application of gradient vector flow (gvf) active contour in searching heart surface chunlei han...
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Application of Gradient Vector Flow (GVF) Active Contour in Searching
Heart Surface
Chunlei Han
Turku PET centreMarch 31, 2005
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Contains
• Active Contour
• Gradient Vector Flow (GVF)
• Results and Demonstration
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Active Contour ModelsNames: 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
Initial line target
The contour is atracted to image boundares controlled by two forces (energies)
Internal force (itself)external force (image)
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Internal energy
s
selastic dsvsE2
2
1
s
ssrigid dsvsE2
2
1
rigidelasticernal EEE int
externalernal EEE
, ssysxv(s)
int
10 where))(),((
External energy
A contour is definded as a parameter curve
Definition of active contour energy
is defined based o image information, such image intensity, edge ect.
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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 .
Internal energy
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Solution of Active Contour (Snake)
1.-0between factors, scaling are and
and and
andmatrix banded nalpentadiago a is
where
,)(
,)(
1111
1111
y
Ef
x
Ef
A
yxfyIAy
yxfxIAx
externaly
externalx
ttytt
ttxtt
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edges toatracts (GVF), flowector Gradient v 3.
),(
edges toatracts ,(gradient)function based-Edge 2.
),(
lines,dart or light toatracts value),(imagefunction based-Line 1.
2yxgradfE
yxfE
exernal
external
External energy
Xu & Price: Snakes, Shape and Gradient Vector Flow. Processing Image on Transactions IEEE1998 ,March, 359-369
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Gradient Vector Flow (GVF)Why need GVFThe 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)
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dxdyffvvuu yxyx
222222 -v
GVF field is defined as the equilibrium solution to the following diffusion equation
1-0 factor, regulation a is andoperator laplace is where
,,,,,,,,,
,,,,,,,,,222
222
yxfyxfyxftyxvtyxvtyxv
yxfyxfyxftyxutyxutyxu
yxxt
yxxt
yxvyxu ,),,( vwhere
Xu & Prince: Snake, shape and gradient vector flow. IEEE trans image processing 1998 ,7:359-369
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Result and Demostration
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Conclusion
GVF active contour is a useful method in heart surface searching