) 8 1 0 2 O S M ( n o it a z i m it p O d n a n o it a l u m i S , g n il e d o M n o e c n e r e f n o C l a n o it a n r e t n I 8 1 0 2 8 7 9 : N B S
I -1-60595- 25 -1 4
c
it
a
m
o
t
u
A
n
o
d
e
s
a
B
m
h
ti
r
o
g
l
A
n
o
it
a
t
n
e
m
g
e
S
e
g
a
m
I
l
e
v
o
N
l
e
d
o
M
e
k
a
n
S
F
V
G
e
u
X -
g
a
n
g
U
H
1 2,, u
X - n
i
l U
a
Q
I
1 *,a
n
d
H
o
n
g
- g
ij
n
T
A
N
G
31CollegeofCommunicaitonandInformaitonEngineering,ChongqingUniverstiyofPostsand a n i h C , 5 6 0 0 0 4 g n i q g n o h C , s n o it a c i n u m m o c e l e T
2ResearchCenterofSystemTheoryand tisAppilcaitons,ChongqingUniverstiyofPostsand a n i h C , 5 6 0 0 0 4 g n i q g n o h C , s n o it a c i n u m m o c e l e T
3NeuLionChinaCo.,Ltd.,ChangningDistrict,Shangha i200335,China
*Correspondingauthor
: s d r o w y e
K Image segmentaiton, G ar dient vector ifeld, Snake model, SUSAN algortihm, Iniita l r u o t n o
c , Ftiitngoutsourcingpolygon.
.t c a r t s b
A Toaddressissuestha tGVFSnakemode lneedstoinitializethecontourmanuallysotha t t c e f f e e h t , d e l d n a h y l l a c i t a m o t u a e b t o n n a c n o i t a t n e m g e s e g a m
i ofsegmentationi salsorelatedt ot he
e g a m i r o f m h t i r o g l a l e v o n a , l a e d i t o n e r a l e d o m e h t f o y c a r u c c a d n a y c n e i c i f f e s t i d n a , r u o t n o c l a i t i n i e h t e c u d o r t n i e W . r e p a p s i h t n i d e s o p o r p s i l e d o m e k a n S F V G c i t a m o t u a n o d e s a b n o i t a t n e m g e s r t a l f " f o s t p e c n o
c edundan tpoint"and" fittingoutsourcingpolygon" .In ouralgorithmthediscrete . m h t i r o g l a n o i t c e t e d r e n r o c N A S U S y b d e n i a t b o t s r i f s i e g a m i t e g r a t f o t e s s t n i o p e g d e e r u t a e f , t e s s t n i o p e g d e e t e r c s i d f o n o g y l o p g n i c r u o s t u o g n i t t i f e h t g n i d n i f , y l d n o c e
S Finally,t heGVFSnake
e h t e t e l p m o c o t e v r u c r u o t n o c l a i t i n i e h t s a n o g y l o p g n i c r u o s t u o g n i t t i f e h t g n i s u y b d e v l o v e s i e v r u c r u o t n o c l a i t i n i e h t s a n o g y l o p g n i c r u o s t u o g n i t t i f e h t t a h t d e v o r p y l n o t o n s i t I . n o i t a t n e m g e s e g a m i e r e h t o t e g r e v n o c n a c e v r u
c a ltarge timage edgeby thealgorithm in theory ,bu ttheexperimenta l , y c a r u c c a n o i t a t n e m g e s e h t e v o r p m i y l e v i t c e f f e n a c m h t i r o g l a d e s o p o r p e h t t a h t w o h s o s l a s t l u s e r a e h t f o y c n e i c i f f e e h t e v o r p m i d n a , l e d o m e h t f o s n o i t a r e t i f o r e b m u n e h t e c u d e r y l t a e r
g lgorithm.
