TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4808 ~ 4
8
1
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.552
6
4808
Re
cei
v
ed
De
cem
ber 3
0
, 2013; Re
vi
sed
March 14, 20
14; Accepted
March 28, 20
14
Hard-Disk Stereo Vision Measurement System
Calibration Using Light Plane Constraint
Rui-Yin Tan
g
, Peng-Fei
Li*
Coll
eg
e of Elec
trical Eng
i
ne
eri
ng, Heb
e
i U
n
ited
Un
iversit
y
, 46
Xin
h
u
a
Roa
d
,
T
angsha
n, 0
630
09,C
h
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 1481
02
776
@
qq.com
A
b
st
r
a
ct
T
h
is pap
er pro
pose
d
a cal
i
bra
t
ion metho
d
of s
heet-of-l
i
ght vi
sion
me
asure
m
e
n
t sensor b
a
sed o
n
light p
l
an
e con
s
traint. T
h
roug
h capturi
ng 1
2
imag
es
of different directi
on from h
o
m
e
m
ade
circular
calibr
a
tio
n
targ
et, the center o
f
the circle and
the
lig
ht stripe i
s
extracted bas
ed on H
a
lc
on p
l
atform of
Germa
n
y. T
he exper
imenta
l
results obta
i
n
e
d
the intr
insic p
a
r
ameters, extrinsic par
a
m
eter
s and rad
i
al
distortio
n
coeffi
cient of the no
nlin
ear
mo
del.
At the same ti
me th
e lig
ht
pla
ne constra
i
nt e
quati
on is g
o
t
base
d
on PCA
pla
ne fitting
me
thod. T
he resu
l
t
s show
t
hat th
e cali
bratio
n method is si
mple
and rel
i
ab
le,
and the
met
h
o
d
does n
o
t nee
d any aux
ili
ary adj
ustment. T
he w
o
rk laid the
better foun
dati
on for hard
dis
k
pla
nen
ess visi
on meas
ure
m
e
n
t.
Ke
y
w
ords
:
li
g
h
t plan
e constr
aint, lin
e she
e
t-of-lig
ht sensor,
calibr
a
tion
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
In planen
ess
measurement
with pa
rticul
ar ap
plication
for co
mpute
r
hard
-
di
sk
su
rface at
a foreign
-
fou
nded ente
r
p
r
i
s
e in Singa
p
o
re, the
req
u
e
sts o
n
the planen
ess me
asu
r
em
ent of the
hard
-
di
sk su
rface is ve
ry high to re
alize ze
ro
waste
prod
uctio
n
. On the ba
si
s of our previous
study
，
in
ord
e
r to i
m
prove the
accu
racy of m
e
a
s
ureme
n
t sy
stem, on
th
e condition
s of
laboratory, we determin
e
to use line sheet-of
-
light vision mea
s
u
r
eme
n
t syste
m
to detect the
plane
ne
ss of
the hard di
sk. The mea
s
ured obje
c
t is
h
a
rd
-di
sk
surfa
c
e of com
put
er; see Fi
gure 1.
On the an
alysis of the ma
thematical m
odel of
the li
ne sh
eet-of-li
ght vision me
asu
r
em
ent, it is
key to dete
r
mine suitable
calib
ration
method a
nd
calib
ration
pa
ramete
rs. T
h
e pap
er i
s
m
a
inly
studie
d
the calibratio
n
me
thod of the line she
e
t-of
-li
ght vision se
nso
r
s o
n
ba
se of light plane
con
s
trai
nt. Halco
n
, po
we
rful platform
fo
r imag
e p
r
o
c
essing
algo
rit
h
m, is
used t
o
dete
r
mine
the
came
ra p
a
ra
meters (both i
n
terio
r
and ex
terior p
a
ra
me
ters) and light
plane pa
ram
e
ters, to lay the
foundatio
n for the application of the hard di
sk plan
en
ess vision me
asu
r
ing
syste
m
.
