TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.4, April 201
4, pp. 2690 ~ 2
6
9
6
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i4.4250
2690
Re
cei
v
ed Au
gust 11, 20
13
; Revi
sed O
c
t
ober 1
9
, 201
3; Acce
pted
No
vem
ber 7,
2013
Error Elimination Algorithm in 3D Image
Reconstruction
Jin Xian-Hu
a
1
*, Zhao Yuan-Qing
2
1
Computer T
eachin
g
Dep
a
rtment, An
yan
g
N
o
rmal Un
iversit
y
, An
ya
ng He
n
an 45
50
00, Chi
n
a
2
School of Co
mputer an
d Informatio
n
Engi
n
eeri
ng,
An
ya
ng
Normal Un
iver
sit
y
, An
ya
ng 4
550
00 ch
ina;
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
y
u
anq
in
g_zh
ao0
1@1
63.co
m
1
A
b
st
r
a
ct
In process of t
h
ree-
di
me
nsio
nal (3
D) reco
n
s
tructi
on,
effective matchi
ng of
feature is the
key poi
n
t
of accur
a
te rec
onstructio
n
i
n
l
a
ter stag
e. In
order t
o
e
l
i
m
i
n
ate the
error
o
f
mo
de
lin
g d
i
stortion
caus
ed
b
y
inacc
u
rate fea
t
ure matchin
g
in the proc
e
ss of 3D
ima
ge reco
nstruct
i
on, a featur
e
match
i
ng
err
o
r
eli
m
i
nati
on
me
thod bas
ed o
n
collisi
on d
e
te
ction is pres
en
ted. A 3D ima
ge reco
nstructi
on mathe
m
atic
al
mo
de
l is establish
ed to op
erate
the sol
u
tion of imag
e
3D reconstru
c
tion an
d ca
mer
a
spac
e matri
x
ele
m
ents of
ex
terior or
ie
ntatio
n. T
he
error of
the fe
ature
matchin
g
i
n
3
D
dyna
mic
mo
de
ling
is
eli
m
in
ate
d
accord
ing t
o
th
e resu
lt of the
collis
io
n tw
o gr
ay di
gital
i
m
a
g
e
s are
use
d
to
carry out si
mul
a
tion
exp
e
ri
me
nt.
Experi
m
ental r
e
sults sh
ow
that t
he
prop
o
s
ed a
l
gor
ith
m
can effectiv
el
y eli
m
i
nate th
e error
of fea
t
ure
match
i
n
g
an
d i
m
pr
ove the ac
curacy of the mo
de
lin
g.
Ke
y
w
ords
:
3D
reconstructio
n
,
elements of e
x
terior ori
ent
ati
on, ca
mera ca
li
bratio
n, gray le
vel i
m
a
g
e
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The obj
ective
worl
d is three-di
men
s
ion
a
l spa
c
e, b
u
t the image
s
acq
u
ire
d
by existing
techn
o
logy is two-dim
e
n
s
i
on, three
-
dim
ensi
on recon
s
tru
c
tion te
ch
nique i
s
prop
ose
d
to obtai
n
3D info
rmatio
n and ma
ke
reasona
ble ex
pre
ssi
on of
3
D
inform
ation
possible. 3
D
recon
s
tru
c
tio
n
is the m
o
st i
m
porta
nt field
of com
pute
r
vision
resea
r
ch [1, 2]. Th
e
goal i
s
to ma
ke the
co
mpu
t
er
has the
abilit
y of cogni
zin
g
3D e
n
viron
m
ental in
formation thro
u
gh the 2
D
im
age, incl
udin
g
the
perceptio
n of geometri
c informatio
n of object
s
in the 3D envi
r
onment, su
ch as the sh
ape,
positio
n, posture, etc., an
d ca
n de
scri
be, st
ore, re
cog
n
ize and
unde
rsta
nd
them. With the
contin
uou
s d
e
velopme
n
t o
f
comp
uter
scien
c
e
and
tech
nolo
g
y, image
-ba
s
e
d
3D
re
con
s
tru
c
tion
has
bee
n
widely u
s
e
d
in indu
stri
al mea
s
u
r
e
m
ent, archit
ectural de
si
gn, entertai
n
ment,
archae
ologi
cal, e-co
mme
rce, medi
cal i
m
age p
r
o
c
e
s
sing a
nd othe
r fields.