n o it c u d o r t n I e c n i
S Activecontourmodel ,orSnakemodel ,wasfirsti ntroducedbyKasse ta.li n1987[1],i thas l e d o m e k a n S f o e l p i c n i r p n i a m e h T . n o i s i v r e t u p m o c d n a s i s y l a n a e g a m i n i d e z i l i t u y l e v i s n e t x e n e e b r a d n u o b e h t d n i f o t s
i y oft argeti magebyminimizingt hecurveenergyfunction .Atraditiona lactive l e d o m r u o t n o
c isrepresentedbyanelasticcurveX(s)=(x(s) ,y(s)),s∈[0,1] , ti movest hrought hespatia l : n o i t c n u f y g r e n e g n i w o l l o f e h t e z i m i n i m o t e g a m i n a f o n i a m o d 1 t x e t n i
0(E (X(s)) E (X(s)))ds
E=
∫
+ ( 1) wheret hei nterna lenergy 2 2t n
i (X(s)) ( X (s) X (s) ) 2
E = α ′ +β ′′ ensuresthecontourcontinuousandsmooth n o i t a m r o f e d g n i r u
d . theexterna lenergyEext(X(s)) attractst hesnaket ot hedesiredi magefeatures. However ,thetraditiona lSnakemode lissensitiveto initialization ,limited to capturerange ,and
y r a d n u o b o t e c n e g r e v n o c r o o
p concavities[2 .] Todea lwitht heseproblems, manyimprovedmethods d r a w r o f t u p n e e b e v a
h [3-7]. Thegradien tvectorflow(GVF)Snake [3 ]h asarelativelargecapture s e i t i v a c n o c e m o s t c a r t x e n a c d n a e g n a
r . However ,GVF sh a difficultyinextracting targe tboundary e v r u c r u o t n o c l a i t i n i e h t n e h
w is farfrom thetarget. Moreover ,the number ofiterations increase s a e s o l c s a t e s e b d l u o h s r u o t n o c l a i t i n i e h t , e r o f e r e h T . y l t a e r g e c u d e r y c n e i c i f f e e h t d n a , y l d i p a r . r u o t n o c e u r t e h t o t e l b i s s o
p Therearesevera lmain methods of setting the initia lcontour are as s d o h t e m r e h t o ) 3 ; e c n e r e f f i d e g a m i e c n e u q e s ) 2 ; g n i t t e s e v i t c a r e t n i l a u n a m ) 1 : s w o l l o
f [8-12] . I n
o t e l b i s s o p m i n e v e r o t l u c i f f i d y r e v s i t i , s e s a c e m o
h t e m r e h t o n o d e s a b t l u s e r n o i t a t n e m g e s e h t g n i s u , t n e s e r
p odsastheinitia lcontourhasbeen oneof
d o h t e m l u f s s e c c u s t s o m e h
t . Hsu e tal .[8] used the genetic algorithm to find automatically the ,
n o i t c e t e d e c a f r o f r o t c e t e d e g d e y n n a C f o s r e t e m a r a
p andt henusethePoissonGVFmode ltoextrac t
h Z . s r u o t n o c e c a
f oue tal .[9 ]obtaine dthei nitia lsegmentationcurvebydesigningat exturedetector e
r p e h t e v o r p m i n e h t d n
a -segmentationresultsbyusinganadaptiveactivecontouralgorithm .Liu e t .
l
a [10]selectedt heappropriatet hresholdfordifferenti maget odividei ti ntot woregions:t arge tand l a i t i n i e h t s a y r a d n u o b t c e j b o m u m i x a m e h t e k a t d n a , k r a m y b s t c e j b o l l a m s e h t e v o m e r , d n u o r g k c a b
s c a v o K . e g a m i e h t t n e m g e s o t l e d o m e k a n S F V G e h t f o r u o t n o
c e ta.l [ 11 ] defined anewexterna l
e c r o
f ,they detecte d the related loca lstructure ofeach feature key point, obtaine d convex hul lof f
o r u o t n o c l a i t i n i e h t s a t e s s t n i o p e r u t a e f d e d n e t x
e snake .Moreover, eu d s the key points set ot
g n i p p a m e g d e e r u t a e f w e n e h t e t u p m o
c .They achieved a good segmentation effec twhen thetes t a
h e g a m
i d apoorcontrast ,highcurvature ,andcomplexboundaries. Zhoue ta.l [12] used theconvex t
n i o p e g d e e h t f o l l u
h s se tdetectedbySUSANoperatorast hei nitia lcontourofSnakemodel .Bu t ti e
g d e e v a c n o c e h t t a n o i t a m r o f e
d slowly ,requiresmanyi terationsandhasl essefficiency.
In thispaper ,based ontheanalysisofGVF ,anove lalgorithm forimagesegmentation based on l
e d o m e k a n S F V G c i t a m o t u
a isproposed. eW pu tforwardt heconceptsof"fla tredundan tpoint"and g
n i c r u o s t u o g n i t t i f
" polygon".Theoretica lanalysisand experimenta lresultsshowtha to urmethod y
l n o t o
n overcomest heshortcomingsofGVFeffectively ,bu talsoi mprovest heanti-noiseabilityand r
e t t e b s a
h r le -a timeperformanceandsegmentationeffectsthanotheri nitializationmethods.
F V
G SnakeModel s a w w o l f r o t c e v t n e i d a r
G proposed b Xy uandPrinceasanewexterna lforceforactivecontourmode l e
k a n s l a n o i t i d a r t e h t f o s e u s s i e h t e m o c r e v o o
t .TheGVFi savectorfieldV=(u(x,y),v(x,y))obtained o
f e h t g n i z i m i n i m y
b llowingenergyfunctiona : l
2 2
2 2 2
2 ) )
( ( )
(V λ ux uy vx vy f V f dxdy
ε = ∫∫ + + + +∇ −∇ (2) wheref istheedgemap. λisaregularizationparameter(morenoise,i ncreaseλ) .
g n i s
U thecalculusofvariations ,GVFi sobtainedbysolvingt hefollowingEulerequation:
2 2 2
2 2 2
, 0 ) (
) (
. 0 ) (
) (
y x x
y x y
f f f u u
f f f v v
λ λ
∇ − − + =
∇ − − + =
)( 3
t a h t d n u o f e b n a c d l e i f e c r o f F V G f o s i s y l a n
A the ∇f isavectort ha tdirectedt ot het ruecontour , d
l e i f e c r o f e h
t Visonthetruecontourand itsdirection pointstothetruecontour ,and theregionis [
e r u t a r e t i l e h t n i " a e r a e v i t c e f f e " n a s a d e n i f e
d 13] ,whentheinitia lcontourisse tin thisregion ,the f
o n o i t c a e h t r e d n u r u o t n o c e u r t e h t o t e g r e v n o c l l i w e v r u
c GVFfield.
