TELKOM
NIKA
, Vol.13, No
.2, June 20
15
, pp. 604 ~ 6
1
3
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i2.1432
604
Re
cei
v
ed
Jan
uary 17, 201
5
;
Revi
sed Ap
ril 1, 2015; Accepte
d
April 2
0
, 2015
An Image Registration Method Based on Wavelet
Transform and Ant Colony Optimization
Dape
ng Zha
ng
1
, Jia
y
an Li
2*
1
Information Engi
neer D
e
p
a
rtment, Hena
n V
o
catio
nal and T
e
chnical
Institute,
Z
hengz
ho
u 45
004
6, Hen
an, Chin
a
2
Education
a
l A
d
ministrati
on D
epartme
n
t, Henan
Voc
a
tio
nal
and T
e
chnica
l Institute,
Z
hengz
ho
u 45
004
6, Hen
an, Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 3757
96
05@
q
q
.com
A
b
st
r
a
ct
Imag
e re
gistrat
i
on, as o
ne
of t
he bas
ic tasks
of image
proc
essin
g
, is the
process to re
gi
ster tw
o
imag
es a
b
o
u
t the s
a
me
ob
jec
t
ive or
back
g
ro
und
w
h
ich
ar
e
acqu
ired
i
n
d
i
fferent ti
mes, dif
f
erent se
nsors,
different persp
ectives
a
nd different
sh
ooti
ng cond
itions.
In t
he i
m
ag
e reg
i
s
t
ration, b
e
caus
e of the
pro
b
le
ms
that the i
m
ag
e
infor
m
atio
n is
co
mplic
ated, they h
a
ve stro
ng corre
lati
on
and i
n
co
mplet
eness, in
accur
a
cy
and
non-c
onst
r
uction
occur i
n
differe
nt lev
e
ls in th
e
proc
essin
g
, to app
ly the
meth
od
of computati
o
na
l
intell
ig
ence i
n
f
o
rmatio
n
proc
essin
g
in the i
m
a
ge re
gi
strati
on can h
a
ve b
e
tter results than the traditi
o
n
a
l
computati
on methods.
T
h
is p
aper
prop
oses
an i
m
a
ge r
egis
t
ration
meth
od
base
d
on w
a
v
e
let dec
o
m
pos
iti
o
n
and
ant co
lony
opti
m
i
z
at
ion,
w
h
ich div
i
des t
he pr
ocess
of
imag
e reg
i
stration
into co
arse
registrati
on a
n
d
refine
d registra
tion throu
gh w
a
vel
e
t deco
m
p
o
sitio
n
techni
q
ue. In the coarse regist
ration,
the transform
ation
para
m
eter valu
e of the image
approx
i
m
atio
n
comp
on
ent is acqu
ired thr
o
u
gh ant col
ony
opti
m
i
z
at
ion w
h
i
l
e
the cha
ngi
ng
p
a
ra
meter v
a
lu
e
of the ori
g
in
al
imag
e is
o
b
ta
ine
d
by the
an
t colony s
earc
h
metho
d
in th
e
refine
d reg
i
stra
tion. T
he si
mul
a
tion
exp
e
ri
me
nt show
s
that this re
gistratio
n
met
hod
has th
e char
acteristic
s
of anti-no
ise, fast speed, h
i
gh
accura
cy an
d hig
h
registrati
o
n
success rate.
Ke
y
w
ords
: Image R
egistrati
o
n
, W
a
velet T
r
ans
form, Ant Co
lony Opti
mi
z
a
t
i
on
1. Introduc
tion
The im
age
s
acq
u
ire
d
by
d
i
fferent
sen
s
o
r
s or by the
same
sen
s
o
r
i
n
differe
nt times
an
d
perspe
c
tives
are
usually d
i
fferent, whi
c
h is ba
d
for the target d
e
tection
sy
ste
m
, the comp
uter
vision
syste
m
and
the
ima
ge fu
sion
an
d
whi
c
h
w
ill
m
a
ke
the
sy
ste
m
ge
nerate e
rro
r i
n
form
ation
of the target [
1
]. The p
r
o
c
e
s
s to elimi
nat
e the
differen
c
e i
s
call
ed i
m
age
re
gistration. The
ba
si
c
probl
em of image regi
stration is to propo
se
an im
age tran
sfo
r
mation meth
od to be use
d
to
corre
c
t the coordi
nate
s
a
nd deformati
on of the
image. For exa
m
ple, the image
s of the same
scene ta
ken
at different times o
r
by di
fferent
se
nso
r
s from different persp
ecti
ves may hav
e
some tran
slat
ion and
rotation and they
are in diffe
re
nt coo
r
dinate
system
s;
therefore, they n
eed
to be co
rrect
ed. The
r
e a
r
e many re
asons
cau
s
in
g the imag
e def
ormatio
n
. For instan
ce, in
the
remote
sen
s
i
ng imag
e, the sen
s
o
r
noi
se, the c
han
ges
su
ch a
s
the deformation, moveme
nt o
r
gro
w
th of th
e
obje
c
ts to
be
take
n, atmo
spheri
c
ch
ang
e and
lightni
n
g
a
s
well a
s
clou
d covera
ge
and sha
d
o
w
may
re
sult
in
deform
a
tion of
different
fo
rms in the
im
age. Th
e diff
erent
ca
uses
and
forms of im
ag
e defo
r
matio
n
have
re
quire
d different
co
rrespon
ding
i
m
age
re
gist
ra
tion techniq
u
e
s
[2].