Figure 1. Measu
r
ed O
b
je
ct: Hard-disk o
f
Compute
r
2. Sheet-of-light Vision Measur
e
ment
Principle
The me
asure
m
ent pri
n
ci
pl
e of structu
r
e
d
light
is to
g
enerate a thin
luminou
s
straight line
by a laser lin
e proj
ecto
r a
nd proje
c
t ont
o the surfa
c
e
of the obje
c
t
that is to be
measured. T
hen,
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Hard-Di
sk Stereo Vi
sion M
easurem
ent
System
Ca
lib
ration Usin
g Light Plane…
(Rui
-Yin Tan
g
)
4809
the strip
e
im
age mo
dulat
ed by the ob
ject heig
h
t
is formed in
camera. As shown in Fig
u
r
e 2,
c
c
c
c
z
y
x
o
is cam
e
ra
coordi
nate sy
stem, and defi
ne it is the world
coo
r
din
a
t
e(
w
w
w
w
z
y
x
o
)
system of th
e hard
-
di
sk measured sy
stem. Point
c
O
is ce
nter of p
e
rs
pe
ctive projectio
n
,
c
c
z
o
optical
axis
o
f
came
ra
，
i
i
i
y
x
o
is image co
ordi
nate system,
wh
ere
i
o
is int
e
rsection poi
n
t
betwe
en opti
c
al axis
c
c
z
o
and i
m
age pla
ne.
Dista
n
ce bet
wee
n
point
i
o
and
c
o
is focal l
ength.
Linea
r st
ruct
ured li
ght la
ser p
r
oje
c
ts li
ght plane, th
e 3D
coo
r
di
n
a
te of
P
on th
e light plan
e
is
)
,
,
(
c
c
c
C
z
y
x
P
, of cause, it is on the su
rface
of obje
c
t. The point
P
is proje
c
ted
throug
h the
proje
c
tion
ce
nter of
the le
ns to
the
poin
t
'
P
in the
imag
e pla
ne. Th
e
points,
su
ch
as
P
, depe
nd
on the h
e
ight
of the obje
c
t
,
thus, if the
obje
c
t
onto
whi
c
h the l
a
ser line i
s
proj
ected
differs
in
height, the lin
e is not ima
g
ed a
s
a st
rai
ght line but repre
s
e
n
ts a
pro
fi
le of the
obje
c
t. Usin
g
this
pro
fi
le, we ca
n obtain the
h
e
ight differe
n
c
e
s
of the obj
ect. In ord
e
r t
o
get many th
e obje
c
t heig
h
t
pro
fi
le
s, the object shoul
d be mo
ved by a scanni
ng sy
stem.
Figure 2. Sheet-of-lig
ht Vision Mea
s
u
r
em
ent Princi
ple
2.1. Nonlinear Camera Models
The tran
sformations from
the pixel
co
ordin
a
tes to t
he
worl
d
coo
r
dinate
sy
ste
m
ca
n b
e
expre
s
sed m
a
thematically as:
0
0
1
0
00
0
1
00
0
0
01
10
0
1
0
1
00
1
w
w
c
w
u
X
dx
uf
Rt
Y
Zv
v
f
Z
dy
=
1
1
0
0
1
0
0
0
0
0
0
0
0
w
w
w
y
x
Z
Y
X
t
R
v
a
u
a
(
1
)
Her
e
,
/,
/
xy
a
f
dx
a
f
d
y
.
After the p
r
oj
ection
to the
i
m
age
plan
e,
l
ens di
stortion
s
cau
s
e
the
coordi
nate
s
T
v
u
)
,
(
to
be mo
dified.
This i
s
a t
r
an
sform
a
tion th
at can
be m
odele
d
in the
image
plan
e
alone, i.e. ,3
D
informatio
n is unne
ce
ssary
.
For mo
st le
nse
s
, t
he di
st
ortion
can
be
approximated
sufficie
n
tly well
by a radial di
stortion, give
n by:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4808 – 4
813
4810
v
u
v
u
k
v
u
)
(
4
1
1
2
~
~
2
2
(2)
Therefore,
camera imagi
ng mod
e
l in
clude
s 6 extri
n
si
c pa
ram
e
ters (
z
y
x
t
t
t
,
,
,
,
,
)
and 6 int
r
insi
c pa
ram
e
ters
(
0
0
,
,
,
,
,
v
u
d
d
k
f
y
x
). Togethe
r re
pre
s
ente
d
by vector
)
,
,
,
,
,
,
,
,
,
,
,
(
0
0
z
y
x
y
x
t
t
t
v
u
d
d
k
f
c
. Coo
r
din
a
tes of
calib
rating
point
s in
3
D
spa
c
e
a
r
e
i
M
.
