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C Automaiton, BeiijngUnionUniverstiy, No.97,NorthFourth ,
t s a E d a o R g n i
R BeiijngChaoyangDistrict.
: s d r o w y e
K Machinevision, Image processing, Cricular marking, Cameracailbraiton.
.t c a r t s b
A Camera calibration is one of the research hotspots in the field of computer vision .Its e h t y b n e k a t s e g a m i e l p i t l u m r o e l g n i s y b a r e m a c e h t f o l e d o m r e t e m a r a p e h t e n i m r e t e d o t e s o p r u p
m a r a p e h t t e g n e h t d n a , a r e m a
c etersofthecamera .Aiminga ttheproblemofcameracalibration ,a d
e t n e s e r p s i e t a l p r e k r a m r a l u c r i c g n i s u y b s r e t e m a r a p a r e m a c g n i n i a t b o f o d o h t e
m .Afterseparating
e h t t c a r t x e o t d e s u s i r o t a r e p o y n n a C e h t , e t a l p r e k r a m r a l u c r i c e h t d n a d n u o r g k c a b e h
t markerplate ,
e h T . s r e t e m a r a p a r e m a c e h t n i a t b o o t d e s u s i d o h t e m g n i t t i f e s p i l l e e r a u q s t s a e l r a e n i l n o n e h t d n a
t i , e v i t c e f f e d n a e l b i s a e f s i d o h t e m n o i t a r b i l a c d e s o p o r p e h t t a h t w o h s s t l u s e r n o i t a r b i l a
c hasgood
. s s e n t s u b o r d o o g d n a n o i s i c e r p n o i t a r b i l a c
n o it c u d o r t n I
D 3 n i d e s u y l e d i w s i t i d n a , y g o l o n h c e t n o i s i v r e t u p m o c n i p e t s y e k a s i n o i t a r b i l a c a r e m a C
, n o i s i v r a l u c o n o m n o d e s a b s i n o i t a r b i l a c a r e m a C . s d l e i f r e h t o d n a n o i t a m i t s e e d u t i t t a , n o i t c u r t s n o c e r
i t l u m d n a n o i s i v r a l u c o n i
b -vision ,anddifferen tmethodscorrespondt odifferen tcameramodel .The t n e r e f f i d e h t o t g n i d r o c c A . l e d o m r a e n i l n o n d n a l e d o m r a e n i l , s e p y t o w t o t n i d e d i v i d e b n a c l e d o m
f l e s , n o i t a r b i l a c l a n o i t i d a r t o t n i d e d i v i d e b n a c , s d o h t e m n o i t a r b i l a
c -calibration and active
n o i s i
v -basedcalibrationmethod . t
e h
T raditiona l calibration used objec t such as a two-dimensiona lcalibration plate and a e
e r h
t -dimensiona lcalibration plate with known dimensions[1] .By establishing a correspondence i
s t i d n a t c e j b o n o i t a r b i l a c a f o t n i o p a n e e w t e
b magepoin,t su i ng algorithm to obtain thecamera's o
w t l a c i s s a l c a d e s o p o r p i a s T . s r e t e m a r a p l a n r e t x e d n a l a n r e t n
i -step calibration method in 1986 , e h t r o f t p e c x e s r e t e m a r a p l a n r e t x e a r e m a c e h t e v l o s o t t n i a r t s n o c y t i m r o f i n u l a i d a r e h t s e s u t s r i f h c i h w
a r
t nslationi nt hedirectionoft heoptica laxisoft hecamera ,andt hensolvet heotherparametersoft he a
r e m a
c [ . ]23 . Abdal-Aziz in the early 1970s proposed a direc tlinear transformation(DLT) of the d
o m r a e n i l a d e h s i l b a t s e h c i h w , d o h t e m n o i t a r b i l a c a r e m a
c e loft hecamerai maginggeometry ,which b
i l a c e b n a
c rated linear camera parameters[ . 4] Zhang of Microsof tVisua lResearch Institute pu t d e s u y l e d i w n e e b s a h d o h t e m s i h T . e t a l p m e t d r a o b r e k c e h c n o d e s a b d o h t e m n o i t a r b i l a c a d r a w r o f
i c e r p h g i h s t i f o e s u a c e
