slide1 l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
A Seeded Image Segmentation Framework Unifying Graph Cuts and Random Walker Which Yields A New Algorithm PowerPoint Presentation
Download Presentation
A Seeded Image Segmentation Framework Unifying Graph Cuts and Random Walker Which Yields A New Algorithm

Loading in 2 Seconds...

play fullscreen
1 / 19

A Seeded Image Segmentation Framework Unifying Graph Cuts and Random Walker Which Yields A New Algorithm - PowerPoint PPT Presentation


  • 183 Views
  • Uploaded on

A Seeded Image Segmentation Framework Unifying Graph Cuts and Random Walker Which Yields A New Algorithm . Ali Kemal Sinop * Computer Science Department Carnegie Mellon University Leo Grady Department of Imaging and Visualization Siemens Corporate Research.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'A Seeded Image Segmentation Framework Unifying Graph Cuts and Random Walker Which Yields A New Algorithm' - havily


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

A Seeded Image Segmentation Framework Unifying Graph Cuts and Random Walker Which Yields A New Algorithm

Ali Kemal Sinop *

Computer Science Department

Carnegie Mellon University

Leo Grady

Department of Imaging and Visualization

Siemens Corporate Research

* work done while author was at Siemens Corporate Research

outline
Outline
  • Review of seeded segmentation – Graph Cuts and Random Walker
  • Our generalized framework
  • The q = ∞ case
  • Comparison
  • Conclusion
seeded segmentation review
Seeded Segmentation Review

Interactive segmentation

  • Four parts:
  • Input foreground/background pixels (seeds) from the user
  • Use image content to establish affinity (metric) relationships between pixels
  • Perform energy minimization over the space of functions defined on pixels
  • Assign a foreground/background label to each pixel corresponding to the value of the function at that pixel
seeded segmentation review graph cuts

abstraction

Seeded Segmentation Review – Graph Cuts

Graph cuts

Abstract image to a weighted graph

Compute min-cut/max-flow

44 image

44 weighted graph

3

1

2

2

1

4

S

T

5

6

1

seeded segmentation review random walker

abstraction

3

1V

1

2

2

1

4

5

6

1

Seeded Segmentation Review – Random Walker

Random Walker

Abstract image to a weighted graph

44 image

44 weighted graph

Compute probability that a random walker arrives at seed

Random walk view

Steady-state circuit view

outline6
Outline
  • Review of seeded segmentation – Graph Cuts and Random Walker
  • Our generalized framework
  • The q = ∞ case
  • Comparison
  • Conclusion
generalized seeded segmentation framework

Choice of q determines solution properties:

q = 1 Graph Cuts

q = 2 Random Walker

q =∞ ?

Generalized seeded segmentation framework

‘Algorithm A’

generalized seeded segmentation q 1
Generalized seeded segmentation: q = 1

Graph Cuts

Note: If x is binary, energy represents cut size

Unary terms implicit

generalized seeded segmentation q 2

Z

1

2

[

]

(

(

)

)

D

r

u

g

u

x

y

=

;

2

­

r

r

0

¢

g

u

=

Generalized seeded segmentation: q = 2

Random Walker

Solution to random walk problem equivalent to minimization of the Dirichlet integral

with appropriate boundary conditions.

The solution is given by a harmonic function, i.e., a function

satisfying

generalized seeded segmentation q 210

1

1

T

T

T

1

0

¡

¢

[

]

(

)

D

A

C

A

L

x

x

=

=

F

B

x

x

x

x

x

=

=

;

2

2

r

L

r

0

0

¢

g

x

u

=

=

Generalized seeded segmentation: q = 2

Random Walker

Energy functional:

Subject to boundary conditions at seed locations

Euler-Lagrange:

outline11
Outline
  • Review of seeded segmentation – Graph Cuts and Random Walker
  • Our generalized framework
  • The q = ∞ case
  • Comparison
  • Conclusion
the q case13
The q = ∞ case

Problem: Uniqueness

Multiple solutions minimize functional

Solution:

Find the solution that additionally

minimizes the (q = 2) energy

outline14
Outline
  • Review of seeded segmentation – Graph Cuts and Random Walker
  • Our generalized framework
  • The q = ∞ case
  • Comparison
  • Conclusion
comparison theoretical
Comparison - Theoretical

Metrication

q = ∞

q = 1 (Graph Cuts)

q = 2 (Random Walker)

slide16

Comparison - Quantitative

Stability relationship

slide17

Comparison - Qualitative

q = 1

(Graph Cuts)

q = 2

(Random Walker)

q = ∞

outline18
Outline
  • Review of seeded segmentation – Graph Cuts and Random Walker
  • Our generalized framework
  • The q = ∞ case
  • Comparison
  • Conclusion
conclusion
Conclusion

1) Graph Cuts and Random Walker algorithms may be seen as minimizing the same functional with respect to an L1 or L2 norm, respectively

2) The L∞ case was previously unexplored, may be optimized efficiently and produces “tight” segmentations with minimum sensitivity to seed number

More information

L∞ paper:

http://cns.bu.edu/~lgrady/sinop2007linf.pdf

Random walkers paper:

http://cns.bu.edu/~lgrady/grady2006random.pdf

Random walkers MATLAB code:

http://cns.bu.edu/~lgrady/random_walker_matlab_code.zip

MATLAB toolbox for graph theoretic image processing at:

http://eslab.bu.edu/software/graphanalysis/