Proje
c
tion coordi
nate
s
o
b
tained th
ro
ugh the
ca
mera m
odel
are
)
,
(
c
M
i
, coordi
nates of
calib
ration p
o
ints extra
c
t
ed from 2
D
image
s are
i
m
.
Then, the
ca
mera p
a
ram
e
ters
ca
n be
determi
ned b
y
minimizing
the distan
ce
of the extract
ed mark cent
ers
i
m
and thei
r proj
ectio
n
s
)
,
(
c
M
i
:
k
i
i
i
c
M
m
c
d
1
2
min
)
,
(
)
(
(3)
Her
e
,
mn
k
is the numbe
r of cal
i
bration m
a
rks.
2.2. Light Plane Equa
tion
By above ma
thematical
m
odel of
stru
ct
ured
light vi
si
on me
asurin
g sy
stem
，
lig
ht plane
proje
c
ted
by
optical
p
r
oje
c
tor a
nd th
e m
easure
d
o
b
j
ec
t
s
u
r
f
ac
e in
te
r
s
e
c
t a
n
d
for
m
c
h
ar
ac
te
r
i
s
t
ic
light st
ripe.
An arbitra
r
y
point in
characteri
st
ic
stri
pe
can
be
e
x
presse
d by
a ray an
d o
p
t
ical
plane. T
he im
age
coo
r
din
a
tes in
ca
mera
image
plane
of the feature
points
on th
e
light stri
pe
can
be obtai
ned
by image p
r
oce
s
sing. According to
th
e ca
mera m
odel, a featu
r
e poi
nt’s im
age
coo
r
din
a
tes
corre
s
p
ond
s
only the ray
throug
h the
came
ra
opti
c
al
cente
r
, that is it can
be
obtaine
d the 3D came
ra coordi
nate
s
e
quation of
th
e ray. If we can obtain the
equation of t
he
light plane i
n
the cam
e
ra coordi
nate
system, t
he ray
equatio
n and
the light pla
ne eq
uation
can
only determi
ne the 3
D
co
ordin
a
tes i
n
the came
ra
coordi
nate of t
he feature p
o
int on the li
ght
stripe.
The light plan
e equatio
n in the
w
w
w
W
z
y
x
O
coo
r
dinat
es can expre
s
sed:
0
w
w
w
w
w
w
w
d
z
c
y
b
x
a
(4)
3. Calibratio
n
Process
Design
Figure 3. Cali
bration Bo
ard
and Specifi
c
Dimen
s
io
ns
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Hard-Di
sk Stereo Vi
sion M
easurem
ent
System
Ca
lib
ration Usin
g Light Plane…
(Rui
-Yin Tan
g
)
4811
Calib
ration
m
e
thod thi
s
pa
per
re
sea
r
ch
ed choo
se
s o
ne pla
ne
circular ta
rget. Resp
ect to
the ang
ular
p
o
int extra
c
ting of the che
s
sbo
a
rd,
cente
r
extra
c
ting al
gorithm
ha
s strong
anti-n
o
i
s
e
ability, the al
gorithm
is si
mple
and fast
. The
cali
brati
on board an
d specifi
c
dim
ensi
o
ns i
s
shown
in Figure 3.
Definiting the
world
coo
r
di
nate system
origin i
s
at the cente
r
of the ce
ntral of the
board,
z
axial is verti
c
al to
the
calib
ration
boa
rd
up
ward, co
ordi
nate
dire
ction
ca
n be
uni
quel
y
determi
ned b
y
the black b
o
x in the triangle at the upp
er left corner.
The sp
ecifi
c
algorith
m
and
the steps a
r
e
as follows
：
(1) Collect
a
set of im
age
s of th
e targe
t
at
variou
s p
o
sition
s, see
Figure
4. Of cou
r
se,
the target fea
t
ure point
s sh
ould be lo
cat
ed in the cam
e
ra view field.