For issu
es related imag
e
matching in
3D
re
con
s
t
r
uct
i
on p
r
o
c
e
ss,
re
se
ar
ch
ers h
a
v
e
prop
osed a n
u
mbe
r
of solu
tions [3]. Literature p
r
op
osed a hierarchi
c
al imag
e ma
tching mo
deli
ng
algorith
m
ba
sed
on
wave
let tran
sform
a
tion, intere
st points
extracted f
r
om
e
a
ch l
a
yer
of the
image
de
co
mpositio
n a
r
e matched,
with p
a
rall
el
strategi
es
to improve
the comp
uting sp
eed,
however,
th
e spe
c
ial
p
r
iori
requi
rem
ent
i
s
set up
as p
r
emi
s
e to
the
assu
ming
th
at algo
rithm
can
effectively extract inte
re
st points, and lim
it its
applicati
on. Feature-b
a
se
d method
extract feature
spa
c
e fro
m
the image
s wai
t
ing to be matched firstly, match the im
age
s ba
sed o
n
the use of the
corre
s
p
ond
en
ce
between f
eature
s
[4,
5]. The m
e
t
hod
utilize
s
the
salient featu
r
e
s
of th
e ima
g
e
,
with a
sm
all amou
nt of
cal
c
ulatio
n, fast
spee
d
and
othe
r
cha
r
a
c
teri
stics, ha
s a
ce
rtain
robu
stne
ss of the image di
stortion, noi
se and oc
clu
s
i
on, but the matchin
g
perfo
rmance dep
en
ds
largely
on fe
a
t
ure extractio
n
qu
ality. If the pixel q
ua
lit
y is low, it wil
l
result in the matchi
ng
error
occurs, so as to lead to error in po
st-mo
deling [6, 7].
To solve this pro
b
lem, thi
s
pa
pe
r intro
duces th
e fe
ature m
a
tchi
ng e
rro
r eli
m
ination
algorith
m
ba
sed on
pixel e
r
ror collisio
n d
e
tection, in
th
e case of
sol
v
ing linea
r a
n
d
nonli
nea
r, the
error compo
nent, calib
rat
i
on interval
comp
osed of
pixel erro
r, detect colli
sion behavio
r o
f
mathemati
c
al
model
s ca
u
s
ed the
error in the
pro
c
e
ss of pixel
correspon
den
ce, and ope
ra
te
simulatio
n
experim
ent of reco
nstructio
n
,
in order
to eliminate feat
ure matching
erro
r duri
ng the
pro
c
e
ss of 3
D
re
con
s
truct
i
on, and imp
r
ove the
pre
c
i
s
ion a
nd a
c
cura
cy of mod
e
ling [8, 9].
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Erro
r Elim
ination Algorithm
in 3D Im
age Re
con
s
tru
c
tio
n
(Jin Xia
n
-Hua)
2691
2.
Image Featu
r
e Matc
hing in 3D
Image Reco
nstruc
tion Proces
s
Image featu
r
e matching
cal
c
ulate
s
th
e co
rr
espon
d
i
ng relation
ship of featu
r
e point
s
extracted
fro
m
the left a
n
d
rig
h
t imag
es
by a
cert
ain
standa
rd.
First, sele
ct
the ap
propri
ate
primitive, and
then get the
corre
s
p
ond
en
ce rel
a
ti
on
shi
p
betwee
n
the primitives o
f
two images
by
cal
c
ulatin
g .As shown in Fi
gure
1,
x is the point that
spa
c
e p
o
int
X of 3D imag
e proj
ecte
d o
n
to
the p
r
ima
r
y i
m
age,
and
C
is the
opti
c
al
cente
r
of the
came
ra. P
re
pre
s
ent
s th
e
proje
c
tion
ma
trix
of this image
,
1
TT
PP
P
P
is the inve
rse m
a
trix of P. Because
that point
Px
satis
f
y the
equatio
n
xP
X
,
Px
and
C
are both o
n
the proje
c
ti
on line of sp
a
t
ial point X.
Figure 1. The
Epipolar G
e
o
m
etry Relatio
n
shi
p
of Single Image
As sh
own in
Figure 2, the
proje
c
tion
p
o
int of C on t
h
e second i
m
age i
s
'
e
.