Image regi
stration could
b
e
dated
ba
ck to as
early
a
s
the
1970
s i
n
Ameri
c
a
an
d there
are
plenty
of rese
arche
s
ab
out r
egist
ratio
n
techniq
ue i
n
ma
ny fi
eld
s
. Cu
rre
ntly, the do
me
stic
a
nd
oversea
s
ap
plicatio
n field
s
with lot
s
o
f
re
se
arche
s
on image
registration te
chni
que in
clu
de:
infrared im
ag
e p
r
o
c
essin
g
, rem
o
te
sen
s
i
ng ima
g
e
pro
c
e
ssi
ng, di
gital map
lo
cati
on a
nd
medi
cal
image proce
ssi
ng [3]. Usually, the registratio
n
of the transl
a
tio
n
, rotation, scalin
g and the
transl
a
tion dif
f
eren
ce
s in g
eometri
c di
stortion a
r
e the
main re
se
arch
content
s. After doze
n
s
of
years of re
search, ima
g
e
regi
stratio
n
tec
hni
que
ha
s ma
de
cert
ain re
se
arch
achi
evemen
ts;
however, the
r
e a
r
e
still some limitatio
ns in
the
a
p
p
licatio
ns. So
far, many i
m
age
regi
stration
method
s hav
e been rai
s
e
d
in the world and these
methods ca
n be divided
into: manual
regi
stratio
n
a
nd a
u
tomati
c re
gistration
while
the
latter i
n
cl
ude
s t
he featu
r
e
-
ba
sed
meth
od
and
the grayscal
e-ba
se
d method [4]. The grayscale
-
b
a
se
d method
is stron
g
ly depe
ndent o
n
the
image g
r
ay
scale
and
gre
a
tly sen
s
itive to the imag
e scalin
g an
d rotation; b
e
sid
e
s, it is
very
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
An Im
age Registration Met
hod Based on Wavele
t Transform
and Ant Colony ... (Dapeng Z
h
ang)
605
compli
cate
d and
the appli
c
ation ha
s
hu
ge
re
stri
ctio
n
s
. Instea
d of
dire
ctly ope
ra
ting on the im
age
gray, the fea
t
ure-ba
sed m
e
thod ten
d
s
to extrac
t co
ntrol st
ru
cture in the feat
ure
spa
c
e
a
nd
reali
z
e im
ag
e re
gistratio
n
. With the
developm
e
n
t of com
p
utation intelli
gen
ce, intelli
gent
algorith
m
s
are increa
sin
g
l
y
used i
n
im
age regi
st
rati
on an
d play
an impo
rtant
influen
ce o
n
the
effects an
d efficien
cy of the image re
gistration [5].
With the feat
ure
-
ba
se
d im
age regi
strati
on as th
e fou
ndation, this
pape
r imp
r
ov
es
such
method by i
n
tegratin
g wavelet analy
s
is a
nd a
n
t colo
ny optimi
z
ation
so a
s
to expand t
h
e
appli
c
ation ra
nge of the matchin
g
algo
ri
thm and make the matchi
ng effects m
o
re out
standi
ng
while p
r
e
s
e
r
ving its origi
nal pe
rform
a
nce. Ta
ki
n
g
the mutual i
n
formatio
n a
s
the si
milarity
measure of t
he ima
ge
re
gistratio
n
, it
can
autom
atically a
d
just t
he tra
n
sfo
r
m
a
tion p
a
ram
e
ter
scope
s of co
arse regi
stration
a
n
d
refin
e
d
regi
strati
on
and it
ha
s
a
bright
ap
plica
t
ion p
r
o
s
pe
ct
as
a universal fu
lly-automati
c
image
regi
stration metho
d
. This p
ape
r first explai
ns t
he pri
n
ci
ple a
n
d
mathemati
c
al
model of im
a
ge re
gist
ratio
n
as
we
ll a
s
t
he re
gist
ratio
n
method
ba
sed on fe
ature
s
;
then it p
r
op
o
s
e
s
the
ba
si
c
workflo
w
o
f
fully-
autom
atic m
u
tual-i
nformatio
n
i
m
age
re
gistration
according to
wavelet the
o
ry and ant
colo
ny optim
ization a
nd its final pa
rt is the sim
u
lat
i
on
experim
ent a
nd analy
s
is.
2. Principles of Image Re
gistra
tion
2.1. Definitio
n
and Math
e
m
atical
Model of Image Registration
Image regi
stration is th
e p
r
ocess to m
a
tch,
overlay
or p
r
o
c
e
ss t
w
o o
r
mo
re i
m
age
s of
the same
scene a
c
qui
red
at different times by
different sen
s
o
r
s (im
agin
g
device
s
) u
n
d
e
r
different
conditions (weat
her, illuminati
on, camera
position and angle) an
d it i
s
a fundamental
probl
em of image processi
ng.