F V
G expandst hecapturerangeandrelaxest herequirementsforsettingt hei nitia lcontour .Bu tthe G
f o n o i s n a p x e e h t d n a , d l e i f F V G f o e p o c s e h t n o s d n e p e d r u o t n o c f o e g n a r e r u t p a
c VFfieldi sbased
l a n o i t a t u p m o c s t i , r e v o e r o M . y l p r a h s e s a e r c n i l l i w t s o c n o i t a t u p m o c s t i , s n o i t a r e t i f o r e b m u n e h t n o
t a e r g o s l a s i y t i x e l p m o
c when theinitia lcontourisfaraway from the"effectivearea" .In addition , v
e r p o t d e m r o f e b l l i w " e g d e e s l a f
" entt hecurvefromapproachingt herea ledgebecauseoft hel oca l y
g r e n e f o m u m i n i
m .I tisobviouslytha ttheinitia lcontoursettingisdirectlyrelatedt ot heefficiency s
t l u s e r n o i t a t n e m g e s l a n i f e h t f o y c a r u c c a e h t d n a m h t i r o g l a e l o h w e h t f
o .
w e
N Automa itcGVFSnakeMo del
Int hispaper ,weuset heSUSANoperatort odetectt hepointsse toffeatureedget oformanewfitting F
V G e s u n e h t d n a , r u o t n o c e z i l a i t i n i e h t s a n o g y l o p g n i c r u o s t u
o force field to ge tthe fina limage
s e c o r p e h T . s t l u s e r n o i t a t n e m g e
Step 1:UsingSUSANcornerdetectionalgorithmtoobtain thediscretefeatureedgepointsse tof .
e g a m i t e g r a t
.t e s s t n i o p e g d e e t e r c s i d f o n o g y l o p g n i c r u o s t u o g n i t t i f e h t g n i d n i F : 2 p e t S
3 p e t
S :The GVF Snakecurveisevolved by using thefitting outsourcing polygon as theinitia l n
i n w o h s s a , n o i t a t n e m g e s e g a m i e h t e t e l p m o c o t e v r u c r u o t n o
c Figure1 .
e h T
l a n i g i r o
e g a m i
e h T
t n e m g e
s
-n o i t a
s t l u s e r
╙
╚
╛
n o i t c e t e d r e n r o c N A S U
S Featuresedgepointsset
t e s s t n i o P
, g n i l p m a s
d n a g n i n i b m o C
g n i t r o s
t a l f e h t e t e l e D
s t n i o p t n a d n u d e r
g n i t t i F
g n i c r u o s t u o
n o g y l o p
e z i l a i t i n I
f o r u o t n o c
l e d o m
e h t e t a r e t I
e k a n S F V G
e d o
m l
e t a l u c l a C
F V G e h t
d e l i f V
e t a l u c l a C
e g d e e h t
p a m f
e r u g i
F 1. AutomaticGVFSnakemodel.
N A S U
S Ed Dge eteciton t
e d N A S U
S ectionoperatori safamouscornerdetectingoperatorproposedbySmithe ta.li n1997 .I t [
t e g r a t f o r e n r o c d n a e g d e e h t t c e t e d y l e v i t c e f f e n a
c 14] .Thismethoddefinesaconcep tofeachi mage
s s a h c i h w , ) N A S U ( s u e l c u n g n i t a l i m i s s a t n e m g e s e u l a v i n u , t n i o
p ociatedwithi tal oca lareaofsimilar
h t i w t i e r a p m o c d n a e g a m i e h t n i l e x i p h c a e f o e u l a v N A S U e h t e t a l u c l a c o t s i e l p i c n i r p s t I . s s e n t h g i r b
d l o h s e r h t
a T,t hecomparedresul tcanbeusedforaj udgemen twhethert hepixeli sedgepoin.t
0 0 0
0
0 0
) , ( ) , ( 1
) , ; , (
) , ( ) , ( 0
fi fi
T y x f y x f y
x y x
C = f x y −− f x y ≤>T
( 4)
where (x0 ,y0)isthecoordinateofnucleusinimage ,(x ,y)isthecoordinateofotherpixel ,C isthe
. e u l a v y a r g f o t l u s e r n o s i r a p m o c
t r o f s e r u t a e f e m o s e r a e r e h
T heUSANvalueofeachpixel . tI takest hemaximumwhent henucleus t i ; e g d e e h t o t g n i s o l c s i s u e l c u n e h t n e h w e s a e r c e d l l i w t i ; a e r a m r o f i n u e l a c s y a r g n i s e t a c o l l e x i p
f o s c i t s i r e t c a r a h c e s e h t e s u a c e B . t n i o p r e n r o c a s i s u e l c u n e h t n e h w m u m i n i m e h t s e k a
t USANcan
t n i o p r e n r o c d n a e g d e , y l e t a r u c c a e g a m i e h t n i s r e n r o c d n a s e g d e f o n o i t i s o p e h t k r a
m s caneasilybe
. d e t c e t e
d ThethresholdTno tonlycanfiltersomenoisebu talsotakesmal lcalculatedcost .Besides t
o n s i r o t a r e p o N A S U S f o y t r e p o r p e h t , e s e h
t sensitivefort hesizeoft emplate ,andi tsparametersi s t
n e m e l p m i y l i s a e n a c t i d n a , e s o o h c o t y s a
e automatically .