A
ssumin
g
that
'
P
is the projectio
n
matri
x
of the 2nd
image, we
ca
n obtain the follow e
quatio
n:
''
eP
C
(1)
Figure 2. The
Epipolar G
e
o
m
etry Relatio
n
shi
p
of Two
Images
Point
Px
is on the epipol
ar g
eometry line
'
l
of 2nd image,
accordi
n
g to proje
c
tion
prin
ciple
we can obtain:
''
'
'
'
lP
C
P
P
x
e
P
P
x
(2)
Then we get the follow e
q
u
a
tion:
''
Fe
P
P
(3)
Acco
rdi
ng to the assum
p
tio
n
that the orig
in of
the world c
o
ordinate is
the c
e
nter of the
1st image, th
en the proj
ect
i
on matrixe
s
of the two image
s are:
|
PK
I
0
''
|
PK
R
t
Then, we
can
obtain that:
x
x
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 2690 – 2
696
2692
1
0
C
1
T
K
P
0
(4)
Take Eq
uatio
n (4) into
(3),
the result is shown as follo
w:
''
'
'
'
'
1
'
1
T
F
e
P
PP
C
P
PK
t
K
R
K
K
t
R
K
(5)
E
is
the k
e
y matrix,
E
tR
. The relationship of
E
and fund
ame
n
tal matrix
F
is
descri
bed a
s
Equation (6):
'
T
E
KF
K
(6)
The 3
D
con
v
ersio
n
is
p
e
rform
ed a
c
cording to t
he corre
s
po
nding
relatio
n
shi
p
to
compl
e
te the
image
re
con
s
tru
c
tion. F
r
o
m
the reco
n
s
truction
pri
n
ci
ple me
ntione
d above, it
can
be seen th
at traditional
re
con
s
tru
c
tion
method
co
m
p
letes
the co
o
r
dinate matrix
tran
sform
a
tion
and the re
co
nstru
c
tion b
a
s
ed on the g
eometri
c ch
aracte
ri
stics or
pixel gray
feature. Ho
weve
r, it
is difficult to
en
sure the
accu
ra
cy of
the
featu
r
e
matching
in
the p
r
o
c
e
s
s of
3D ima
ge
recon
s
tru
c
tio
n
, and a larg
er erro
r o
c
curred in the p
r
o
c
e
ss of mat
c
hing will
cau
s
e the deviatio
n
of
the image
proje
c
tion m
a
trix, resulti
ng in fals
e
matchin
g
whe
n
cal
c
ul
ating the feature
corre
s
p
ond
en
ce rel
a
tion
shi
p
, large
r
error for recon
s
tru
c
tion, disto
r
tion and
so on
[10, 11].
3.
Error Elimin
ation Algori
t
hm for Con
f
lict in Featur
e Matc
hing
3.1. Collision Detection
Whe
n
the ca
mera
parame
t
ers a
r
e o
b
tai
ned, co
mbin
e
d
with the a
c
quire
d feature points,
a mathemati
c
al virtual mod
e
l can b
e
est
ablished.
The
virtual model
is then used
to represent the
error
of featu
r
e mat
c
hin
g
and a
d
ju
sted,
so
as to
co
mplete the
error
elimin
ation of the m
a
tching
and lay
a go
o
d
found
ation f
o
r the l
a
tter p
a
rt of t
he m
o
deling. T
he
calcul
ation p
r
o
c
e
ss
of the e
r
ror
elimination al
gorithm i
s
as
follows [12-1
4
].
Figure 3. Schematic for F
e
ature Poin
t Collision E
rror
Matching Det
e
ction
A virtual mathematical cal
i
bration a
r
e
a
, wh
ich is an
irre
gula
r
poly
gon area, is
formed
based o
n
ma
ny pro
c
e
s
se
s of pixel mat
c
hing. Ta
ki
n
g
one ran
dom match point
a
s
the
ve
rtex,
and
whe
n
the coo
r
dinate val
ue
of the vertex is a
c
hi
eved, t
he a
sso
ciate
d
co
rresp
ondi
ng rel
a
tion
shi
p
betwe
en the
vertex and ot
her pixel mat
c
hin
g
point
s
sho
u
ld be
co
nstru
c
ted,
so
as to obtain
the
2D
coo
r
din
a
te are
a
of the
pixel point
s
whi
c
h may
cause a mat
c
h co
nflict e
r
ror a
r
ea, a
nd
build
stable feature point
s mat
c
hing rel
a
tionshi
p
bet
ween vertices t
h
rough
vertex collision. The
coo
r
din
a
tes o
f
the vertices are matched
base
d
on se
lection to buil
d
the mappin
g
relation
shi
p
betwe
en the
corre
s
po
ndi
ng vertex a
nd the ch
ar
acteri
stics of
the grad
ual
chan
ging a
r
ea.