Two imag
es of the same scene taken unde
r dif
f
erent imagin
g
conditio
n
s may be
different i
n
d
e
f
ormation
an
d
rotatio
n
. Ima
ge
regi
stra
tio
n
is to m
a
ke t
he im
age
s
wit
h
different g
r
a
y
scale
s
a
nd
g
eometri
c t
r
an
sform
a
tion i
n
to the
imag
es with
con
s
ist
ent g
r
ay
scal
e an
d g
eom
e
t
ry.
Assu
me that
the two-dime
nsio
nal a
rray
s
1
(,
)
f
xy
and
2
(,
)
f
xy
stan
d
for the g
r
ay-scale valu
es
of
the corre
s
po
nding
gri
d
p
o
sition
s i
n
th
e two
imag
e
s
, then
the
r
e
exists such
a tran
sfo
r
mat
i
on
relation b
e
tween the two i
m
age
s.
21
(,
)
(
(
(
,
)
)
)
f
xy
g
f
h
x
y
(1)
In this
formula,
g
is the grayscale or
radi
cal transfo
rmat
ion functio
n
and
h
refers
to the
two-di
men
s
io
nal co
ordi
nat
e transfo
rmat
ion. Acco
rd
i
n
g to the prop
erty of affine transfo
rmati
on,
its affine tran
sform
a
tion m
odel is:
co
s
s
i
n
si
n
c
o
s
x
xx
y
yy
(2)
In this
formula,
,
x
and
y
are th
e regi
stratio
n
para
m
eters o
f
these two i
m
age
s.
2.2. T
y
pes of Image Tran
sforma
tion
The mo
st fun
damental
pro
b
lem for all i
m
age r
egi
stration tech
niq
ues i
s
to find
out the
prop
er ima
g
e
tra
n
sfo
r
ma
tion o
r
m
a
p
p
ing type
to
match two
imag
es correctly. After
the
con
s
i
s
ten
c
y of the image
feature i
s
est
ablished, t
he
matchin
g
fun
c
tion is al
so
establi
s
h
ed. We
hope to tran
sform the o
b
se
rvan
ce i
m
age to ma
ke
it registe
r
with the referen
c
ed ima
ge.
Therefore,
th
e de
sig
n
of
m
appin
g
fun
c
ti
on
shall
co
n
s
i
der an
d g
e
t cl
ose
d
to
the
consi
s
tent
co
n
t
rol
points of the
observan
c
e i
m
age an
d the
refere
nced i
m
age a
s
mu
ch as po
ssible.
1) Rigi
d-Bo
dy Tran
sform
a
tion
If the dista
n
c
e
between
the two
poin
t
s of
the
first image
rem
a
ins the
sa
me whe
n
transfo
rme
d
to the
se
co
nd ima
ge, t
hen thi
s
ki
n
d
of tran
sfo
r
mation
is called
rigid
-
b
ody
transfo
rmatio
n. Rigi
d tra
n
s
form
can
b
e
de
com
p
o
s
ed into: tran
slation,
rotati
on a
nd
(mirror)
revers
al. Its
trans
form formula is
as
follows
:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 604 – 61
3
606
21
21
co
s
s
in
sin
c
os
x
y
t
xx
t
yy
(3)
In this
formula,
x
t
and
y
t
are the transl
a
tion
while
is the ro
tation angle.
2) Affine Tran
sform
a
tion
If the transfo
rmed st
raig
ht line in the first
image
remai
n
s the
strai
g
h
t
line whe
n
m
appe
d
in the second image
and maintai
n
an
equilibrium
relation, such t
r
ansform
a
tion is called affine
transfo
rmatio
n. Affine transformation
can b
e
di
vid
ed into line
a
r
(mat
rix) tra
n
sformation
and
transl
a
tion tra
n
sformation
with a tran
sfo
r
mation form
ula as follo
ws:
21
21
co
s
s
i
n
*
sin
c
os
x
y
t
xx
s
t
yy
(4)
In this formula,
x
t
and
y
t
are
th
e tra
n
sl
ation;
is the
rotatio
n
an
gle
and
s
is the
scaling.