b s nio [ . 5] However,i ft het arge toft hismethodi st oosmalli nt hewholef ieldof s d o h t e m n o i t a r b i l a c l a n o i t i d a r t e h t h g u o h t l A . d e c u d e r y l t a e r g e b l l i w y c a r u c c a n o i t a r b i l a c e h t , w e i v
s i y c a r u c c a n o i t a r b i l a c d n a , e r u t a m n e e b e v a h s m h t i r o g l a n o i t a r b i l a c d n
a high ,butt heirenvironmenta l
. r o o p s i y t i l i b a t p a d
a Thedisadvantageoft hismethodi si tneedt oproducehigh-precisioncalibration ,
s t c e j b
o undernoconditionsplacedcalibrationobjec tsituationcanno tbecalibrated . f
l e s e h
T -calibrationmethoddoesno trequireacalibrationobject ,onlyusedindividua lconstraints d
n
a thesceneconstraints ,andr elyonaf ewi magesbetweent hecorrespondingpointst ocalibration[ . 6] 2
9 9 1 n
I , Faugerasfirs tproposedt heconcep tofcameraself-calibration. In1997HartleyproposedQR d
o h t e m n o i t i s o p m o c e
d .Thecalibration processofthecameraself-calibrationmethodissimpleand s ' a r e m a c e h t n i g n i t s i x e s t n i a r t s n o c e h t d n a e n e c s e h t n i n o i t a m r o f n i e h t y b y l t c e r i d d e t a r b i l a c e b n a c
d n a d e t a c i l p m o c t u o h t i w s r e t e m a r a p n w
o expensivecameramarkerpoints .Thecalibrationresponse l
a e r r o f e l b a t i u s s i t I . t s a f s
i -timeonline measuremen tsystem. However ,this method is no thigh .
r b i l a c e h
T ation method based on activevision isthecalibration of known cameraundercertain n
o i t o
m [7.8 . t] I needshighprecisionactivevisionplatform .Theexperimenta lconditioni shighandi t l
o r t n o c t o n n a c r o n w o n k n u s r e t e m a r a p n o i t o m e h t r o f e l b a t i u s t o n s
i themovemen toft hecamera.
, e r o f e r e h
T acalibrationmethodofcameracalibrationwithcircularmarkplatei si ntroducedi nt his e
v o b a e h t d n A . r e p a
p -mentionedmethodi sdifferen,tt hemethodused t hecircularmarkingboard to a
r b i l a c a r e m a c e h t e v e i h c
a tion. Experiments show tha t this method has high accuracy ,good .
e g n a r n o i t a c i l p p a e d i w d n a s s e n t s u b o r
l e d o M g n i g a m I a r e m a C
, a r e m a c e h t f o l e d o m g n i g a m i e h t d n a t s r e d n u o t d e e n t s r i f , n o i t a r b i l a c a r e m a c e h t e r o f e
B thecamera
e e r h t a s t c e j o r
p -dimensiona lsceneontothetwo-dimensiona limageplaneofthecamerathrough an s
n e l g n i g a m
i , theprojectionscanbedescribedbyani magingt ransformation ,thati scamerai maging .l
e d o
m Cameraimaging mode lisa rea lcamera geometricabstraction ,the imaging process is the o t g n i d n o p s e r r o c l e d o m g n i g a m i a r e m a c t n e r e f f i d , t n i o p l a i t a p s e h t f o y h p a r g o t o h p n o i t a m r o f s n a r t
t n e r e f f i d , s r e t e m a r a p t n e r e f f i
d parametercollectionalsorequiresadifferen tsolution .A tpresen,tt he e
l o h ( l e d o m r a e n i l : e r a s l e d o m g n i g a m i n o m m o c e r o
m imagingmodel)andnonlinearmode.l
y l n o m m o
C Us Ced oordinateSystem
e t a n i d r o o c d l r o w e h t e n i f e d e w , y l e v i t i u t n i e r o m s s e c o r p g n i g a m i a r e m a c e h t e b i r c s e d o t r e d r o n I
m e t s y
s X( ,Y,Z)t,hecameracoordinatesystem( x ,y ,z),t hei magingcoordinatesystem( u, )v ,t hei mage r
( m e t s y s e t a n i d r o o
c , )c .Thesmal lholei magingmode lshowni nFig . . 1
e r u g i
F 1 .Thesmal lholei magingmodel.