Thro
ugh
the mappin
g
rela
tionshi
p,
the corre
s
p
ondin
g
coo
r
dinate
s
of
the fe
ature
point
s
whi
c
h
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Erro
r Elim
ination Algorithm
in 3D Im
age Re
con
s
tru
c
tio
n
(Jin Xia
n
-Hua)
2693
may cau
s
e
matchin
g
error can be
de
termine
d
cle
a
rly, and the
measure
sta
ndard is
whe
t
her
there i
s
a
coll
ision
phe
nom
enon
amon
g
the imag
e pix
e
ls featu
r
e
p
o
ints of th
e e
rro
r a
r
ea. If so,
errors
will be produced. T
he
schemati
c
for
colli
sion detection of
feature poi
nts is shown i
n
Figure 3.
zz
z
M
NQ
and
1
zz
z
HK
G
in Fig
u
re 3 d
enote th
e se
nsitive
gradient
ran
ge
whe
r
e th
e
matchin
g
error phe
nom
e
non may occur, an
d the
range d
e
scribe
s
the co
rrel
a
tion of the
corre
s
p
ondin
g
self-cro
ss
detectio
n
co
ordin
a
tes. If
the point
z
H
rep
r
ese
n
ts the
di
agon
al cro
ss
point, an
d, at
the
sam
e
ti
me, thro
ugh
the midp
oint
of
zz
z
M
NQ
, it is
po
ssible to
obtain
the
spatial po
siti
on co
rrel
a
tio
n
of the two gradi
ent triangl
e ran
g
e
s in acco
rdan
ce with
th
e
relations
h
ip between
F
X
n
and
H
X
m
, a
s
is
shown in
formula (7).
1
Gz
z
H
zz
X
GM
X
HM
()
()
m
Gz
m
HH
X
Xm
m
X
Xm
m
(7)
Her
e
,
m
G
X
denote
s
the directio
n vector of
G
X
, while
m
H
X
indicat
e
s the di
re
ction vecto
r
of
H
X
. Through t
he analy
s
is of
the correlatio
n of
and
H
Xm
, if
the sig
n
s of th
e two
cha
r
a
c
teri
stic data valu
es are
differe
nt, then the li
n
e
form
ed by
point
z
H
and p
o
int
1
z
H
is
intersectin
g
o
r
tang
ent wit
h
zz
z
M
NQ
.
Some col
lisions will
arise
in the
connections of
the
feature poi
nts in the gradie
n
t range, that
is, erro
rs
exi
s
t in the match of the two
.
Therefo
r
e, 2D
c
o
or
d
i
na
te
(,
)
x
y
of the matchi
ng
point ca
n b
e
obtaine
d b
a
se
d on the
corre
s
p
ondin
g
colli
sion
phen
omen
on,
and then be
adju
s
ted to el
iminate the
error a
nd en
su
re the accuracy of matching
.
3.2. Calculati
on for th
e Exterior Orien
t
ation Eleme
n
ts
The mat
c
hin
g
error
are
a
c
h
i
eved, from e
quation
Et
R
we
obtain that the
k
e
y matrix,
relating
to th
e exteri
or ori
entation
ele
m
ents of
the
ca
mera,
can
be
de
com
p
o
s
ed
to
cal
c
ul
ate
rotation matri
x
R and tran
slation matrix.
Larg
e
amou
n
t
of experimental studie
s
show
that one
of the key
matrix eigenv
alue is
zero and th
e other two
are equ
al. Therefo
r
e,
11
0
T
E
U
di
ag
V
can be got after
decompo
sin
g
the key matri
x
.
Solve the equ
ation
0
T
E
t
,
3
00
1
T
tU
u
can b
e
obtaine
d.
Assu
ming
rot
a
tion matrix is
01
0
10
0
00
1
W
, throug
h equatio
n
TT
T
R
Et
, we k
n
ow
that rotation
matrix is
repres
ented as
T
R
UWV
or
TT
R
UW
V
.
