ntially a squa
re
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
A Neighb
or-finding Algo
rith
m
Involving the
Applicatio
n of SNAM in Binary-im
ag
e …
(Defa Hu
)
1323
with the si
de
length of 1, thus S
N
AM a
c
tually
involves only two types of
sub-pattern
s, na
mely,
squ
a
re a
nd li
ne se
gment. The sp
ecifi
c
definition is a
s
follows:
Defini
tion 1
In the SNAM-ba
s
ed
bi
nary ima
ge
rep
r
e
s
entatio
n, if
s
j
={
x
j
,
y
j
,
Length
j
}
neigh
bors
s
i
={x
i
,y
i
,Length
i
}
in the direc
t
ion D=(EAST
,SOUTH,WEST,NORTH):
(1)
When
s
i
is sq
ua
re an
d
s
j
is sq
ua
re, their neig
hbo
r relatio
n
ship
is sh
own in F
i
gure 5
and follo
ws th
e followin
g
formula:
i
i
j
j
i
i
i
j
Length
y
y
Length
y
Length
x
x
1
(1)
i
i
j
j
i
j
i
j
Length
y
y
Length
y
Length
x
x
1
(2)
(a)
Th
e scop
e
of
s
i
’s
east nei
ghb
ors
(b)
Th
e scop
e
of
s
i
’s
we
st neigh
bo
rs
(c) The
scope
of
s
i
’s
south n
e
igh
b
o
rs
(d)
Th
e scop
e
of
s
i
’s
north nei
ghb
o
r
s
Figure 5. The
process of a
n
ti-pa
cki
ng a
binary ima
ge
with SNAM
j
i
j
i
i
j
j
i
Length
y
y
Length
x
x
Length
x
1
(3)
j
i
j
i
i
j
j
i
Length
y
y
Length
x
x
Length
x
1
(4)
(
2
) When
s
i
is squ
a
re
o
r
point
a
nd
s
j
is lin
e
seg
m
ent, their nei
ghbo
r
relatio
n
shi
p
i
s
sho
w
n in Fig
u
re 6 an
d follows the follo
wing formula:
(a)
Th
e scop
e
of
s
i
’s
east nei
ghb
ors
(b)
Th
e scop
e
of
s
i
’s
we
st neigh
bo
rs
(c) The
scope
of
s
i
’s
south n
e
igh
b
o
rs
(d)
Th
e scop
e
of
s
i
’s
north nei
ghb
o
r
s
Figure 6. The
neighb
or rela
tionshi
p between squa
re
s
i
and line seg
m
ent
s
j
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ISSN: 16
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930
TELKOM
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Vol. 13, No
. 4, Decem
b
e
r
2015 : 131
9 – 1329
1324
i
i
j
i
i
i
j
Length
y
y
y
Length
x
x
(
5
)
j
i
j
i
j
i
j
Length
y
y
y
Length
x
x
(
6
)
j
i
j
i
i
j
j
i
Length
y
y
Length
x
x
Length
x
1
(
7
)
1
1
i
j
i
i
j
j
i
y
y
Length
x
x
Length
x
(
8
)
(
3
) When
s
i
i
s
lin
e
segm
e
n
t and
s
j
is square o
r
poin
t, their n
e
igh
bor rel
a
tion
sh
ip follo
ws
the followin
g
formul
a:
i
j
j
i
i
i
j
y
y
Length
y
Length
x
x
1
(9)
i
j
j
i
j
i
j
y
y
Length
y
Length
x
x
1
(10
)
j
i
j
i
i
j
j
i
Length
y
y
Length
x
x
Length
x
1
(11
)
1
1
i
j
i
i
j
j
i
y
y
Length
x
x
Length
x
(12
)
(4)
Wh
en
s
i
is li
ne
se
g
m
ent an
d
s
j
is li
ne
se
g
m
ent, be
cau
s
e th
e min
o
r-di
ago
nal
scanni
ng m
o
de o
n
ly gen
erates
hori
z
o
n
tal line
s
whi
c
h
only h
a
ve
so
uth an
d n
o
rth
neig
hbo
rs, th
eir
neigh
bor
relat
i
onship follows the followi
n
g
formula:
1
1
i
j
i
i
j
j
i
y
y
Length
x
x
Length
x
(13
)
1
1
i
j
i
i
j
j
i
y
y
Length
x
x
Length
x
(14
)
3.2. Grid Arr
a
y
SNAM doe
s
not involve the re
co
rdin
g
of the
spati
a
l-po
sition rel
a
tionship
wit
h
cod
e
s,
thus
neigh
bo
r-findi
ng b
e
comes an i
n
e
fficient pr
oce
s
s of repe
ated defin
itio
n-based sea
r
ches
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TELKOM
NIKA
ISSN:
1693-6
930
A Neighb
or-finding Algo
rith
m
Involving the
Applicatio
n of SNAM in Binary-im
ag
e …
(Defa Hu
)
1325
throug
hout the co
de array. Therefore, the nei
gh
bor-findin
g
process
can
be simplifie
d
by
con
s
tru
c
ting
an inte
rmedi
ate structu
r
e
and
re
st
orin
g the po
sitio
n
relatio
n
shi
p
s a
m
ong
sub-
patterns
.