e t a n i d r o o c D 3 l a i t a p s d e n i f e d y r a r t i b r a n a s i ) Z , Y , X ( m e t s y s e t a n i d r o o c d l r o w e h t f o t n i o p e h T
m e t s y
s ; the camera coordinate system (x ,y ,z) takes the camera's optica lcenter as the origin of e n a l p e g a m i e h t o t r a l u c i d n e p r e p e n a l p e g a m i e h t d n a , s i x a l a c i t p o e h t g n o l a s i x a z e h t , s e t a n i d r o o
c ;
imaging coordinatesystem (u ,v)to the intersection of theoptica laxisand theimageplaneas an e h t f o s i x a e h t o t l e l l a r a p e r a s e x a v d n a u e r e h w , ) 0 v , 0 u ( s e t a n i d r o o c t n i o p l a p i c n i r p e g a m i e h t , n i g i r o
x m e t s y s e t a n i d r o o c a r e m a
c -axisandy-axis,t hecoordinatesystemisaplanerectangularcoordinate m
e t s y
s ; theimagecoordinatesystem(r ,c)istheplanerectangularcoordinatesystem on theimage , .
n i g i r o e h t s i e g a m i e h t f o r e n r o c t f e l r e w o l e h t d n a
n o it a m r o f s n a r T e h
T Rela itonshipo fT h Ce ameraCoordinateSystem
l a e d i e h
T smal lholeimaging mode lisalinearmodel ,asshownin Fig 1 .Le tPw(Xw,Yw,Zw)bea , ' x (' P t c e s r e t n i e n a l p e g a m i e h t d n a r e t n e c l a c i t p o e h t d n a w P n e e w t e b n o i t c e s r e t n i e h t , e c a p s n i t n i o p
t n i o p g n i g a m i g n i d n o p s e r r o c e h t o t w P t n i o p l a i t a p s e h t , )'
y , fort hefollowingt ransformations: )
1
( Thepoin tPw(Xw,Yw,Zw)isconvertedt oapoin tPc(xc ,yc ,zc)i nt hecameracoordinatesystem, thetransformationcanbeseenasbeingdonebyrotationand translationoperations, thespecific
s i a l u m r o
f PcT=RPwT+TT ,amongR(a ,b ,c)i sarotationmatrix, T(t1,t 2,t 3)i st hetranslation r
o t c e
v . Thesix parameters(a ,b ,c ,t1 ,t2 ,t3) in R and T arecalled externa lparameter ,which d l r o w e h t d n a m e t s y s e t a n i d r o o c a r e m a c e h t n e e w t e b p i h s n o i t a l e r l a n o i t i s o p e h t e n i m r e t e d
) 2
( Thepoin tPc(xc ,yc ,zc) is transformed to thepoin tP('x' ,y )' in theimagecoordinatesystem, whichistransformedintoaperspectiveprojectionrelationship .Therelation isx'=y*xc/zc ;y '=
. a r e m a c e h t f o h t g n e l l a c o f e h t s i ’ f ‘ e r e h w , c z / c y * f ) 3
( TransformsP('x' ,y )'i ntoapoin tPn(u ,v)int hei magingcoordinatesystem ,theformulai su-u0= =
x d /'
x sy*x ; v-’ v0=y/'dy=sy*y', among(u0 ,v0)i st hei mageprincipa lpoin tcoordinate ,dx,dyi s x
e h t n i e z i s l a c i s y h p e h
t - andy-axisdirections. )
4
( After severa ltimes between the coordinate system transformation, the resulting relationship s
i n P d n a m P n e e w t e
b Eq.1 : ,
( 1) f
= x f , m e h t g n o m
A *sx ,fy =f*s ,y Nis3*4 matrix ,called theprojection matrix. N1 isentirely x
f y b d e n i m r e t e
d , yf , 0u ,v0 ,sincetheyareonlyrelatedtotheinterna lmechanismofthecamera ,i tis l a n r e t x e d n a l a n r e t n i s ' a r e m a c e h t , t n i o p s i h t t A . a r e m a c e h t f o s r e t e m a r a p l a n r e t n i e h t d e l l a c
. d e c u d o r t n i n e e b e v a h s r e t e m a r a p
l e d o M g n i g a m I a r e m a
C CameraCailbra itonBasedonCircularMarkingBoard
. n o i t a r b i l a c a r e m a c f o s i s a b e h t s i n o i t c e s s u o i v e r p e h t n i d e b i r c s e d e l p i c n i r p e h
T I tneedt oknowt he
n i s t n i o p e h t t c e j o r p n e h t d n a , m e t s y s e t a n i d r o o c d l r o w e h t n i s t n i o p e c a p s D 3 h g u o n e f o s e t a n i d r o o c
d r o o c e g a m i e h t o t e c a p s e h
t inatesystem, and establish algebraic relations .Therefore ,thecamera e
c a p s f o s e t a n i d r o o c e h t n i a t b o o t s t n i o p o t n i d e d i v i d s i s s e c o r p n o i t a r b i l a
c ;to determine the
. s t n i o p e t a n i d r o o c e h t n e e w t e b e c n e d n o p s e r r o c
d r a o B g n i k r a M r a l u c r i C
u c r i c , r e p a p s i h t n
I larmarkplateast hecameracalibrationt arget ,asshowni nFig . .2
g i
F u 2 .re Circularmarkingboard.