Key matrix
E
is kn
own,
ba
se
d on th
e a
ssumption th
at
the proje
c
tion
matrix of the
1st
image is
|
PK
I
0
, there are followi
ng four po
ssi
b
le pr
oj
ectio
n
matrixes for t
he 2nd ima
g
e
:
'
3
|
T
PU
W
V
u
3
|
T
UWV
u
G
Xm
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02-4
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TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 2690 – 2
6
96
2694
3
|
TT
UW
V
u
3
|
TT
UW
V
u
(7)
Figure 4
sh
o
w
s th
e fou
r
p
o
ssible
proje
c
tion m
a
trixe
s
. The
differe
nce
between
(a) an
d
(b) is that the
tran
slation
vector of the
1
s
t came
ra i
s
i
n
verted to
th
e on
e of th
e
2nd
cam
e
ra.
The
differen
c
e bet
wee
n
(a)&
(c)
and (b
)&(d
) is inverted ba
seline. The differen
c
e b
e
twe
e
n (a)&
(b
) an
d
(c
)&(d
) is th
at came
ra B
rotated 9
0
°
a
rou
nd
the
baseline. Th
erefo
r
e, only
in (a)
are
the
recon
s
tru
c
tio
n
point in f
r
o
n
t of the two
came
ra
s.
Th
at is to
say, the exa
c
t proj
ection
matrix
can
be foun
d fro
m
the four
re
sults
by
verifying wh
ether a sp
atial poi
nt is in fro
n
t of both the t
w
o
came
ra
s.
Figure 4. The
Four Po
ssibl
e Proje
c
tion
Matrixes
3.3. The Solution for 3
D
Coordin
a
te
of the Poin
ts
The al
go
rithm to solve th
e 3
D
coo
r
din
a
tes
ca
n mai
n
ly be divid
e
d
into t
w
o typ
e
s: lin
ear
and n
online
a
r
. Lots
of parameters
relat
ed to no
n
line
a
r meth
od
could in
crea
se
the amo
unt
of
comp
utation
and
compl
e
xity and lead t
o
cum
u
lative
error o
c
cu
rred to re
sult
s. So this a
r
ticle
adopt
s line
a
r method
to
calcul
ate the
coo
r
din
a
te
of
3D spatial
points,
and
then
uses lea
s
t-
s
q
ua
r
e
s
c
o
nstr
a
i
n
t
me
th
od fo
r
co
rr
ec
tion
. T
h
e
me
t
hod is
s
i
mple,
but may get error
res
u
lt: loca
l
optimal re
sult
.
4. Experimenta
l
4.1. Camera
Calibra
tion Experiment
Figure 5. Fea
t
ure Points B
a
se
d on Harri
s
Co
rne
r
Detection Meth
o
d
The calibratio
n
of Tsai
ca
mera i
s
fulfilled in
the MA
TLAB platform in this
paper. In this
experim
ent, the Cann
on A
75 digital
ca
mera i
s
u
s
e
d
to obtain the f
a
ce i
m
age,
a
nd the
size of
the
acq
u
ire
d
ima
ge is 2
048
×1
536 pixel
s
, the si
ze
of the
pixel unit is 0
.
00257
8×0.0
0257
8mm. T
h
e
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TELKOM
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ISSN:
2302-4
046
Erro
r Elim
ination Algorithm
in 3D Im
age Re
con
s
tru
c
tio
n
(Jin Xia
n
-Hua)
2695
calib
ration te
mplate is a
printed 8
×
1
2
che
c
kerb
oard-like pap
er,
and the size of each g
r
i
d
is
20×20 m
m
.
Figure 5
are
the
captu
r
e
d
calibrati
on
template i
m
age
and
the
feature
poi
nts
extracted by
usin
g Ha
rri
s corne
r
dete
c
to
r re
spe
c
tively.
The cali
bratio
n results a
r
e
as follo
ws:
Effective foca
l length f = 9.4223m
m
Disto
r
tion fact
or k
= 0.0020
Tran
sfo
r
mati
on matrix R a
nd T are:
0
.
69
25
0
.
71
31
0
.
10
94
0
.
52
82
0
.
60
44
0.5
9
6
4
0
.
49
14
0
.
35
52
0.7
9
5
2
R
,
21.
1152
104.
9076
767.
5377
T
Usi
ng the
calcul
ated
ca
mera
as mo
del in th
e e
x
perime
n
t, the interi
or
ori
entation
element
s are:
107
5.4
438
5
0
497.
71
314
0
1
078.