e h
T Deifni itono fF tl Ra edundan tPoin tandFtiitngOutsourcingPolygon n
o it i n if e
D 1Le tPi-1 ,PiandPi+1aret hreepointsi nt heplanet ha tdono tcoincidewitheachother .If
e l g n a f o e u l a v e h
t θbetweent hevectors PiPi−1
dan PiPi+1
f o e g n a r e h t n i h t i w s
i Tθandπ,t hent hepoin t
Piisconsideredt oafla tredundan tpoin tcorrespondingt oTθ.
n
I definition1 ,Tθisusuallygreatert hanorequalt o5π/6toensurethefittingeffect .Avectordo t
a s i t n i o p a r e h t e h w e n i m r e t e d o t d e s u s i d o h t e m t c u d o r
p fla tredundan tpoint .Takeany poin tPi ,
t n i o
p s Pi-1andPi+1 ea r beforeandafteradjacen tpoin tofPi, respectively .Asshowni nFigure2 . iP
iP-1 θ P+i1
2 e r u g i
e l g n a e h
T θbetweent hevectors PiPi−1
da n PiPi+1
: ) 5 ( n o i t a u q e g n i w o l l o f s a d e t a l u c l a c s
i
1 1
1 1 s o c c r
a i i i i
i i i i
P P P P
P P P P
θ − +
+ −
⋅ =
)( 5
Thefollowingj udgmen tformulaisusedtoensureθiswithint herangeofTθandπ.
, s o c s o c , 1
. s o c s o c , 0
T C
T
θ
θ
θ θ
≤
= >
)( 6
whereCist heresultsoft hej udgment ,1meansPiist hefla tredundan tpoint ,and0meansno.t 2
n o it i n if e
D Givenapointsse tM,t hepointsPi (i=1 ,2,. .. ,m ,wheremist henumberofelementsof
M)areconnectedi nacounterclockwiseordert oformaclosedpolygonL .Accordingt ot hedefinition n
o g y l o p e h t n o s t n i o p t n a d n u d e r t a l f e h t e v o m e r o t
1 L ,maintaint heorigina lorderoft heconnection
andobtainanewclosedpolygon ,whichi scalledfittingoutsourcingpolygon.
Accordingt ot hel iterature[13],i tcanbeseent ha tnomatterhowcomplext het ruecontoursoft he i
g e r n i a t r e c n i r u o t n o c e u r t e h t o t l a c i t r e v s i d l e i f e c r o f F V G e h t , e r a e g a m
i ons .Ift hei nitia lcontouri s
n a c e W . d l e i f e c r o f F V G e h t y b r u o t n o c e u r t e h t o t e g r e v n o c n a c e v r u c e h t , " a e r a e v i t c e f f e " e h t n i t e s
t a h t e v o r
p thecurvecanconvergest ot herea lcontouraccuratelywhenusingthe"fittingoutsourcing "
n o g y l o
p whichdefinedi nt hispaperast hei nitia lcontourcurve.t hef ollowingt heoremsareobtained: .
1 m e r o e h
T Usingt hef ittingoutsourcingpolygonoft heedgepointsse tast hei nitia lcontourcurve r
u c s i h t t a h t e r u s n e n a c t i , e g a m i n a t n e m g e s o t l e d o m e k a n S F V G e h t f
o ve converges to the true
. e g a m i e h t f o r u o t n o c
:f o o r
P Le tthe X-direction sampling precision of the edgefeature points se tS be p pixels ,the e
h t n i y c a r u c c a g n i l p m a
s Y-directioni sqpixels ,10≤p ,q≤15,t heboundarypointsse taftersamplingi s
M ,Piist heelementi nM .Accordingt ot herequirementsofdefinition1,t hepointsse tafterremoving
n i s t n i o p t n a d n u d e r t a l f e h
t MiscalledQ ,andt hef ittingoutsourcingpolygoni sf ormedbyconnecting
Qincounterclockwiseorder. t
a h t g n i m u s s
A Pi-1 ,Pi ,Pi+1aret het hreeadjacen tpointsi nM(theydono tcoincidewitheachother) ,
f
i Piisno tafla tredundan tpoint ,keept hispoin tandobtaint hefittingstraight-linesPiPi-1 ,PiPi+1; if
Piisafla tredundan tpoint ,removei tandgett hefittingstraight-linePi-1Pi+1 .Theset wocasescanbe
. y l e v i t c e p s e r s d o h t e m g n i w o l l o f e h t y b d e t a r t s n o m e d
t h g i a r t s g n i t t i f e h T )
1 -linesarePiPi- 1andPiPi+1 .SincepointsPi-1 ,Pi ,Pi+1belongtothese tR ,i t
t a h t s n a e
m Piisont herea lcontour .Therefore,PiPi- 1andPiPi+1arel ocatedi nt he“effectivearea".