A
n
×
n
matrix, namely grid matrix
, c
a
n be
c
o
ns
truc
ted for
a
n
×
n
bina
ry i
m
age. Ea
ch
unit
is first a
s
sign
ed with a val
ue of 1; then
the
SNAM coding
re
sult
of the image
is re
ad, an
d the
positio
n
that each sub
-
patt
e
rn co
rr
espo
nds to in th
e
grid
matrix, th
e structu
r
e
of
whi
c
h i
s
sh
o
w
n
in
Figure
7, is re-filled wi
th
a value,
whi
c
h i
s
equal to
“t
he st
orage serial
number for t
he
corre
s
p
ondin
g
sub
-
p
a
ttern
+ 2” be
ca
use the se
rial n
u
mbe
r
of the SNAM co
de
array begin
s
fro
m
0 and also 1 has b
een u
s
e
d
for pre
-
fillin
g; and then the SNAM co
de and the filled value for e
a
ch
sub
-
patte
rn
make
up
a
grid array,
with
the fille
d
val
ue a
c
ting
a
s
the corre
s
po
nding
index.
Thus
the only
step
for findin
g
th
e nei
ghbo
r
of som
e
bl
ock i
s
to
scan
the
pixel value
s
surro
undi
ng t
h
is
block
- if a
different valu
e that is not
1 an
d
dete
c
ted, the sub-pattern th
at this in
dex val
u
e
c
o
rres
ponds
to in the grid
matrix is
t
he neigh
bor that
is bein
g
se
archin
g for.
(a) SNA
M
-b
a
s
ed
segm
ent
ation of an 8×8 image
(b) T
he corre
s
po
ndin
g
grid
matrix
Figure 7. The
neighb
or rela
tionshi
p between line
seg
m
ent
s
i
an
d line se
gment
s
j
Without th
e
appli
c
ation
of the g
r
id m
a
trix
method,
neigh
bor-findi
ng
would
be
a very
time-con
sumi
ng pro
c
e
s
s of traversin
g
the entire SNA
M
code list to
make one
-b
y-one jud
g
me
nt
as to
wheth
e
r th
e
curre
n
tly acce
sse
d
SNAM
su
b-patte
rn
me
ets the
cond
ition for neig
hbor
relations
h
ip. With grid matrix, the operation sc
op
e of
neigh
bor-findi
ng in
ce
rtain dire
ction ca
n be
limited to the pixels on th
e boun
dary
block of
su
b-pattern
s, thu
s
the ope
rati
on load
can
be
signifi
cantly cut.