The mo
re co
mmon two
-
di
mensi
onal aff
i
ne tran
sform
a
tion formul
a is as follo
ws:
13
21
1
1
2
1
23
22
1
2
2
1
a
xa
a
x
a
ya
a
y
(5)
3) Proje
c
tion
Tran
sfo
r
mati
on
If the transfo
rmed st
raig
ht line in the first
image
remai
n
s the
strai
g
h
t
line whe
n
m
appe
d
in the secon
d
image
but
the parallel
relation
ship m
a
intain
s the
same,
su
ch t
r
an
sform
a
tion
is
calle
d p
r
oje
c
t
i
on tra
n
sfo
r
m
a
tion, which
can
be
sh
o
w
n by the
line
a
r
(matrix) transfo
rmatio
n
in
high-dimen
s
i
onal spa
c
e. Its tran
sformati
on formul
a is:
1
1
1
1
2
1
13
21
1
2
2
1
23
22
31
1
3
2
1
3
3
31
1
3
2
1
33
ax
a
y
a
a
x
a
y
a
xy
ax
a
y
a
a
x
a
y
a
(6)
4) No
n-li
nea
r Tran
sfo
r
mati
on
Non
-
line
a
r tra
n
sformation
can tran
sfo
r
m
straig
ht
line i
n
to cu
rve. In the two-dime
nsio
nal
spa
c
e, it can
be expre
s
sed
by the following formul
a:
(,
)
(
,
)
x
yF
x
y
(7)
In this
formula,
F
refers to
any function
form to map
the first image to the se
con
d
image.
2.3. Featur
e-based Image
Registration
The meth
od
s of image
re
gistratio
n
ca
n be divid
e
d
into two
kin
d
s: g
r
ayscal
e-ba
se
d
method an
d feature
-
ba
se
d method. As the mo
st
freque
ntly see
n
method, th
e feature
-
ba
sed
image regi
stration
sele
cts the
features whi
c
h ca
n
be
easily
extracted and
which ca
n rep
r
e
s
ent
the simila
rity of the image
s to be regi
stered as th
e re
gi
stration
ba
sis for the image
s with diffe
re
nt
prop
ertie
s
.
The featu
r
e-based regi
stration alg
o
rith
m take
s
cert
ain imag
e fe
ature
s
(point,
line an
d
regio
n
)
as th
e re
gistration
primitives.
Firstly,
extra
c
t the features
su
ch
a
s
th
e
points, lin
es
and
regio
n
s with
obviou
s
g
r
ayscale
cha
nge
s from
two i
m
age
s an
d form feature
set. Then
sele
ct
the
feature
s
with
a co
rrespon
ding rel
a
tion a
s
much
as
po
ssible from the
corre
s
p
ondin
g
feature
poin
t
sets of th
ese
image
s by
u
s
i
ng featu
r
e
m
a
tchin
g
al
gori
t
hm. As fo
r th
e no
n-feat
ure
point
s, p
r
o
c
e
s
s
and d
edu
ce t
he corre
s
po
n
d
ing mat
c
hin
g
relatio
n
thro
ugh
su
ch met
hod
s a
s
interpolation
so
a
s
to
reali
z
e th
e p
e
r-pixel regi
stration
betwee
n
two
im
ag
es. The
co
re
st
eps of featu
r
e-ba
se
d ima
g
e
regi
stratio
n
al
gorithm i
n
cl
u
de: feature e
x
tracti
on, feat
ure m
a
tchi
ng,
model
para
m
eter e
s
timat
i
on,
image tran
sformatio
n
an
d
grayscal
e int
e
rpol
ation [6
]
.
The entire
algorith
m
flo
w
is
as foll
o
w
s in
Figure 1.
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TELKOM
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An Im
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hod Based on Wavele
t Transform
and Ant Colony ... (Dapeng Z
h
ang)
607
Figure 1. The
flow cha
r
t of image regi
stration
3. Wav
e
let Anal
y
s
is
3.1. Mallat Algorithm
Mallat al
gorit
hm (nam
ely the two-scale
equatio
n)
is the m
o
st fu
nd
amental
characteri
sti
c
the multi-sca
l
e analy
s
is g
i
ves the
scal
ing fun
c
tion
()
t
and the
wav
e
let functio
n
()
t
and it
descri
b
e
s
the
internal
relat
i
onship bet
ween the two neigh
borhoo
d
scal
e
spa
c
e
s
1
j
V
and
j
V
or
betwe
en the
basi
c
fun
c
tion
s of the neigh
borh
ood
scal
e spa
c
e
j
V
and the wavelet space
j
W
.
()
t
and
()
t
can
b
e
expa
nde
d
linea
rly wit
h
the
orth
o
gonal
ba
si
s
1,
()
n
t
of the
1
V
spa
c
e.
01
,
0
11
,
1
()
(
)
()
2
(
)
(
2
)
()
(
)
()
2
(
)
(
2
)
n
nn
n
nn
th
n
t
h
n
t
n
th
n
t
h
n
t
n
(8)
Here, the ex
pan
sion
coef
ficients
01
()
,
(
)
hnh
n
are
01
,
1
1
,
()
,
,
(
)
,
nn
hn
h
n
and
they are dete
r
mine
d by
()
t
an
d
()
t
, which h
a
ve nothing to d
o
with the sp
ecific
scale.