t h g i a r t s g n i t t i f e h T )
2 -linei sPi-1Pi+1 .Wej us tneedt oprovet hatt hedistancefromPi toPi-1Pi+1 is
i t c e f f e " f o e g n a r e h t n i h t i
w vearea" .Fromt hedefinition1wecanseet ha tθ�[Tθ,π] ,andt hesampling
n o i s i c e r
p a rep dan qrespectively ,so 2 2 1
1 i 2
i P p q
P− + ≤ +
e l g n a i r t e h t n I
. Pi-1PiPi+1,l ett hel engthof
Pi-1 Pi+1 is a .I tcan beseen fromFigure3 tha twhen a isfixed ,the valueof d increaseswith the
f o e s a e r c e
d θ .When θisthesameand Piisin thecenterlineof Pi-1Pi+1 ,d obtains themaximum
m o r f n e e s e b n a c t I ; e u l a
v Figure4t ha twhenθisfixed,t hevalueofdincreasesasabecomingl arger . e
c n a t s i d e h t , e r o f e r e h
T d between Pi and Pi-1 Pi+1ismaximized when θ takes theminimumand a
d n a m u m i x a m e h t s e k a
t Piisi nt hecenterl ineofPi-1Pi+1.
d
a θ1
θ4 θ3 θ2
a θ θ
θ
i P
i
P -1 Pi+1
d θ
d e g n a h c n u n i a m e r a f o h t g n e L . 3 e r u g i
F . Figure4 .Angleθremainsunchanged. Figure5 .distancefrompointt ol ine.
n i n w o h s s a , e c n e
1
1 2
) 2 / ( n a t
/
i i P P
d
θ + −
= )( 7
n e h w n e h
T θ=150° ,a=30 2 ,p=15 ,q=15 ,d takethemaximum ,d=5.68 .Because d∈(0 ,5.68) ,
g n i t t i f " e h t h t i W . d l e i f e c r o f F V G e h t f o " a e r a e v i t c e f f e " e h t n i s i e v r u c " n o g y l o p g n i c r u o s t u o g n i t t i f "
n o g y l o p g n i c r u o s t u
o " astheinitia lcurveand using GVF forcefield for curve evolution ,i tcan be d
e h s i n i f f o o r P . y l l a u t n e v e r u o t n o c e u r t e h t o t s e g r e v n o c e v r u c e h t t a h t d e e t n a r a u
g .
m h ti r o g l
A Descrip iton
p e t
S 1 :Obtaint hedatacoordinatesandnumbernoft hediscretefeaturepointsse.t p
e t
S 2:X-directionsampling .Att hef irs,tf indt hemaximumandminimumpointsoft heX-direction :
t e s s t n i o p e t e r c s i d d e n i a t b o e h t n i e t a n i d r o o
c x_max ,x_min .Divideal lthepointsinto mxintervals r
i e h t f o e z i s e h t o t g n i d r o c c
a X coordinates ,wheremx=(x_max−x_min) pand p is the sampling e
h t f o s t n i o p m u m i n i m d n a m u m i x a m e h t d n i f n e h T . h t d i
w Y-directioncoordinatein theinterva li ,
d e l l a c e r a y e h
t k[i].minyandk[i].maxyrespectively ,wherei=1,2,3,…,mx ,Asshowni nFigure6 .For convenience ,thepoin tin Figure6 is actually apixel .Finally ,extremepointsk[i].miny, k[i].maxy,
n i m _
x dan x_maxinofeachi nterva larestoredi nt hecoordinatearraypoint_Xsampilng[ ]. e
h t n i g n i l p m a S : 3 p e t
S Y-direction likestep 2 .Find the maximum and minimum pointsofthe
Y-directioni nt heobtaineddiscretepointsset:y_minandy_max,t hesamplingwidthi sq ,andsampled y
a r r a e t a n i d r o o c e h t n i d e r o t s e r a s t n i o
p point_Ysampilng[] .Thesamplingresultsareshowni nFigure .
7
n i m _ X
x a m _ X y
n i m . ] 1 [
K K[2].miny y n i m . ] 3 [ K
y n i m . ] x m [ K
y x a m . ] 1 [ K
y x a m . ] 2 [ K
y x a m . ] 3 [ K
y x a m . ] x m [ K
Ă Ă
n i m _ Y
x a m _ Y
x x a m . ] 1 [ K
x x a m . ] y m [ K
x x a m . ] 3 [ K
x x a m . ] 2 [ K x
n i m . ] 1 [ K
x n i m . ] y m [ K
x n i m . ] 3 [ K
x n i m . ] 2 [ K
n o i t c e r i d X e h t n o t e s t n i o p e l p m a S . 6 e r u g i
F . Figure7 .Samplepointsse tont heYdirection.
y a r r a n i t a h t s t n i o p e h t t r o S . 3 d n a 2 s p e t s f o s t l u s e r g n i l p m a s e h t e n i b m o C : 4 p e t
S point_
g n il p m a s
X []andarraypoint_Ysampilng[]andstoret hemi nto arraypointAll[] ,asshown in Figure8 , t
e s a p u e k a m s t n i o p g n i l p m a s l l a e r e h
w M .Accordingtotheformula(8) ,wecanfindthecenterof n
o i t i s o p s s a
m P(x0,y0)ofpointsset .Theredandbluedotscoincidewitheachotherpartiallyi nFigure
o t ,l a t n e d i c n i o c e r a y e h t t a h t s n a e m t i ,
8 facilitate et h observation ,representedbypartia lcoincidence.
