3D Segmentation3D Segmentation Using Using

Level Set MethodsLevel Set Methods

Heriot-Watt University, Edinburgh, Scotland

Zsolt  Husz

Mokhled  Al-Tarawneh Ízzet  Canarslan

University of Newcastle upon Tyne, England

Istanbul Technical University, Turkey

Péter  Horváth Sebahattin  TopalUniversity of Szeged,

Hungary Middle East Technical University,

Ankara, Turkey

Input: Medical and/or other images

Operation: Compute gradient image. Define a transform,

for example polar, a cost function, for example

circumference and gradient. Minimize path in

transformed data by cost minimization. Alternative, use

a snake for example using Greedy algorithm. The

object is to find an algorithm to link the points

identified on a gradient map to give continuous

enclosing contours. Think out extension to 3d

Output: Contour (with image)

3D Segmentation Using 3D Segmentation Using Level Set MethodsLevel Set Methods

Initialization

Gradient

Visualisation / Post-processing

Narrow Band

Reinitialisation Level Set

• Browse between images• Initialize a sphere• Initialize a region in a slice• Replicate or clear region• Starting process• End program

Active Contours

)()()( ExtInt EEE

Problems:

• Initialization

• Topological changes

• 3D implementation

2

1

0

22

)(

)('')(')(

IE

dsssE

Ext

Int

[Kass, Witkin, Terzopoulos ’88]

Level-Set methods

Embed the contour to a higher dimension space level set function: .

dppI

dppI

E

dppINE

EALE

Ext

Ext

Ext

22

22

221

21

12

1

2

))((

2

))(()(

)()(

)()()()(

0

[Osher and Sethian ‘88]

Level set extension to 3DThe contour moves in a 3D space (3)

Energy minimization: Gradient Descent Methodlocal optimization

)()()()( 1 ExtEVSE

t

E

t

V

t

S

t

E Ext

)()()()( 1

It

E 2)(

zzyyxx IIII 2

Visualisation

• Interface between algorithms: 3D matrix volume

• 3D volume matrix• Conversion to VRML → flexibility Two approaches:

• triangular mesh• marching cubes

Examples:

Conclusions• Pros

– noise prone– 3D segmentation is natural– isolated components are permitted

• Cons– LS is parameterised– LS slower than 3D snakes– processing resources (CPU, memory)

• Future work– automatic parameter adjustment– multi-scale processing– combined intensity and edge based segmentation

References[1] S. Osher and J. A. Sethian, “Fronts propagating with curvature

dependent speed: Algorithms based on Hamilton-Jacobi formulations”, J. Comp. Phys., vol. 79, pp.12–49, 1988

[2] M. Kass, A. Witkin, and D. Terzopoulos. Snakes, “Active Contour Models”, International Journal of Computer Vision 1(4), pp.321–331, 1988

[3] T. Chan and L. Vese, “An Active Contour Model without Edges” in SCALE-SPACE ’99: Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision, pp. 141–151, Springer-Verlag, 1999

[4] C. Xu and J. L. Prince, “Snakes, Shapes, Gradient Vector Flow”, IEEE Transactions on Image Processing, Vol. 7, no. 3, pp. 359-369, 1998

Thank you for your attention

Questions?