Proje
c
t any
()
f
t
to the spa
c
e
s
of
j
V
,
j
W
respe
c
tively and get the followin
g
:
__
22
,,
(
)
2
(
2)
2
(
2)
jj
jj
jk
jk
kk
f
tc
t
k
d
t
k
(9)
Im
age registra
tion
Reg
i
stratio
n
evaluation
Determ
inati
o
n
o
f
hom
onym
ous poi
nts
Im
age pre
p
roc
e
ssing
Feature
extraction
Feat
ure
m
a
t
c
hing
Det
e
rm
i
n
at
i
on
of
space
t
r
a
n
sf
orm
a
t
i
on m
odel
Est
i
m
a
t
i
on of
m
odel
param
e
ters
Im
ag
e in
terpo
l
atio
n
an
d tran
sform
a
t
i
o
n
Im
ag
e acq
u
i
sitio
n
Refere
nce im
age
Im
age to be
re
gistered
Reg
i
stratio
n resu
lt
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 604 – 61
3
608
,,
,
jk
j
k
cd
are the expa
nsio
n co
effici
ents of
j
scale and
,0
1
,
,
1
1
,
(2
)
,
(2
)
jk
j
m
jk
j
m
mm
ch
m
k
c
d
h
m
k
c
(10)
Gene
rally,
,,
,
jk
j
k
cd
are call
ed the
scaling
co
efficient a
nd
wa
velet coeffici
ent. Form
ula
(
1
0)
d
e
s
c
r
i
bes
th
a
t
,,
,
jk
j
k
cd
in the
j
spa
c
e
can
be
obtained f
r
o
m
the wei
ght
sum of the
scalin
g
coeffici
ent after the filters
01
()
,
(
)
hnh
n
in the scale
space of
1
j
and t
hey can
be e
x
pande
d to a
n
y
scale
spa
c
e if
decompo
se
d
contin
uou
sly [7]. As indi
cat
ed in Fig
u
re
2, the re
con
s
t
r
uctio
n
form
ul
a
is:
1,
,
0
,
1
(2
)
(
2
)
jm
j
k
j
k
kk
cc
h
m
k
d
h
m
k
(11)
Figure 2. Wa
velet decom
p
o
sition di
agra
m
3.2. Image Wav
e
let Deco
mposition a
nd Rec
ons
tr
uction
As a multi-scale image g
e
o
metri
c
analy
s
is t
ool, wave
let transfo
rm
has ex
celle
nt spa
c
e-
domain
an
d
freque
ncy
-
do
main lo
cality
and it
ha
s
been
wid
e
ly
applie
d in th
e imag
e fu
si
on.
Wavelet de
compo
s
ition a
nd re
con
s
tru
c
tion is to u
s
e two one
-di
m
ensi
onal filters to
reali
z
e
the
fast wavel
e
t
decompo
sitio
n
of two
-
dim
e
nsio
nal ima
g
e
and
then
re
alize th
e ima
ge recon
s
tru
c
tion
with two one
-dimen
sion
al filters. Figu
re 3 is
the diagram of the image after thre
e-level wavelet
decompos
i
tion [8].
Figure 3. Three-level im
ag
e wavelet de
compo
s
ition di
agra
m
3
1
H
3
L
3
2
H
3
3
H
2
1
H
2
2
H
2
3
H
1
1
H
1
3
H
1
2
H
I
npu
tsig
n
a
l
0
()
hn
1
()
hn
↓
2
↓
2
0
()
hn
1
()
hn
↓
2
↓
2
0
()
hn
1
()
hn
↓
2
↓
2
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TELKOM
NIKA
ISSN:
1693-6
930
An Im
age Registration Met
hod Based on Wavele
t Transform
and Ant Colony ... (Dapeng Z
h
ang)
609
Her
e
,
L
is the
low-f
r
eq
uen
cy part
of the
image
an
d i
t
gathers its
main e
n
e
r
gy. And
12
3
,,,
(
1
,
2
,
3
)
jjj
HHH
j
are the high
-f
requ
en
cy co
mpone
nts in
the hori
z
o
n
tal, vertical and
diago
nal
dire
ction
s
in the
h
j
t
level. The
y
are the ima
ge detail
s
.
4. Basic Implementa
tion
of An
t Colon
y
A
l
gorithm
Ant colony algorithm is first used to sol
v
e the traveling sale
sm
an
problem (TSP). TSP
probl
em refers to the p
r
ob
lem in term
s
of the
sho
r
te
st path when
traveling
sal
e
sma
n
iterat
es
throug
h all
ci
ties in o
ne
certain a
r
e
a
. In ord
e
r
to ill
ustrate th
e thoug
ht of this alg
o
rithm
more
conveniently, we still take the solution of
traveling sal
e
sman probl
e
m consi
s
ted by
n
cities on
the flat surfa
c
e a
s
an
exa
m
ple to analy
z
e the b
a
si
c prin
ciple of
ant
colony
al
g
o
rithm. Fo
r other
forms of o
p
timization
an
al
ysis, the
corresp
ondi
ng
o
p
timization
al
gorithm
will
be mo
dified
and
obtaine
d on the ba
sis of such p
r
obl
em.