0
) , (
1
M y x
x x
n ∈
=
∑
0) , (
1
M y x
y y
n ∈
=
∑
( 8)wherenist henumberofpoints.
n i m _ Y
x a m _ Y n
i m _ X
x a m _ X ) 0 y , 0 x ( P
n i m _ Y
x a m _ Y n i m _ X
x a m _ X
X
Y
t s r i f e h T
t n a r d a u q
h t r u o f e h T
t n a r a u q d
r i h t e h T
t n a r d a u q
P α
d n o c e s e h T
t n a r d a u q
) 0 y , 0 x ( P r e t n e c y r a b d n a M t e s s t n i o p d e l p m a S . 8 e r u g i
s s a m f o r e t n e c e h t g n i k a T : 5 p e t
S P(x0 ,y0)asvirtua loriginofcoordinate,t hei magei sdividedi nto
n i n w o h s s a , s t n a r d a u q r u o
f Figure9 .Points ofeach quadran tare connected in counterclockwise a
x e n a s a t n a r d a u q t s r i f e h t g n i k a T . y l e v i t c e p s e r , r e d r
o mple ,pointsoft hefirs tquadran tarese tasA1,
A2, A3 ,…, Am .Thepoin tPisusedast hestartingpoint ,vectorsPA1 ,PA2 ,PA3 ,… ,PAmconsis tofP
n a t t n e g n a t r a l u g n a e h t e t a l u c l a c o t t n a r d a u q t s r i f f o s t n i o p r e h t o d n
a αofeachvector .Accordingt ot he
f o e z i
s tanαindescendingorder ,whent hesizeoftanαissame ,onlyoneoft hemi sretained ,andal l s t n i o P . e c n e u q e s w e n a m r o f o t r e d r o e s i w k c o l c r e t n u o c e h t n i d e n i a t b o s i t n a r d a u q t s r i f f o s t n i o p e h t
p m o c e r a s t n a r d a u q h t r u o f d n a d r i h t , d n o c e s f o t e
s letedi nt hecounterclockwiseorderi nt urnt oobtain :
e c n e u q e s w e n
a K1, K2, K3, K4 .Pointsi neachquadran tareconnectedi nt heorderofsequencesK1,
K2, K3, K4 ,andconnectingthestartingpointsandendpointsoffirs tandsecondquadrants ,second n
a dt hirdquadrants,t hirdandfourthquadrantst oobtainaclosedpolygon ,asshowni nFigure1 0. :
6 p e t
S To determinewhether theintermediatepoin tofthreeadjacen tpoints is afla tredundan t t
n i o
p bydefinition 1,i fyes ,deletei t .Thus ,anewpointsse tQisobtained ,andQisasubse tofM .The f
o s t n i o p g n i t c e n n o c y b d e n i a t b o n o g y l o
p Qincounterclockwiseorderisusedastheinitia lcontour n
i n w o h s s A . e v r u
c Figure1 1.
n i m _ Y
x a m _ Y n i m _ X
x a m _ X
X
Y P
t s r i f e h T
t n a r d a u q e
h T
d n o c e s
t n a r d a u q
d r i h t e h T
t n a r d a u q
h t r u o f e h T
t n a r a u q
n i m _ Y
x a m _ Y n i m _ X
x a m _ X
X
Y P
t s r i f e h T
t n a r d a u q
h t r u o f e h T
t n a r a u q d
r i h t e h T
t n a r d a u q
e h T
d n o c e s
t n a r d a u q
. 0 1 e r u g i
F Sor tandconnec tRwithclockwise. Figure11 .Initia lcontourcurve.
l a n o it a t u p m o
C Complextiy
g n i z y l a n
A thet imecomplexityofo urmodel ,iti sfoundt hatt het imeofalgorithmi smainlyusedt o d
n i
f thei nitia lcontour ,calculateGVFf orcef ieldandevolutionoft hecontourcurve.I nouralgorithm , A
S U S f o y t i x e l p m o c e m i t e h
t Nedgedetectionalgorithmandfittingoutsourcingpolygonalgorithm e
r
a O(mn) da n O(n)respectively (nisthenumberofelements in points set) .In addition ,sincethe i
n
i tia lcontourofourmethodiscloset ot het ruecontour,i ti sknownf romt heorem1thatt heirdistance t
s u
j abou tsevera lpixels .Therefore ,required GVF field capture rangeis relatively small ,and the e
c n e g r e v n o c e h t d n a d l e i f F V G f o s n o i t a r e t i f o r e b m u
n timeofcontoursarereducedcorrespondingly .