3.3. Grid Arr
a
y
After
the storage queu
e
V
of the S
N
A
M
algo
rithm f
o
r bi
na
ry ima
ge a
s
well
a
s
the
V-
gene
rated
gri
d
matrix
M
an
d
gr
id
ar
ra
y
T
is give
n, th
e se
arch fo
r t
he nei
ghb
or
R
of a
given
sub
-
pattern
r
= (
x, y, Length
) wil
l
becom
e very easy. Take
the sea
r
ch for east nei
ghb
or for exampl
e:
first of all, judge the sub-pattern type of
r
accordin
g to its
Lengt
h
; then determine wh
ethe
r
r
is
clo
s
e to
the
ri
ght bo
und
ary
of the
ima
ge
according
to t
he a
b
sci
s
sa
x+Le
ngth
of
r
’
s
end
point,
an
d
if it is,
r
’s e
a
st neighb
or
R
i
s
an
empty set, otherwise
the value
s
for the rig
h
t bou
ndary of
r
su
b-
pattern
in th
e
gri
d
a
r
ray are ind
e
xes of
all its
neig
h
b
o
rs - then,
co
mpare the
m
with the
valu
es
on
the rig
h
t bo
u
ndary
of the
grid
array o
n
e
by o
ne,
a
n
d
ad
d the
s
e
positio
n-stora
ge in
dexe
s
to
th
e
neigh
bor set
R
as l
ong a
s
there i
s
no 1
-
value index.
Becau
s
e
ea
ch index in the
SNAM cod
e
lis
t
corre
s
p
ond
s t
o
one
an
d on
ly sub
-
pattern
, the indexe
s
can
lead
to t
he nei
ghb
orin
g mod
e
ls. T
h
e
algorith
m
pri
n
cipl
es for
n
e
ighb
or-findin
g
in vari
ou
s
dire
ction
s
are
basi
c
ally the
same, thu
s
the
east
w
ard
nei
ghbo
r-fin
ding
is u
s
ed
he
rei
n
ag
ain
as
a
n
exam
ple to
explain
the
specifi
c
al
gorit
hm
executio
n ste
p
s a
s
follows:
Input:
gr
id
ar
r
a
y
T
, the
gi
ven coordina
tes
(
x
,
y
) of t
he
starting
p
o
int of
sub
-
p
a
ttern
r
,
image re
sol
u
tion n, and code array
V={V_
s
,V_l,V_p}
, where
V_s
,
V_l
and
V_p
re
spe
c
tiv
e
ly
rep
r
e
s
ent the
code a
r
ray set for squ
a
re,
line segm
ent
and isol
ated
point.
Outpu
t
:
the
set
E_R
of sub
-
patterns of
r
’
s
ea
st neigh
b
o
rs
Step 1
Custo
m
ize a
set
E_R
and initiali
ze it to be empty.
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930
TELKOM
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Vol. 13, No
. 4, Decem
b
e
r
2015 : 131
9 – 1329
1326
Step 2
Inp
u
t
the given
co
ordin
a
tes
(
x
,
y
) of th
e sta
r
ting point of
sub
-
patte
rn
r
that is
use
d
for
nei
ghbo
r-fin
ding,
and match t
he startin
g
p
o
int’s coordin
a
tes with the
code a
r
ray to
prod
uce the b
a
si
c inform
ation and
seri
al numbe
r (in
d
e
x
) of sub-pattern
r
.
Step 3
Use t
he ba
si
c information of the
sub
-
patte
rn
t
o
judg
e the b
a
si
c type of it: if it is
squ
a
re
or i
s
ol
ated-p
o
int, ju
mp to Step 4;
if it is line se
gment, whi
c
h
mean
s it ha
s no ea
st o
r
west
neigh
bors, ju
mp to Step 5.
Step 4
Via t
he
coo
r
din
a
tes
(
x
,
y
)
of
r
’s
s
t
arting point, find
r
’
s
right
-mo
s
t e
ndpoi
nt
(x+len
gth,y)
in the grid matrix
M
. I
f
r
is close to the rig
h
t bounda
ry of the image, that is,
x+len
g
t
h
is eq
ual to n
,
then it doe
s not h
a
ve e
a
st o
r
we
st
neigh
bors, th
us g
o
to Ste
p
5; othe
rwi
s
e,
thorou
ghly scan M for pixe
l units lo
cate
d within the
area
(
x+le
ngt
h+
1, y+
l
engt
h
-1
) on the
ri
ght
side of the i
m
age’ ri
ght boun
dary, an
d judge wh
e
t
her its num
erical value
(index
) m is 1
(re
pre
s
e
n
ting
white
poi
nt):
if it is not
1,
use
m
to
find
the
co
rre
sp
o
nding
sub-pat
tern i
n
the
gri
d
array
T
, and reco
rd it in
E_R
.
