Transcript Application of Gradient Vector Flow (GVF) Active Contour

Application of Gradient Vector Flow
(GVF) Active Contour in Searching
Heart Surface
Chunlei Han
Turku PET centre
March 31, 2005
Contains
• Active Contour
• Gradient Vector Flow (GVF)
• Results and Demonstration
Active Contour Models
Names: Snake, Active Contour, Deformable Model
First introduced in 1987 by Kass et al, and gained popularity since then.
Kass et al: Snakes: active contour models. International Journal of Computer Vision, 321-331, 1987
The contour is atracted to image boundares
controlled by two forces (energies)
Internal force (itself)
external force (image)
Initial line
target
Definition of active contour energy
A contour is definded as a parameter curve
v(s)  ( x( s), y( s)) where s  0,1
E  Eint ernal  Eexternal
Internal energy
Eint ernal  Eelastic  Erigid
Eelastic 
Erigid 
1
2



s
v
s ds

2s
1
2



s
v
ss ds
2 s
External energy
is defined based o image information, such image intensity, edge ect.
Internal energy
Elastic Energy is treated as an elastic rubber band possessing
elastic potential energy. Responsible for shrinking of the
contour
Rigid Energy is considered to behave like a thin metal strip
giving rise to bending energy. Bending energy is minimum for
a circle.
Solution of Active Contour (Snake)
xt  ( A  I ) 1 xt 1  f x  xt 1 , yt 1 
yt  ( A  I ) 1 yt 1  f y xt 1 , yt 1 
where
A is a pentadiagonal banded matrixand
Eexternal
Eexternal
fx 
and f y 
and
x
y
 and  are scaling factors,between 0 - 1.
External energy
1. Line- based function(image value),atractsto light or dart lines,
Eexternal  f ( x, y )
2. Edge - based function(gradient), atractsto edges
Eexernal   gradf ( x, y )
2
3. Gradient vectorflow (GVF), atractsto edges
Xu & Price: Snakes, Shape and Gradient Vector Flow. Processing Image on Transactions IEEE
1998, March, 359-369
Gradient Vector Flow (GVF)
Why need GVF
The original active contour can not move in many cases, such as
•
concavities
•
initial line is far away from object
•
initial line acrosses with object (has points inside and outside of object)
GVF field is defined as the equilibrium solution to
the following diffusion equation

    u  u  v  v   f v - f
2
x
2
y
2
x
2
2
y
2
dxdy
where v  u( x, y), vx, y 


v x, y, t    vx, y, t   vx, y, t   f x, y  f x, y   f x, y  
ut x, y, t    2u x, y, t   u x, y, t   f x x, y  f x x, y   f y x, y 
2
2
2
t
2
x
x
2
y
where  is laplaceoperatorand  is a regulationfactor,0 - 1
Xu & Prince: Snake, shape and gradient vector flow. IEEE trans image processing
1998, 7:359-369
Result and Demostration
Conclusion
GVF active contour is a useful method in
heart surface searching