01
663
39
6.8
371
4
00
1
K
4.2. Simulation Experime
nt for
Reco
n
s
truc
tion
Based
o
n
the
propo
se
d al
g
o
rithm, the
re
con
s
tru
c
tion
experim
ent i
s
ca
rri
ed
out.
First, th
e
experim
ent is performed fo
r two imag
es,
and the re
sul
t
s are
sho
w
n
in Figure 6.
(a) rec
o
n
s
tru
c
tion
re
sult
s
(b)
cha
r
a
c
teri
stics of the co
rre
sp
ondi
ng result
s
(c) re
con
s
truction in three
d
i
mensi
onal sp
ace stru
cture
Figure 6. 3D
Re
con
s
tru
c
tio
n
Based o
n
T
w
o Image
s
Table 1. The
Erro
r of Reve
rse P
r
oje
c
tion
Anti-erro
r
1st image
2nd image
3rd image
4th image
5th image
Max er
ror
x
0.5736
0.5453
0.5649
0.2952
0.2239
Min error
y
0.3071
0.3136
0.9759
0.9548
1.0390
Ave error
x
0.1289
0.1221
0.1562
0.0599
0.0630
Ave error
y
0.0631
0.0641
0.2700
0.2596
0.2950
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TELKOM
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KA
Vol. 12, No. 4, April 2014: 2690 – 2
696
2696
Table 2. Experime
n
tal Tim
e
Dense matching
Reconstructi
on Optimazation
Time
consumed Number
of
points
33
4
min
23
4
min
44
min
162min 44349
Table 1 a
nd
2 sho
w
the e
x
perime
n
tal result
s. Due t
o
the relative
ly large pe
rspective
transfo
rmatio
n between th
e first ima
ge
and the
se
co
nd imag
e, the
numbe
r of m
a
tchin
g
poi
nts i
s
fewer, the a
c
curacy of the
fundame
n
tal matrix is
lower, thus, lea
d
to the back-proje
c
tion e
r
ror
getting la
rge
r
. As a
re
sul
t
of the o
p
timization
u
s
in
g erro
r eli
m
i
nation m
e
tho
d
, there
i
s
n
o
signifi
cant growth of the
back-p
r
oj
ect
i
on er
ror in
the fourth image an
d the fifth image.
Accordi
ngly, in the
case of
hi
gher preci
s
ion
of camera
calibrati
on,
the algorithm will not affect
the sub
s
e
que
nt image re
co
nstru
c
tion
wh
en there i
s
a large
r
erro
r in the interme
d
i
a
te image.
5. Conclu
sion
The p
ape
r int
r
odu
ce
d the
colli
sion
dete
c
tion
algo
rith
m. It is dem
o
n
strate
d that
the erro
r
of mism
atch
in im
age
feature
mat
c
hing i
s
better
eliminate
d
an
d the
three
-
dim
e
n
s
i
onal
recon
s
tru
c
tio
n
of the entire mod
e
l is achiev
ed. It basi
c
ally meets the dim
ensi
onal ima
ge
recon
s
tru
c
tio
n
for its stabl
e and relia
ble
,
high prec
i
s
i
on, anti-interf
eren
ce a
b
ility. Furtherm
o
re
, i
t
provide
s
a th
eoreti
c
al
refe
ren
c
e
for errors elimi
natio
n of fe
ature
matchin
g
i
n
t
h
ree
-
dim
e
n
s
i
onal
image re
con
s
tru
c
tion and
provide
s
strong sup
port
f
o
r the i
n
-d
ep
th study of t
h
ree
-
dim
e
n
s
i
onal
image recon
s
truction. It also has a
certai
n pra
c
ticality in appli
c
ation
field.
Referen
ces
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y
rov
o
i. F
o
rmatio
n
of a
r
bitrar
y
a
x
is
ymmetric relati
vistic beams.
Journ
a
l of Co
mmu
n
icati
o
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s
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e
chno
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d
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ics
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5-17
1.
[2]
VV Solov’ev. Implementa
tio
n
of finite-state
machi
nes b
a
se
d on pr
ogr
am
mabl
e lo
gic IC
s
w
i
t
h
the h
e
l
p
of the merge
d
model
of Me
al
y an
d Moor
e
machin
es.
Jo
urna
l of Co
mmu
n
ic
ations T
e
chn
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lo
gy a
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Electron
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13; 58 (2): 17
2
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177.
[3]
AV Kl
yuev. D
e
tection
of a rand
om proc
es
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i
t
h
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e of a do
pe
d
Schottk
y
d
i
o
d
e
.