t ,l e d o m e k a n s F V G l a n i g i r o e h t n
I henumberofi terationsofGVFfieldV isaboutt enst ohundreds , e
h t d n
a evolutionoft hecontourcurvei saboutt enst ohundreds .B utint hispaper ,calculati ngvector w
o l
f fieldjustneedseveralt odozensoft imes,t heevolutionofthecontourcurveist enst ohundreds . c i t a m o t u a e h t , n o i t c a r e t n i l a u n a m y b e v r u c r u o t n o c l a i t i n i e h t g n i t t e s f o s m h t i r o g l a h t i w d e r a p m o C
a i t i n
i lizingcontourcurvealgorithmofthispaperi smoreefficient .Insummary,t heproposedmethod n
i t n e m e v o r p m i t n a c i f i n g i s a s a
h convergenceefficiencyt hanorigina lGVFSnakemode.l
l a t n e m i r e p x
E Resu tl sandAnalyssi t
c e s s i h t n
I ion ,weshowtheperformance oft heproposedmethodbypresentingexamplesonvarious d
n a c i t e h t n y
s realimage ,al lexamplesarei mplementedi nWindowsMicrosof tXPsystem ,machine .t
n e m n o r i v n e a 9 0 0 2 R b a l t a M n o d e s a b d n a y r o m e m B G 2 , 0 3 4 E D A P K N I H T
, y l t s r i
F acomparativeanalysisisperformedonsyntheticimagewithU-shaped inFigure1 2. T he r
e t e m a r a
p ofGVFi sλ=0.2 ,andt henumberofi terationsofvectorflowfieldi s30.Figure12(a)i st he ,
e g a m i l a n i g i r
o Figure1 2(b)i st hei nitia lcontourwhichse tbyartificia lway,Figure12(c)showst he u
n s t i d n a , l e d o m e k a n S F V G f o t l u s e
r mberofiterationsis40 .Figure1 (d2 )istheinitia lcontourof e
h t y b d e n i a t b o s i h c i h w n o g y l o p g n i c r u o s t u o g n i t t i
n w o h
s i nFigure1 (e2 )andi ti si terated20t imes .Theexperimentalr esultsshowt hatt heinitia lcontour y
b d e n i a t b
o proposed algorithm is closer to the true contour of the image ,so tha tthe number of f o e s a c e h t n i y l s u o i v b o d e v o r p m i s i e c n e g r e v n o c f o t c e f f e e h t d n a , y l t a e r g d e c u d e r s i s n o i t a r e t i
. n o i s s e r p e d
( )a (b) (c) (d) ( e) e
r u g i
F 1 . 2 Experimentsoni mageU.
, y l d n o c e
S thel eafi magei st estedi nFigure13.t heparameterofGVFisalsoλ=0.2 ,andt henumber .
0 1 s i d l e i f w o l f r o t c e v f o s n o i t a r e t i f
o Figure13(a)istheorigina limageofleaf ,Figure13(b)isthe r
u o t n o c l a i t i n
i whichse tbyartificia lway ,Figure13(c)showst heresul tofGVFSnakemodel ,andi ts s
i s n o i t a r e t i f o r e b m u
n 100 .thei nitia lcontouroffittingoutsourcingpolygonandresul toft hispaper n
i n w o h s e r
a Figure13(d)a )nd( e respectively ,iti si terated40t imes.Asshowni nFigure13 ,wecan e
l d n a
h imagesegmentation automatically ,and no tonly reducethenumberofiterationsgreatly,bu t n
a c o s l
a converget odetailsofimagewel.l
( )a (b) (c) (d) ( e) e
r u g i
F 1 . 3 Experimentsonl eafi mage.
Finally ,Figure14 shows experimenta lresultstested on flower image .the parameter of GVF i s s
n o i t a r e t i f o r e b m u n e h t d n a , 5 2 . 0 =
λ ofvectorflowis25.Figure14(a)i st heoriginali mageofflower , u
g i
F r 14e (b)istheinitia lcontourwhichse tbyartificia lway ,Figure14(c)showstheresul tofGVF .l
e d o m e k a n
S thei nitia lcontouroffittingoutsourcingpolygonandresul tofthispaperareshown in e
r u g i
F 14(d) a )nd ( e respectively .Asshown in Figure1 ,4 the contour curve can converge to the l
l e w s l a t e p e h t n e e w t e b n o i s s e r p e
d ,ouralgorithmi mprovest hesegmentationaccuracygreatly.