Figure 4. Coll
ect a Set Vari
ous Po
sition’
s Image
s of the Target
(2) Extra
c
t the edge of ci
rcular of the tar
get usin
g Ca
nny operator,
get the edge
of sub-
pixel pre
c
isi
o
n, and then e
x
tract circul
ar tar
get co
ntou
r and fit ellipse usin
g the al
gebraic
distance least
square
ellipse fitting algori
t
hm;
(3) Ba
sed o
n
elliptic minim
u
m circum
scribed qu
adril
ateral cente
r
co
ordin
a
tes, det
ermin
e
the corre
s
p
o
n
d
ing rel
a
tion
betwe
en calib
rating poi
nt and proj
ectio
n
image; se
e Fi
gure 5.
Figure 5. Extract Edge an
d
Center
Coo
r
dinate
s
(4)
Dete
rmin
e the inte
rnal
and exte
rnal
para
m
eters
)
,
,
,
,
,
,
,
,
,
,
,
(
0
0
z
y
x
y
x
t
t
t
v
u
d
d
k
f
. The
came
ra
calibration
co
rre
sp
ond
s to
an
o
p
timization
of
the inte
rn
al
para
m
eters a
nd the
po
se
s of
the cam
e
ra
s
and of the calibratio
n
obj
ects' po
se
s
such that the
back p
r
oje
c
ti
on of cali
brat
ion
obje
c
t feature point
s into
the mod
e
led
came
ra
s fits
the actu
al ob
serve
d
p
r
oje
c
tions a
s
well
a
s
possibl
e. Not
e
that the optimizat
ion needs an initial estimate for
the internal
c
a
mera parameters
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4808 – 4
813
4812
(5) Extra
c
t e
a
c
h a
r
ticl
e opti
c
al featu
r
e
p
o
ints o
n
the
referen
c
e
targ
et image
s, u
s
ing the
came
ra inte
rnal paramete
r
s a
nd the ta
rget plan
e eq
uation in ca
mera
coo
r
din
a
te; calculate
the
coo
r
din
a
tes
o
f
each
point
of the light st
ripe in th
e ca
mera
co
ordi
n
a
te syste
m
. Fit the light pla
n
e
usin
g PCA algorithm of so
many points.
At la
st, we ca
n obtain the light plane eq
u
a
tion unde
r th
e
con
d
ition
of
t
he came
ra coordi
nate system.
PC
A al
gorithm
u
s
e
s
simpl
e
statistics
and
matrix
operation
s
, don’t have to
solve the
partial derivatives of the equati
on. So , it
is more
simp
le,
stable and rel
i
able
tha
n
the
least squ
a
re method
.Ass
u
m
ing that the
N light p
o
ints
coo
r
din
a
tes i
n
came
ra
coo
r
dinate sy
ste
m
are
(
ci
x
,
ci
y
,
ci
z
), the cente
r
coo
r
dinate
s
are
,,
ci
c
i
ci
x
yz
, by th
e
covari
an
ce fo
rmula:
1
1
co
v
,
1
N
c
i
ci
ci
ci
i
x
yx
x
y
y
N
(
5
)
Covari
an
ce
matrix can b
e
con
s
tru
c
ted:
c
o
v,
c
o
v,
c
o
v,
c
o
v,
c
o
v,
c
o
v,
c
o
v,
c
o
v,
c
o
v
,
x
xx
y
x
z
yx
y
y
y
z
zx
z
y
z
z
C
(
6
)
(6) Solve th
e eige
nvalue
and ei
genv
ector
of C,
and find th
e
smalle
st ei
genvalu
e
corre
s
p
ondin
g
to the
eige
nvector,
nam
ely to fit
plan
e no
rmal ve
ctor (a, b,
c),
and ta
ke
ce
n
t
er
coo
r
din
a
tes i
n
to the light plane eq
uation
axc + byc
+
czc + d
= 0, the four
th
co
mpone
nt d in the
plane e
quatio
n can b
e
dete
r
mine
d.