First of all
we
sho
u
ld ma
ke
some
assu
m
p
tions i
n
terms of the a
n
t sea
r
ch envi
r
onment
and al
so set some
spe
c
ific param
eters:
Set
()
i
bt
as the a
n
t numbe
r ex
isting at mo
ment
t
by element
i
;
()
ij
t
the ph
erom
one
con
c
e
n
tration
value at mo
ment t on the
path
(,
)
ij
;
n
the city number i
n
TSP and
m
the scale of
the ant
alg
o
rithm, i.e.
the total a
n
t
numb
e
r
a
m
ong
the
a
n
t col
ony,
and
1
()
n
i
i
mb
t
;
()
|
|
ij
i
i
Lt
c
c
C
the set
of ph
erom
one
re
si
due
s on
path
s
am
ong
all
cities
at mom
ent t. At
the initial time of the ant
colo
ny algo
rithm,
phe
ro
mone o
n
ea
ch p
a
th is
u
s
ually
set a
s
a
con
s
tant
()
ij
tc
. During the se
arch pro
c
e
s
s on
the path of the ant
(1
,
2
,
,
)
kk
m
, its
next
sea
r
ch path will be determined by the pherom
o
ne concentratio
n
on different p
a
ths.
()
k
ij
P
t
stand
s
for the selecti
on pr
obability
of the ant
k
transfe
rs to ele
m
ent (city)
j
from eleme
n
t (city)
i
at the
moment
t
.
,
0
k
ij
i
j
k
k
ij
ij
ij
s
a
llow
e
d
tt
if
j
a
ll
owe
d
tt
Pt
Ot
herw
i
s
e
，
(12)
In whic
h,
k
a
llowe
d
stands for the cit
y
allowable to
be sele
cted by ant
k
in the next step,
is the
ph
ero
m
one i
n
ten
s
ity impact
fact
or,
whic
h
sta
nds for sen
s
itive degree
by the a
n
t t
o
pheromo
ne
concentratio
n
and al
so
sho
w
s th
e relative
impo
rtan
ce
of this p
a
th, a
nd the l
a
rg
er
its
value is, the more vulne
r
a
b
le the ant is to the impact of the pherom
one con
c
entration wh
en
sele
cting the
next search
path. The a
n
t is more
vulnerable to
sele
ct the p
a
th with hig
h
er
pheromo
ne concentratio
n
, i.e. the
path that has b
e
en walke
d
b
y
more ant
s. In this way,
the
comm
uni
cati
on info
rmatio
n amo
ng
ant
s i
s
al
so
enh
anced to
ma
ke the
coo
r
di
n
a
ting me
ch
an
ism
more obviou
s
.
refers to the visibility factor, namely
t
he expectation fact
or, which shows the
importance of
the ant’s
own visib
ility to the path
selection, and th
e larger it
s value i
s
, the
more
depe
ndent
th
e ant
on th
e
visibility information
whe
n
sele
cting
the
path. When
the valu
e i
s
v
e
ry
large, the
ant
will select the next search
path by
an
almost greedy rule but
ignori
ng the impact
of
the pheromo
ne.
()
ij
t
is the he
uristi
c functio
n
and its
expression formul
a is as follo
ws:
1
()
ij
ij
t
d
(13)
In whic
h,
ij
d
sta
nds for the
di
stan
ce
betwe
en
two
adja
c
ent ele
m
ent
s. The
smalle
r
ij
d
is ,
the clo
s
er th
e distan
ce be
tween two cities, mean
whil
e the large
r
the
()
ij
t
is, the larger
k
ij
Pt
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93-6
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TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 604 – 61
3
610
is, the larger
the probability of t
he
ant
selects such
city in the nex
t step i
s
, that is to
say, this
function
sho
w
s the expe
cta
t
ion degree val
ue of the an
t from one cit
y
to another.
With the
con
s
tant
sea
r
ch
of ants,
phe
romone
will
b
e
left on
a l
o
t of path
s
. In
order to
prevent that t
he con
s
tant accumul
a
tion
of la
rge
re
si
dual ph
erom
one o
n
ea
ch
path cau
s
e
s
the
ant to ignore
the visibility i
n
formatio
n, the
re
sidu
al phero
m
on
e amount on ea
ch path shoul
d be
update
d
whe
n
every
ant
complete
s o
n
e
se
arch
step
or the
ant fini
she
s
se
arche
s
of
n
c
i
ties
(i.e.
one iteration
of the algo
rithm is complet
ed).Th
u
s, the
pheromon
e
con
c
e
n
tration
on path
,
ij
at
the moment
tn
can b
e
adju
s
t
ed acco
rdin
g to the followin
g
formula:
+1
ij
ij
ij
tn
t
t
(14)
1
m
k
ij
ij
k
tt
(15)
In whic
h,
represents the pherom
one
volatilization factor,
1
the phe
rom
one
re
sidu
al
factor. In
o
r
der to g
e
t
close
r
to
the
ant
gro
u
p
in the
natu
r
e
and
p
r
even
t the ex
ce
ssive
accumul
a
tion
of the phero
m
one, and u
s
ually
'
s
value scope i
s
0,
1
. After one iteration is
finis
h
ed,
ij
t
is used to
sh
ow th
e p
heromone
in
cre
m
ent on
pat
h
,
ij
, and
the i
n
itial
time
0
ij
t
,
k
ij
t
sho
w
s the phe
rom
one am
ount l
e
ft by ant
k
on the path
,
ij
in thi
s
sea
r
ch
pro
c
e
ss. In
the
a
n
t col
ony al
gorithm
, th
e
upd
ating
strategy of
phe
romo
ne
dire
ctly
determi
ne
s the algorith
m
’s
efficien
cy an
d su
cces
s, a
nd the upd
ating stra
t
egy of the pherom
one
is de
cide
d by the probl
em feature
s
to be
resolved [9],[10].