( )a (b) (c) )(d ( e) e
r u g i
F 1 . 4 Experimentsonfloweri mage.
n o is u l c n o C
F V G c i t a m o t u a n o d e s a b n o i t a t n e m g e s e g a m i r o f m h t i r o g l a l e v o n a d e s o p o r p e v a h e w , r e p a p s i h t n I
g d e e h t t c e t e d o t m h t i r o g l a N A S U S s e s u m h t i r o g l a s i h T . l e d o m e k a n
S eoftheimage ,andcalculates
e g d e l a i t i n i e h t s a d e s u s i h c i h w , y l l a c i t a m o t u a s t n i o p e g d e g n i l p m a s e h t r o f n o g y l o p g n i t t i f e h t
g n i t t i f e h t t a h t d e v o r p y l n o t o n e v a h e W . e g a m i e h t f o n o i t a t n e m g e s c i t a m o t u a e h t e z i l a e r o t r u o t n o c
e h t s a n o g y l o p g n i c r u o s t u
o initia lcontourcan convergeto therea ltarge tedgeoftheimagebythis t
a h t w o h s o s l a s t l u s e r l a t n e m i r e p x e e h t d n a , y r o e h t n i m h t i r o g l
a the"fitting outsourcing polygon"
y l t n a c i f i n g i s d e v o r p m i n e e b s a h a e r a n o i s s e r p e d e t a c o l f o y t i l i b a e h t s e k a
. y l s u o i v b o y c a r u c c a d n a y c n e i c i f f e n o i t a t n e m g e
s Att hesamet ime ,theconvergencet imeoft heGVF
. y l t a e r g d e c u d e r s i l e d o m e l o h w e h t f o s n o i t a r e t i f o r e b m u n e h t d n a d l e i f
s t n e m g d e l w o n k c A
n a v d A d n a c i s a B e h t y b d e t r o p p u s y l l a i t r a p s i r e p a p s i h
T ced Research Projec tofCQCSTC (Gran t
) 7 3 0 0 X B j y c j 7 1 0 2 c t s c : o
N .
s e c n e r e f e R
M s s a K ] 1
[ . ,WitkinA. ,TerzopoulosD .Snakes :Activecontourmodels[J] .Internationa lJourna lof 1
2 3 : ) 4 ( 1 , 8 8 9 1 , n o i s i V r e t u p m o
C -331.
[2] Chen L.C. ,Niu Y.M. ,Pan L.H. ,e tal .Research advances on Snake model [J] .Application ,
s r e t u p m o C f o h c r a e s e
R 2014 ,31(7):1931-1936.
[3]XuC. ,PrinceJ.L .Snakes ,shapesandgradien tvectorflow[J] .IEEETransImageProcess ,1998 , 9
5 3 : ) 3 ( 7
1 –369.
[4] ZhuS. ,GaoR .Anove lgeneralizedgradien tvectorflowsnakemode lusingminima lsurfaceand t
n e n o p m o
c -normalizedmethodformedicali magesegmentation[J] .Biomedica lSigna lProcessing& :
6 2 , 6 1 0 2 , l o r t n o
C 1- .1 0
[5] Zhou X. ,Wang P. ,Ju Y. ,e tal .A New Active Contour Mode lBased on Distance-Weighted F
l a i t n e t o
P ield[J] .CircuitsSystems&Signa lProcessing ,2016 ,35(5):1729-1750.
[6]ZhangR ,ZhuS ,ZhouQ .ANove lGradien tVectorFlowSnakeMode lBasedonConvexFunction .
6 5 7 1 : ) 0 1 ( 6 1 , 6 1 0 2 , s r o s n e S . ] J [ n o i t a t n e m g e S e g a m I d e r a r f n I r o f
[7]LiuG.P. ,ZhouZ. ,ZhongH. ,e tal .Gradien tdescen twithadaptivemomentumforactivecontour s
l e d o
m [J] .ComputerVision ,IET ,2014 ,8(4) :287-298.
[8] Hsu C.Y. ,WangH.F. ,WangH.C. ,e tal .Automaticextraction offacecontoursin imagesand s
o e d i
v [J] .FutureGenerationComputerSystems ,2012 ,28(1) :322-335.
[9]ZhouH. ,ZhengJ. ,We iL .Textureawarei magesegmentationusinggraphcutsandactivecontours 9
1 7 1 : ) 6 ( 6 4 , 3 1 0 2 , n o i t i n g o c e R n r e t t a P . ] J
[ -1733.
1
[ 0]LiuC.C. ,Tsa iC.Y. ,Tsu iT.S. ,e tal .Ani mprovedGVFsnakebasedbreas tregionextrapolation s
m a r g o m m a m l a t i g i d r o f e m e h c
s [J] .Exper tSystemswithApplications ,2012 ,39(4) :4505-4510. 1
[ 1] Kovacs A. , Szirany i T . Harris function based active contour externa l force for image n
o i t a t n e m g e
s [J] .PatternRecognitionLetters ,2012 ,33(9) :11 -80 1187. ]
2 1
[ ZhouY. ,ChengX. ,LuoJ. ,e tal .Automaticsnakesmode lbasedonmodifiedGVF[J] .Journa lof
2 1 0 2 , s c i h p a r G & e g a m
I ,17(2) :256- 226
�
] 3 1
[ Fan Y.B. ,Liu C.X. ,JiaS.Y. ,e tal .TheResearch ofContourInitialization Algorithmin GVF l
e d o M e k a n
S [J] .Journa lofImage&Graphics ,2008 ,13(1): 85 - .6 3 S
h t i m S ] 4 1
[ .M. ,Brady J.M . SUSAN—a new approach to low leve l image processing J[ .] 5
4 : ) 1 ( 3 2 , 7 9 9 1 , n o i s i v r e t u p m o c f o l a n r u o j l a n o i t a n r e t n