Thecircularplatearoundt heselectionofablackrectangularframe ,makingt hel ogoplatei smore d
e t c a r t x e y l i s a
e , thedirectionmarksoft hecornersoft herectangularbordersmaket heorientationof 7
* 7 n i s e l c r i c d i l o s 9 4 e r a e r e h T . r e n r o c r a l u g n a t c e r e h t o t e u q i n u e t a l p n o i t a r b i l a c e h
t solidcircle ,and
n i o p r e t n e c e h t f o s e t a n i d r o o c e h t g n i t c a r t x e y b d e n i a t b o e r a s t n i o p e t a n i d r o o c d l r o w f o s t e s 9
4 toft he
n o i t a r b i l a c a r e m a c f o l a o g e h t e v e i h c a o t s a o s , e l c r i c d i l o
s .
n o it c a r t x E e r u t a e F
d l o h s e r h t e h t g n i s u y b n o i g e r d n u o r g k c a b e h t m o r f d e t a r a p e s s i n o i g e r r e k r a m r a l u c r i c e h t , y l t s r i F
. d o h t e m n o i t a t n e m g e s
i n i m e l b o r p c i s a b e h t s i n o i t a t n e m g e s e g a m
I mageprocessing .Threshold-basedsegmentationi st he s i t I . d l o h s e r h t f o n o i t c e l e s e h t n i s e i l y t l u c i f f i d s t i d n a , n o i t a t n e m g e s e g a m i f o m e l b o r p c i s a b t s o m
. t c e f f e n o i t a t n e m g e s e h t r o f r o t c a f e v i s i c e d e h t s i e u l a v d l o h s e r h t e h t f o e c i o h c e h t t a h t d e v o r p
e
i s h t i w e c n e r e f f i d l a i t n e s s e o n s i e r e h t d n a , s e u q i n h c e t n o i t a t n e m g e
s nglet hresholdsegmentation .As g
i F n i n w o h
s .3 ,aftert het hresholdi ntervali sdetermined,t het hresholdr egioni ssegmentedt oextrac t n a c t I . d e t a c o l s i e u l a v d l o h s e r h t e h t e r e h w n o i g e r e h t s i n o i g e r d e r e h t d n a , n o i g e r r e k r a m r a l u c r i c e h t
n e e s e
b i F gn i .3abovet het hresholdareaf ort hecircularl ogoversionoft hearea,t hefollowingfigure .
a e r a d n u o r g k c a b e h t s w o h s
g i
F u 3 .re Thresholdregionaftert hedivision.
i t l u m a d e p o l e v e d 6 8 9 1 n i y n n a C . F n h o J s i r o t a r e p o n o i t c e t e d e g d e y n n a
C -leve ledgedetection
e g a m i e h t f o e z i s a t a d e h t e c u d e r o t s i n o i t c e t e d e g d e f o e s o p r u p e h t , l a r e n e g n I . m h t i r o g l a
r o f s m h t i r o g l a y n a m e r a e r e h t h g u o h t l A . s e t u b i r t t a e g a m i l a n i g i r o e h t g n i v r e s e r p e l i h w , y l t n a c i f i n g i s
t u b , d l o s i m h t i r o g l a y n n a C h g u o h t l a , n o i t c e t e d e g d
e i tcanbesaidt hati ti sastandardedgedetection f o e g d e e h t t c a r t x e o t d e s u s i r e t l i f y n n a C , r e p a p s i h t n I . y d u t s e h t n i d e s u y l e d i w l l i t s s i d n a , m h t i r o g l a
g i F n i n w o h s s A . e t a l p r e k r a m e h
t . 4,t heedgeoft hemarkerplatei sdetected ,andt heeffectisgood.