5. Image Re
gistra
tion Process
Bas
e
d
on Wav
e
let Analy
s
is and ACO
The mutual
-i
nformatio
n
image regi
stration pro
c
e
s
s ba
sed o
n
wavelet de
co
mpositio
n
and ant colo
ny optimizati
on incl
ude
s three p
h
a
s
e
s
: pre-pro
c
e
s
si
ng, coa
r
se registration a
nd
refined
regi
st
ration. Th
e core ta
sk i
n
the coarse
re
gistratio
n
is t
o
qui
ckly det
ermin
e
the lo
cal
scope of the
optimum value of the image re
gist
rati
on paramete
r
. In orde
r to overco
me the
sho
r
tco
m
ing
that the image regi
stration me
thod
based on m
u
tual inform
ation ha
s h
uge
comp
utation,
the co
mputati
on in
the
regi
stration
ca
n b
e
red
u
ced th
rough
wavel
e
t decompo
siti
on
in the
co
arse
re
gistration.
After that, an
t colo
ny
opti
m
ization
can
obtain
fa
st co
nverge
nce
from
the relatively
wide
sea
r
ch scope. It is autom
at
ic
and unive
rsa
l
. The re
sult
of the coa
r
se
regi
stratio
n
can be the i
n
itial paramete
r
to be
optimi
z
ed in the
refi
ned regi
strati
on an
d the lo
cal
scope
of
refi
ned
re
gistration p
a
ramete
r ca
n
be
dete
r
mine
d a
c
co
rding to
the
a
c
cura
cy
of
the
image to be
registe
r
ed.
Whe
n
enteri
ng in t
he re
fined regi
stration, we ad
opt the mutual
informatio
n as the mea
s
ure of the image regi
strati
on
. Its essen
c
e
is to search
the regi
strati
on
para
m
eter
un
der the
maxi
mum mutuali
n
formatio
n.
Since th
e mut
ual informatio
n of two ima
ges
has lo
cal extremum in the
sea
r
ch spatia
l sco
pe an
d the co
mputati
on is la
rge, gl
obal optimi
z
a
t
ion
is nee
ded to increa
se the registration sp
eed. In her
e,
refined
regi
stration is re
alized by using a
n
t
colo
ny sea
r
ch method.
The
step
s of t
he fully-a
uto
m
atic m
u
tual-inf
ormatio
n
i
m
age
re
gistra
tion ba
se
d on
wavel
e
t
analysi
s
an
d ACO are indi
cated in Fig
u
re 4.
(1)
The
wavel
e
t decompo
si
tion of the im
age to b
e
re
g
i
stere
d
. Perfo
r
m
th
k
level wav
e
let
decompo
sitio
n
on th
e refe
ren
c
e im
age
A
I
and the
floati
ng ima
ge
B
I
an
d extra
c
t thei
r
th
k
level
approximate comp
one
nts
k
A
L
L
and
k
B
L
L
.
(2)
Coa
r
se re
gistratio
n
of the app
roxima
te
comp
one
nts. Take the
mutual inform
ation of
the approximate com
p
o
nents
k
A
L
L
and
k
B
L
L
as the simil
a
rity measure; registe
r
k
A
L
L
and
k
B
L
L
according to the ant col
ony optimization
and get
the o
p
timum (sub
-optimum) tra
n
sformation
para
m
eters
,,
,
s
xy
of the approxi
m
ate com
pon
ent coeffici
en
t image.
(3)
Refine
d regi
stratio
n
o
f
the original
image. Det
e
rmin
e the scop
e of the refine
d
regis
t
ration parameter, take the mut
ual
informatio
n
of the origi
n
al image
s
A
I
and
B
I
as the
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
An Im
age Registration Met
hod Based on Wavele
t Transform
and Ant Colony ... (Dapeng Z
h
ang)
611
simila
rity me
asu
r
e
and
search th
e
re
gistratio
n
p
a
rameters
,,
,
x
ys
of the o
r
igin
al i
m
age
s
A
I
and
B
I
through
ant colo
ny op
timization.