Journ
a
l of
Co
mmun
icati
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e
chno
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gy and El
ectron
ics.
2013; 58(
2): 178-
184.
[4]
AS Petrov, VV Makeev. An
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ysis
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a
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ics of
microstrip a
n
te
nnas
in th
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w
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e
rang
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a
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i
cat
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e
ch
nol
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n
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s
. 2013; 58(
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: 185-19
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[5]
ZHANG Yan,
REN An-
hu.
Rese
arch o
n
Multip
l
e
F
eatu
r
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d BP N
e
ural N
e
t
w
ork
Lice
nce Pl
ate
Reco
gniti
on S
ystem.
Science T
e
chno
logy an
d
Engi
ne
erin
g
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2
): 5645-
564
8.
[6]
TI Bichutskay
a
, GI Makarov.
C
y
lin
drica
l
irre
gul
arit
y
on a
h
a
lf
-spac
e an
d equ
ival
ent rad
i
ators.
Journ
a
l
of Commun
i
cat
i
ons T
e
ch
nol
og
y and Electro
n
i
c
s
. 2013; 58(
3)
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AM Bobreshov, II
Meshchery
a
ko
v, GK Uskov. Optimization of
the g
eometr
y
of a T
E
M-horn for
radi
ation
of
ultr
ashort
puls
e
s
used
as
an
e
l
e
m
ent of
an
ant
enn
a
arra
y
w
i
t
h
co
ntroll
ed
po
sition
of th
e
main l
obe.
Jo
u
r
nal of Co
mmu
nicati
ons T
e
ch
nol
ogy a
nd Ele
c
tronics
. 201
3; 58(3): 20
3-2
0
7
.
[8]
SHEN
Xi
ao-l
e
i, Z
H
OU W
u
-nen
g. Com
p
re
ssed
S
ensi
n
g
and
Its App
licatio
n i
n
Lic
ense
Plat
e
Reco
gniti
on S
ystem.
Science T
e
chno
logy an
d
Engi
ne
erin
g.
201
2; 12(1
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480
3.
[9]
KS Kalashnik
o
v, BI Shakht
arin
. Esti
ma
ti
on
an
d co
mpen
sa
ti
on
fo
r
th
e i
n
flue
nce
of
interc
han
ne
l
interfere
n
ce
in
rece
ption
of
OF
DM sign
als.
Jour
nal
of
Co
mmu
n
icati
ons
T
e
chno
logy
a
n
d
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ectronics
.
201
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8-21
6.
[10]
SG Kalenkov, GR Lokshin. M
odu
latio
n
micr
oscop
y
a
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nmon
ochrom
atic light ho
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recordin
g.
Journ
a
l of Co
mmu
n
ic
ations T
e
chno
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and
Electron
ics.
20
13; 58(3): 2
17-
220.
[11]
SV Save
l’ev. B
i
furcatio
n effec
t
s
w
i
t
h
a
dditiv
e
l
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in
cr
easi
ng
p
e
rio
d
of osc
ill
a
t
ions i
n
a
s
y
stem
w
i
th
on
e
and a half deg
rees
of
fre
e
d
o
m
.
Journa
l of
Co
mmun
icati
o
ns T
e
ch
nol
ogy
and
Electr
onic
s
. 201
3; 58(
3):
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225.
[12]
YAO Z
h
i-
yin
g
.
Rese
arch
on
High
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a
y
-T
unn
el T
r
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ming B
a
se
d o
n
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ens
e Pl
at
e Rec
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itio
n.
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Gr
igor’evsk
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a
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fe
atures
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ntouri
n
g
of an
optica
l
imag
e un
der
dou
ble Br
ag
g
diffraction c
o
nditi
ons.
Jour
nal
of Co
mmunic
a
tions T
e
chno
logy
an
d
Electron
ics
. 20
13; 58(3): 2
26-
232.
[14]
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i
-Yu Ma, Da-
W
ei Li, F
ang-
W
u
Dong
.
Gro
ss Error Elimin
ation Bas
ed o
n
the Pol
y
n
o
mia
l
Least Sq
uare
Method
in Inte
grated M
onit
o
ri
ng S
y
stem of
Sub
w
a
y
.
Int
e
rn
ation
a
l Jo
urn
a
l
of Electrica
l
a
nd C
o
mpute
r
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in
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2013; 12(
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