g i
F u 4 .re Detectt heedge.
d e s u s i d o h t e m g n i t t i f e s p i l l e e r a u q s t s a e l e h t , y l l a n i
F to obtain the ellipseboundary , and then .t
n i o p r e t n e c e h t e n i m r e t e d
n o it c a r t x E e r u t a e F
e h t , r e p a p s i h t n
I Halcon platform based on the circular marking board camera calibration ,the e
r u t p a c o t d e r i u q e r n o i t a r b i l a
c images ,thenumberofi mageacquisitionsi srelatedtothecalibration .
y c a r u c c a
f o e s u e h t n
I halcon platform cameracalibration required to makeacircularmarking board ,the s
i h t n i d e s u d r a o b o g o
l papersize(24*24)mm. Inordert omaket hecalibrationresul tmoreaccurate , e d a m e b d l u o h s e t a l p e r u s o p x e e h t d n a , d e g n a h c n u e c r u o s t h g i l e h t f o n o i t i d n o c e h t e r u s n e o t d e e n e w
. y a w e m a s e h t n i
: w o l f m h t i r o g l a n o i t a r b i l a C
c e h t e s u , e g a m i e h t e r i u q c A ) 1
( amera to collec ta tleas t10 imagesfrom differen tdirections to , n o i t r o t s i d o t e n o r p e r a a r e m a c e h t f o s r e n r o c r u o f e h t e s u a c e b , a r e m a c e h t f o s r e n r o c r u o f e h t r e v o c
. s t l u s e r n o i t a r b i l a c e h t f o y c a r u c c a e h t t c e f f a l l i w h c i h w
) 2
( Then,t hei magei sseparatedfromt hebackgroundbyt het hresholdsegmentationalgorithm ,and r
e k r a m e h t f o n o i g e r e h t d n a , r o t a r e p o y n n a C y b d n u o f s i e t a l p r e k r a m e h t f o e g d e e h
t plate is
. d e n i m r e t e d
) 3
( Byusingt hel eas tsquaremethodofellipsefitting,t heellipseboundaryi sobtained ,andt hent he b
u s h c a e n i s t n i o p r e t n e c r a l u c r i c 9 4 f o s e t a n i d r o o c e h t d n a , d e n i m r e t e d s i t n i o p r e t n e
c -imageare
. d e n i a t b o
) 4
( Accordingt ot hecoordinatet ransformationrelations,t heobtainedcoordinatepointsarebrough t l
a c e h t y l l a n i f d n a , o t n
) a
( (b) (c) (d)
g i
F u 5.re Calibrationprocess.
g i
F .5 is the process of marking the plate in the process of differen tstates. gF .5 i (a) for the (
; d n u o r g k c a b e h t d n a s n g i s f o n o i t a r a p e
s b ) to obtain the edge profile of the sign board ;(c ) t o s
e t a n i d r o o c t n i o p r e t n e c e h t n i a t b o d n a t n i o p r e t n e c r a l u c r i c e h t e n i m r e t e
d ; (d)istomarkthecenter
o t n e m h s i l b a t s e e h t , n i g i r o e h t s a e t a l p e h t f o t n i o
p f coordinate system .Among them ,the Z-axis .
a r e m a c e h t s d r a w o t n o i t c e r i d e h t , s n g i s l a c i t r e v
si s y l a n A s tl u s e R l a t n e m i r e p x E
e h t n i , s p e t s n o i t a r b i l a c d n a e l p i c n i r p e v o b a e h t o t g n i d r o c c
A Halcon platform to do camera
t n e m i r e p x e n o i t a r b i l a
c . At ota loft wosetsofl andmarki mageswerecollected ,eachwith15i mages. b
a T n i n w o h s e r a d e n i a t b o s t l u s e r n o i t a r b i l a c e h
T . 1:
e l b a
T 1. Cameracalibrationresults.
y f , x f , g n o m
A arer espectivelyt hef ocall engthi nt hexdirectionandt heydirection, unitsarepixels; y
s , x
s aret hecel ldistancesi nt hexdirectionandt heydirection ,unitsareu m;u0,v0ast hemainpoin t s
e t a n i d r o o
c ,units are pixels; X,Y,Z is the relative distance between the camera and the image m
e t s y s e t a n i d r o o
c ,unitsarem m. )
1
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d n o c e s e h t m o r f m m 9 9 6 8 7 .