Figure 4. Image re
gist
rati
on pro
c
e
s
s b
a
se
d on wavelet analysi
s
and ACO
6. Experiment and Per
f
o
r
mance Anal
y
s
is
In order to
verify the p
e
rform
a
n
c
e
of
the al
go
ri
thm of thi
s
pape
r in
the
imag
e
regi
stratio
n
, simulation exp
e
rime
nt ha
s
been
co
ndu
ct
ed on th
e st
anda
rd te
st image Satu
rn
in
the Matlab en
vironme
n
t. The experime
n
t use
s
2-l
e
vel DB4 wavel
e
t decompo
sitio
n
and take
s the
norm
a
lized m
u
tual inform
ation as the
si
milarity m
easure. The p
o
p
u
lation si
ze
s
of the ant col
ony
optimization are all
30,
th
e pherom
one volatilization
factor i
s
0.7, t
he pheromone intensity factor
is 1.0, the e
x
pected
heu
ristic fa
ctor i
s
1.5,
and the
maximum g
eneration i
s
200. In order to
redu
ce th
e i
m
pact th
e ra
ndom fun
c
tio
n
pla
c
e
s
on t
he result, thi
s
pape
r ta
ke
s
the avera
ge
value
of 30 experim
ents a
s
the e
x
perime
n
tal result.
Figure 5
(a
～
d) i
s
the
Sat
u
rn i
m
ag
e re
gistratio
n
re
sult. (a) is the
origi
nal im
a
ge; (b
) i
s
the
imag
e
of (a) after rotati
ng
27
.8
and tra
n
sl
ating
10
x
and
18
y
(firs
t
rotating, then
transl
a
ting an
d then dire
ctl
y
cutting the part out of
the bound
ary);
(c) is the re
gi
stere
d
imag
e
o
f
(b) and
(d
) i
s
the i
m
age
by addin
g
(a
) an
d (c). It can
be
se
en
from
(d) tha
t
the re
gistra
tion
accuracy i
s
very high a
nd
sin
c
e the lin
e
transit
io
n in
the overla
ppi
ng se
amin
g of two image
s is
exactly the same a
s
(a
),
there i
s
no v
i
sual di
slo
c
ati
on. Figu
re 6
has
sho
w
n
that in the pre-
optimizatio
n, the mutual informatio
n value of AC
O increases rapidly
,
s
ugge
sting that ACO ha
s a
Pre
p
r
o
cessing
Coarse
registrat
i
on
Refi
ned re
gistration
Im
age
A
I
Wav
e
let
decom
posi
t
i
o
n
Wavel
e
t
dec
o
m
posi
t
i
on
coefficient
K
A
L
L
K
A
L
L
A
I
Im
age
B
I
Wav
e
let
decom
posi
t
i
o
n
Wavel
e
t
dec
o
m
posi
t
i
on
coefficient
K
B
L
L
K
B
L
L
B
I
s
x
y
ACO re
gistration
k
A
L
L
and
k
B
L
L
ACO rg
istration
A
I
and
B
I
s
x
y
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 604 – 61
3
612
fast converge
nce
speed
a
nd that
A
C
O achi
eves
th
e extremum m
u
tual
info
rmat
ion
value
wit
h
in
50~100
gene
ration
s, indi
cating that ACO ha
s a fa
st regi
stratio
n
speed
and a
h
i
gher
re
gistra
tion
su
ccess rate in
the po
st-re
g
istr
atio
n. Th
erefo
r
e, the
i
m
age
re
gistration meth
od
pro
p
o
s
ed
in
this
pape
r
ha
s o
b
t
ained
high
er mutual
info
rmation val
u
e
(n
amely fitn
ess valu
e) a
nd it
sh
ows t
hat
ACO
ha
s hi
gh
regi
stratio
n
a
c
cura
cy
and th
at it
can
re
sist th
e
interfe
r
en
ce
su
ch
a
s
im
age
missi
ng.
(a)
(b)
(c)
(d)
Figure 5. Saturn ima
ge re
gistratio
n
re
sults
Figure 6. Average fitne
ss e
v
olution cu
rve of
30 image
regist
ration e
x
perime
n
ts in
saturn
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
An Im
age Registration Met
hod Based on Wavele
t Transform
and Ant Colony ... (Dapeng Z
h
ang)
613
7. Conclusio
n
The ima
ge re
gistratio
n
aim
s
to elimin
ate
or
redu
ce dif
f
eren
ce
s of the imag
e in t
e
rm
s of
time, sp
ace,
pha
se
and
re
solutio
n
et
c.
whi
c
h i
s
th
e v
i
tal step
in th
e imag
e fu
sio
n
. Thi
s
p
ape
r
has
combi
ned th
e image’
s
chara
c
te
risti
c
s and the
m
u
tual inform
ation, and t
a
ke
n the m
u
tual
informatio
n a
s
the test of the simila
rity of t
he image
regi
stratio
n
, and also ha
s p
u
t forwa
r
d a kind
of image regi
stration
meth
od ba
sed
on t
he wavel
e
t d
e
com
p
o
s
ition
and the a
n
t colo
ny algo
rithm.
Thro
ugh exp
e
rime
ntal ana
lysis,
su
ch m
e
thod can a
c
curately determine the mat
c
hin
g
point, a
n
d
has
achieved
satisfa
c
to
ry results in
accura
cy,
spee
d and
rob
u
st
ness et
c., which
ca
n be
wel
l
applied to multi-sensor images.
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ces
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n W
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ao
hon
g W
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e
t
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w
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u
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timizatio
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e
rm
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ngi
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