Application of Gradient Vector Flow (GVF) Active Contour in Searching

Heart Surface

Chunlei Han

Turku PET centreMarch 31, 2005

Contains

• Active Contour

• Gradient Vector Flow (GVF)

• Results and Demonstration

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)

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.

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

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

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

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)

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

Result and Demostration

Conclusion

GVF active contour is a useful method in heart surface searching