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2
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w o l l o f e h t , m h t i r o g l a n o i t a r b i l a c a r e m a c e h t , r e p a p s i h t n
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s emanipulatoront hebookoperation .Theparametersobtainedcanbeusedt ocorrectt he n o i t a r b i l a c a r e m a c f o s s e n e v i t c e f f e e h t f o n o i t c e r r o c e h t h g u o r h t o s l a t u b , e g a m i e h t f o n o i t r o t s i d
. y c a r u c c a n o i t a c i f i r e v
fx fy sx sy u0 v0 X Y Z K
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e t e m a r a P s o.
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m o r
F gF . 7i ,wecan seetha tthereisobvious barre ldistortion in the lef timagebook spine .By t a h t e e s n a c e w , e g a m i t h g i r e h t t e g n a c e w , n o i t a r b i l a c a r e m a c y b d e n i a t b o s r e t e m a r a p e h t g n i t c e r r o c
p o t e d i s e h t m o r f o s l a t u B . s u o i v b o s i t c e f f e n o i t c e r r o c e h
t rovet heaccuracyofcalibrationresults.
s n o is u l c n o C
r a l u c r i c e h t n o d e s a b d o h t e m n o i t a r b i l a c a r e m a c e h t t a h t n e e s e b n a c t i , s t l u s e r l a t n e m i r e p x e e h t m o r F
l a u t c a e h t h t i w d e r a p m o c d n a , a r e m a c e h t f o s r e t e m a r a p e h t d e n i a t b o y l l u f s s e c c u s s a h e t a l p r e k r a m
resultsoft hecamerat oachieveagoodaccuracy .Att hesamet ime,i nt heverificationoft hecamera n o i t c e r r o c e h t t a h t n e e s e b n a c t i , d e n i a t b o s e g a m i k o o b d e t r o t s i d e h t g n i t c e r r o c y b , s t l u s e r n o i t a r b i l a c
i m h t i r o g l a e h t , e m i t e m a s e h t t A . d o o g s i t c e f f
e si mplementedonHalconplatform ,whichhasgood .
y t i l i b a t p a d a e d i w d n a y t i l i b a t r o p
t n e m e g d e l w o n k c A
e h d n a ) 4 1 3 0 5 1 0 2 D C T & T I C ( t c e j o r P m a r g o r P r a l o h c S l l a W t a e r G y b d e t r o p p u s n e e b s a h k r o w s i h T
) 8 1 0 2 4 1 4 ( a n i h C f o n o i t a d n u o F e c n e i c S l a r u t a N l a n o i t a
N .Furthermore,t heauthorsalsowouldl iket o .
y d u t s s i h t e k a m o t d e p l e h e v a h o h w l l a k n a h t
s e c n e r e f e R
] 1
[ Ganpathy S. Decomposition oftransformation matrieesforrobo tvision.Proe. I n.t Conference .
9 3 1 ~ 0 3 1 . 4 8 9 1 . n o i t a m o t u A d n a s e i t o b o R n o
] 2
[ Tsa iB.R.Y .AnEfficien tandAccurateCameraCaliberationTechniquefor3DMachineVision .
0 1 0 2 . n o i t i n g o c e R n r e t t a P d n a n o i s i V ' r e t u p m o C n o e c n e r e f n o C E E E I s g n i d e e c o r P / / ] C [
] 3
[ Tsa iR .[J] .Robotics&AutomationIEEEJourna lof ,1987 ,3(4): 33 -2 344.
[4] Abdel-Aziz Y.I,Karara MH. . Urbana :UnivofIllinoisa tUrbana-Champaign ,1971.1~18. [5] Zheng- uy Zo hang. IEEETransactionsonPatternAnalysisandMachineIntelligence. 2000, 22 ( )11 :1330-1334 .
[6] MerrasM. ,AkkadN.E. ,Saaid iA. ,e tal .3DResearch ,2015 ,6(1): 1- .1 4 ]
7
[ HartleyR .Estimationofrelativecamerapositionsforuncali- rb atedcameras .In :ProcEuropean r
e g n i r p S , 8 8 5 S C L N , n o i s i V r e t u p m o C n o e c n e r e f n o
C -Verlag ,1992 .579- 73 . 8 ]
8