Step 5
O
u
tput th
e
E_R
.
4. Experiments and
Anal
y
s
is
The expe
rim
ental enviro
n
m
ent is mad
e
up by
Intel Core i3
-31
1
0
M 2.4GHz p
r
ocesso
r,
2G me
mory,
Microsoft Win
dows 7
Profe
ssi
onal
+ SP
3 ope
ratin
g
system an
d M
A
TLAB7.0-ba
s
e
d
IDE. Figure 8
sho
w
s
eight
256
×25
6
bina
ry image
s wi
t
h
different co
mplexities to
be tested i
n
the
experim
ent. The definition
of image co
m
p
lexity is as follows:
Defini
tion 2
Compl
e
x
i
ty
C
of any
bin
a
ry image
can
be
define
d
i
n
the
followi
ng
way:
cal
c
ulate,
ba
sed o
n
the
giv
en im
age
re
p
r
esent
ation
m
e
thod, the
tot
a
l nu
mbe
r
of
i
t
s no
de
s
N
Q
as
well a
s
the total pixel numb
e
r
N
f
, and p
u
t them in the formul
a of:
C=
Q
N
/
f
N
(15
)
In this pa
pe
r, the LQT
rep
r
e
s
entatio
n method
is rega
rd
ed a
s
a b
e
n
c
hm
ark for
comp
ari
s
o
n
, and
i
m
age
complexity
is measured
by the n
u
mb
er
of LQ
T
segm
entation
blo
c
ks.
Table
1 i
s
th
e comp
ari
s
on
of the
codin
g
pe
rfor
man
c
es
of L
Q
T, S
N
AM a
nd
MD-SNAM. T
herein,
N re
pre
s
e
n
ts the numbe
r
of sub
-
patterns o
r
nod
es,
SNAM is th
e origi
nal sq
uare
NAM-ba
sed
rep
r
e
s
entatio
n meth
od, M
D
-S
NAM i
s
SNAM b
a
sed
on th
e mi
no
r-di
ago
nal
scan,
_
L
QT
T
is the
ratio
of the
total data
am
ou
nt of L
Q
T to
that of T
N
AM,
_
L
QT
R
i
s
the
ratio o
f
the total
dat
a am
ount
of LQT to th
a
t
of RNAM,
_
LQ
T
S
is the
ratio of
the total data
amou
nt of L
Q
T to that of
SNAM,
and
SNAM
MD
LQT
_
is the ratio of the total
data amou
nt of
LQT to that of MD-SNA
M. The spe
c
if
ic
data in th
e e
x
perime
n
tal result i
s
sho
w
n in Fi
gure 8
.
Table
1 sh
ows that, for
the above
ei
ght
image
s, SNA
M
an
d M
D
-S
NAM h
a
ve o
u
tperfo
rmed
LQT, tho
ugh
these
two
al
so have
si
gnifi
cant
differenc
es
in performanc
e
.
The o
r
igin
al SNAM nee
ds three field
s
- coo
r
din
a
tes
of the sta
r
ting
point an
d si
d
e
length
- for re
co
rdin
g squ
a
re, fou
r
fields - coo
r
dinat
e
s
of the starting p
o
i
n
t and of the endpoint - f
o
r
recording line
segme
n
t, and only 2 fields, namely the point coo
r
d
i
nates, for re
cording i
s
olat
ed
point. By co
mpari
s
o
n
, M
D
-S
NAM p
r
o
v
ides a
unifo
rm
stora
ge
st
ructu
r
e
for
all
these types:
for
recording
sq
uare, it i
s
the
sam
e
a
s
S
N
AM; bec
ause
it only gen
erates
hori
z
o
n
tal line
s
, it on
ly
need
s three fields
- co
ordin
a
tes of
the
starting p
o
int a
nd the len
g
th
- for re
co
rdin
g line segme
n
t;
and it also n
eed
s thre
e fields fo
r re
co
rding i
s
olated
point, whi
c
h i
s
re
ga
rded
a
s
squa
re
with
a
side len
g
th o
f
1. Obviously, MD-SNAM
involves
one
less field than the origin
al SNAM for line
segm
ent, but
one
mo
re fie
l
d for i
s
ol
ated
point. After
coding, th
e n
u
m
bers
of line
se