4. Calibratio
n
Experimen
t
s and
Resul
t
s
Acco
rdi
ng to the measure prin
ciple of
li
ne stru
ctu
r
ed
light vision sensor
，
we de
sign
ed a
line st
ructu
r
e
d
light visio
n
sen
s
o
r
, the real obj
ec
t i
s
sho
w
n i
n
Fig
u
re
6. Image
pixels of
cam
e
ra
are 640
(h
)x4
80(vXCCIR), pixel
si
ze
i
s
7.8
7.9
m
.Laser
line p
r
oje
c
tor is
semi
co
nd
uctor red
light lase
r, its wavelength i
s
650
nm
, line width is less than 1mm. The
position an
d
orientation
of the project
o
r with re
sp
e
c
t to the camera a
r
e fixed. Figure 6 is for the designed calibration
target obje
c
ts. Using the fi
xed point pro
v
ided by t
he target, we
cali
brate the line
stru
cture
d
lig
ht
vision se
nsor by above method, t
he results are
sho
w
n in Table 1 to Table 3. Th
e averag
e error
is 0.023m
m.
Figure 6. Rea
l
Object of Lin
e
Structu
r
ed
Light Vision S
ensor
Table 1. Intrin
sic Pa
ramete
rs of Came
ra
f
k
x
d
y
d
0
u
0
v
8.66973
-1467.08
7.88398
7.9 307.073
222.719
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Hard-Di
sk Stereo Vi
sion M
easurem
ent
System
Ca
lib
ration Usin
g Light Plane…
(Rui
-Yin Tan
g
)
4813
Table 2. Extrinsi
c Param
e
ters of
Came
ra
X
Y
Z
40.6145
10.6715
922.203
14.5302
354.384
348.57
Table 3. Light
Plane Param
e
ters
a b
c
d
0.48502
0.09012
0.83951
81.251
5. Measurem
e
nt Accur
a
c
y
Ev
aluation Test
Measuri
ng a
c
curacy of th
e
line structu
r
e
d
li
ght visio
n
measurement
system i
s
ev
aluated
based on sta
ndard height
value
of ha
rd
disk
su
rfa
c
e
provide
d
by
manufa
c
turer. Table
4
sh
o
w
s
the co
mpa
r
ison bet
wee
n
standard h
e
ig
ht value an
d
measure hei
g
h
t value. It ca
n be
see
n
fro
m
Table
4, the
measure a
c
cura
cy of the
calib
rate
d
structured li
ght
measur
ement
system
is le
ss
than 0.023m
m, and root
-mean
-squa
re
erro
r (RMSE
)
is ab
out 0.0
1795m
m, whi
c
h me
ets full
y th
e
requi
rem
ents
of compute
r
h
a
rd di
sk pl
an
ene
ss me
asu
r
eme
n
t.
Table 4. Mea
s
ureme
n
t Accura
cy Evaluation Test
Data
Measure point
Measure height v
a
lue (mm)
Standard height
value (mm)
Error
(mm)
P1 23.398
23.442
-0.044
P2 4.225
4.201
0.024
P3 23.396
23.420
-0.024
P4 21.701
21.611
0.09
P5 9.403
9.418
-0.015
P6 16.518
16.551
-0.033
P7 8.497
8.507
-0.01
P8 6.334
6.313
0.021
P9 6.345
6.317
0.028
P10 23.428
23.446
-0.018
RMSE 0.037618
6. Conclusio
n
Based
on th
e accu
ra
cy requireme
nt o
f
t
he hard
di
sk
plan
ene
ss visual me
asurem
ent
system,
thi
s
pape
r pro
p
o
s
ed
a
calib
rati
on
m
e
thod
of
line
structu
r
ed lig
ht visio
n
me
asure
m
en
t
sen
s
o
r
b
a
se
d on li
ght pl
ane
con
s
trai
nt. Combi
n
in
g with
Hal
c
o
n
software
we can
compl
e
te
quickly the camera calib
ra
tion of internal par
am
eters and extern
al param
eters, and pa
ram
e
ters
of the light plane. And do
not need a
n
y auxiliary
adju
s
tment, calib
ration p
r
oce
s
s is sim
p
le,
reliabl
e and
suitabl
e for field cali
bratio
n, and the
work lai
d
the b
e
tter foundati
on for ha
rd d
i
sk
plane
ne
ss visual mea
s
u
r
e
m
ent.
Ackn
o
w
l
e
dg
ements
This work is
suppo
rted by Nation
al Natu
ra
l Scie
nce Found
ation of Chin
a (No. 51105
273
).
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ces
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n
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u
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