3D Segmentation Using Level Set Methods Zsolt Husz Heriot-Watt University, Mokhled Al-Tarawneh Edinburgh, Scotland Ízzet Canarslan University of Newcastle upon Tyne, Istanbul Technical University, England Turkey Péter Horváth University of Szeged, Hungary Sebahattin Topal Middle.
Download ReportTranscript 3D Segmentation Using Level Set Methods Zsolt Husz Heriot-Watt University, Mokhled Al-Tarawneh Edinburgh, Scotland Ízzet Canarslan University of Newcastle upon Tyne, Istanbul Technical University, England Turkey Péter Horváth University of Szeged, Hungary Sebahattin Topal Middle.
Slide 1
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 2
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 3
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 4
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 5
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 6
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 7
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 8
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 9
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 10
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 11
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 12
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 2
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 3
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 4
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 5
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 6
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 7
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 8
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 9
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 10
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 11
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?
Slide 12
3D Segmentation
Using
Level Set Methods
Zsolt Husz
Heriot-Watt University,
Mokhled Al-Tarawneh Edinburgh, Scotland
Ízzet Canarslan
University of Newcastle upon Tyne,
Istanbul Technical University,
England
Turkey
Péter Horváth
University of Szeged,
Hungary
Sebahattin Topal
Middle East Technical University,
Ankara, Turkey
3D Segmentation Using
Level Set Methods
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)
Gradient
Initialization
Narrow Band
Visualisation /
Post-processing
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
[Kass, Witkin, Terzopoulos ’88]
E () EInt () EExt ()
1
2
2
EInt () ' ( s ) ' ' ( s ) ds
0
EExt () I
Problems:
• Initialization
• Topological changes
• 3D implementation
2
Level-Set methods
[Osher and Sethian ‘88]
Embed the contour to a higher dimension space level
set function: .
E ( ) L( ) A( ) E Ext ( )
E
E
1
Ext
2
Ext
0
( ) N I ( p ) dp
( ) 1
( I ( p ) 1 )
2
2
1
2
dp 2
( I ( p) 2 )
2
2
2
2
dp
Level set extension to 3D
The contour moves in a 3D space (3)
E ( ) S ( ) V ( ) E
1
Ext
( )
Energy minimization: Gradient Descent Method
local optimization
E ( )
t
E ( )
t
S ( )
t
V ( )
I
I I xx I yy I zz
2
t
2
E
1
Ext
t
( )
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?