gment
s a
n
d
isolate
d
point
s vary form
o
ne imag
e to anothe
r,
leadi
ng to the differen
c
e i
n
the
data amo
unt
in
the co
ding
result. The
r
ef
ore, the diff
eren
ce i
n
st
orag
e st
ru
ctu
r
e a
c
tually d
oes
not hav
e a
deci
s
ive im
pa
ct on th
e codi
ng pe
rforman
c
e
s
of
M
D
-S
NAM an
d SNAM. Furthe
rmore,
com
p
a
r
ed
with the ori
g
inal SNAM, MD-S
NAM not only has
a
n
o
p
timized
storage st
ru
cture,
and also ado
pt
s
an imp
r
oved
scanni
ng mo
de -
namely,
the mino
r-di
agon
al sca
n
n
i
ng mod
e
, providing it wit
h
a
stron
g
e
r
ad
a
p
tation to im
age
s’ lo
cal bl
ocky texture
s
, so a
s
to i
n
crea
se
sq
uare
s
an
d d
e
crea
se
node
s. Acco
rding to th
e e
x
perime
n
tal result, rega
rdl
e
ss of ima
g
e
com
p
lexity, MD-S
NAM h
a
s
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
9
30
A Neighb
or-finding Algo
rith
m
Involving the
Applicatio
n of SNAM in Binary-im
ag
e …
(Defa Hu
)
1327
fewer no
de
s,
highe
r
comp
ression
ratio
a
nd b
e
tter
spa
t
ial efficien
cy
than the
ori
g
i
nal SNAM, th
us
it can furthe
r redu
ce the ti
me com
p
lexi
ty of the subseque
nt image
processin
g
.
(a)
Le
na
(b)
Flight (c)
Building
(d)
Boat
(d)
Map (
e
)
Pictu
r
e
s
(f) Baboo
n
(g) Bri
dge
Figure 8. Eight 256 x 256 binary ima
g
e
s
Table 1. Co
m
pari
s
on of the
performan
ce
s of LQT, SNAM, MD-SNA
M algorithm
s
Image
C
N
_
LQ
T
T
_
LQ
T
S
SNAM
MD
LQT
_
LQ
T SNAM
MD-SNAM
Map 0.0882
5780
2708
1090
3.9609
4.2647
10.1613
Pictures 0.0835
5470
742
459
12.9781
16.0064
22.8413
Baboon
0.2601
17047
8668
4204
3.1227
3.8013
7.7719
Bridge 0.1813
1
1881
6057
3411
2.8796
3.7987
6.6760
Lena
0.0981
6430
3077
2466
2.9902
4.0376
4.9976
Flight 0.0850
5568
2253
1946
3.5287
4.7537
5.4840
Building
0.0702
4602
1425
1728
4.0114
6.0236
5.1044
Boat 0.1313
8604
3515
2731
3.3743
4.6094
6.0384
For
squ
a
re
a
nd line
seg
m
ent, MD-S
NA
M gives different definition
s
of neig
hbo
r
, but the
prin
ciple
s
of
sea
r
ching fo
r their neig
h
b
o
rs i
n
t
he gri
d
matrix are i
dentical. In fact, the ope
rat
i
on
amount of fin
d
ing the n
e
ig
hbor
of a line
segm
ent, wh
ich is
1 pixel
in width, is le
ss th
an that
of
fin
d
i
n
g
a sq
ua
r
e
’s
ne
ig
hbo
r
.
Sinc
e
LQT
’
s
ba
s
i
c
r
e
pr
e
s
e
n
t
a
t
io
n un
it is
s
q
ua
r
e
ima
g
e
b
l
oc
k, a
squ
a
re
su
b-p
a
ttern is
cho
s
en as
a ben
chmark for M
D
-SNAM in the
experime
n
t. The expe
rime
nt
is aime
d at compa
r
ing the
performan
ce
s in an e
a
st
ward n
e
ighb
or-find pro
c
e
s
s, and the result is
sho
w
n in Ta
ble 2, whe
r
e,
T
LQT
and
T
MD
-
S
N
A
M
repre
s
ent the execution time of neighbo
r-fin
ding
based
re
spe
c
tively on LQT
and
on M
D
-SNAM, and
t
L-MS
repre
s
e
n
t
s the
spe
ed-up ratio of M
D
-
SNAM-b
ased
neighb
or-find
i
ng to LQT-ba
sed n
e
igh
bor-finding.
It can b
e
se
en fro
m
the
Table
2 that
highe
r
im
ag
e complexity ca
n result in long
e
r
exec
ution of
the eas
t
ward nei
ghbor-finding with t
h
e two algorithms
,
indic
a
ting that image
compl
e
xity is propo
rtion
a
l to the execut
ion ti
me of the co
rrespon
ding
alg
o
rith
m. The average
executio
n time of LQT
-
ba
sed
neig
hbo
r-finding i
s
4.
275
~13.7
16 t
i
mes th
at of neigh
bor-findi
ng
w
i
th
SN
AM ba
s
e
d
on
gr
id a
r
r
a
y,
w
h
ich fu
lly d
e
m
on
strate
s th
at the n
e
igh
bor-f
inding
alg
o
rit
h
m
based
on M
D
-S
NAM i
s
simple
r, fa
ster, a
nd m
o
re supp
ortive
for
other
subsequ
ent i
m
age
pro
c
e
ssi
ng.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No
. 4, Decem
b
e
r
2015 : 131
9 – 1329
1328
Table 2.
Com
pari
s
on of the
execution ti
me of an eas
t
w
ard neig
hbo
r-findi
ng pr
ocess re
spe
c
tively
with the LQT
-
based alg
o
rit
h
m and with
MD-S
NAM-b
a
se
d algo
rith
m
Image
C
Execution time (
m
s)
Speedup ratio
T
LQ
T
T
MD
-
S
N
A
M
t
L-
M
S
Map 0.0882
18.764
1.368
13.716
Pictures 0.0835
17.976
1.872
9.602
Baboon
0.2601
24.653
3.896
13.190
Bridge 0.1813
22.889
2.769
9.930
Lena
0.0981
19.774
1.608
5.611
Flight 0.0850
18.991
1.347
4.275
Building
0.0702
17.437
1.246
4.552
Boat 0.1313
20.988
2.157
6.581
5. Conclusio
n
This p
ape
r, firstly, improv
es the
scann
ing mo
d
e
of the origi
nal
SNAM so th
at it can
handl
e imag
e
s
with va
rio
u
s texture characteri
stics;
se
con
d
ly, optim
ize
s
the
stora
ge st
ru
cture f
o
r
sub
-
patte
rn
s so a
s
to elim
inate the sto
r
age differen
c
e in variou
s
sub
-
patte
rn
s; thirdly, reali
z
es
the de
scriptio
n of the po
sit
i
on rel
a
tion
sh
ips am
ong
su
b-patte
rn
s wit
h
the gri
d
a
r
ray; and finall
y
,
use
s
the grid
array to limit the range of
one-di
re
ction
a
l neighb
or-finding to the boun
dary of the
grid a
r
ray that the ben
ch
mark blo
c
ks corre
s
po
nd
to, thus crea
ting a ne
w neigh
bor-findi
ng
algorith
m
, wh
ich ha
s hig
h
e
r
executio
n ef
ficien
cy
than the cla
s
sic L
Q
T-ba
se
d met
hod an
d ca
n be
applie
d in i
m
age
ope
rat
i
ons
su
ch
a
s
cal
c
ulation
of geo
metric p
r
op
ertie
s
and
mome
nt
gene
ration.
Ackn
o
w
l
e
dg
ements
This
work wa
s sup
p
o
r
ted by
Gua
ngxi Natural
S
c
ien
c
e Fou
ndatio
n
Pro
g
ram (Grant
No.
2013
GXNSF
BA01927
5, Grant No. 201
3GXNSFBA0
1927
6)
, Gu
a
ngxi Unive
r
sit
y
of Science
and
Tech
nolo
g
y
Re
sea
r
ch Progra
m
(Gra
nt No. 2
013YB
227, G
r
ant
No. 20
13YB2
28)
and
Nati
onal
Natural Scie
n
c
e Fou
ndatio
n of China (G
rant No: 61
20
2464
).
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n
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