1
GRAPH CUT
Chien-chi Chen
Outline
2

Introduction
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

Graph cut
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




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Concept of graph cut
Hard and smooth constrains
Min cut/Max flow
Extensive of Graph cut


Interactive segmentation
Related work
Grab cut
Paint Selection
Unsupervise graph cut
Conclusion
Reference
Outline
3

Introduction
Demo
 Related work


Graph cut
Concept of grap hcut
 Hard and smooth constrains
 Min cut/Max flow
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
Extensive of Graph cut
Grab cut
 Paint Selection
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
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Unsupervise graph cut
Conclusion
Reference
Interactive Segmentation
4
Related Work
5

Scribble-based selection
 Graph

cut
Painting-based selection
 Paint
Selection
 http://www.youtube.com/watch?v=qC5Y9W-E-po

Boundary-based selection
 Intelligent
Scissor
 http://www.youtube.com/watch?v=3LDsh3vi5fg
Outline
6

Introduction



Graph cut







Concept of graph cut
Hard and smooth constrains
Min cut/Max flow
Extensive of Graph cut


Demo
Related work
Grab cut
Paint Selection
Unsupervise graph cut
Conclusion
Reference
Concept of graph cut
7

Characteristic
 Interactive
image segmentation using graph cut
 Binary label: foreground vs. background

Interactive
 User

labels some pixels
Algorithm setting
 Hard
constrains
 Smoothness constrains

Min cut/Max flow
 Energe
minimization
Labeling as a graph problem
8
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Each pixel = node
Add two nodes F & B
Labeling: link each pixel to either F or B
F
B
Desired result
Data term
9
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
Put one edge between each pixel and F & G
Weight of edge = minus data term
 Don’t
forget huge weight for hard constraints
 Careful with sign
F
B
Smoothness term
10


Add an edge between each neighbor pair
Weight = smoothness term
F
B
Energy function
11


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Labeling: one value per pixel, F or B
Energy(labeling) = hard + smoothness

Will be minimized

E( A)    R( A)  B( A)
Hard: for each pixel
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

One labeling
(ok, not best)
Probability that this color belongs to F (resp. B)
R( A)   R p ( Ap )
pall
Smoothness (aka regularization):
per neighboring pixel pair



Penalty for having different label
Penalty is downweighted if the two
pixel colors are very different
B( A)   B{ p, q}   ( Ap , Aq )
{ p, q}N
Data
Smoothness
Min cut
12




Energy optimization equivalent to min cut
Cut: remove edges to disconnect F from B
Minimum: minimize sum of cut edge weight
http://www.cse.yorku.ca/~aaw/Wang/MaxFlowSt
art.htm
F
B
Outline
13

Introduction



Graph cut







Concept of graph cut
Hard and smooth constrains
Min cut/Max flow
Extensive of Graph cut


Demo
Related work
Grab cut
Paint Selection
Unsupervise graph cut
Conclusion
Reference
Extensive of Graph cut
14



Grab cut
E(φ,S,x, λ) = Ecol(φ,S,x) + Ecol(,S,x, λ)
Ecol ( , S , x)   D(Sn , , xn ) :Gaussian mixture model
n

1
Ecoh (S , x,  )    ( Si  S j ) exp{
|| xi  x j ||2}
2
i, jadj.
2

Image
Extensive of Graph cut
15

Paint selection
B- user brush, F- existing selection
F’- new selection, U- background
R-dilated box, L- local foreground,
dF-frontal foreground
Extensive of Graph cut
16


E(X)= E( X )   Ed ( x p )    Ec ( x p , xq )
p
p, q
Hard constrains
f
L(local foreground) to build GMM
p ()
 Background model is randomly sampling a number
(1200 points)from background to build GMM
b

 Using
p ()
Ed ( x p )  (1  x p )  K
p  S
Ed ( x p )  x p  K
p  S B
Ed ( x p )  x p  L pf  (1  x p )  Lbp p U | ( S  S B )
Extensive of Graph cut
17
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Smoothness constrains

Ec ( x p , xq ) | x p  xq | (   || I p  I q ||  )
1
  0.05,   (|| I p  I q ||2 )1

Adding frontal forground

Ed ( x p )  (1  x p )  K
p  S F
Outline
18

Introduction



Graph cut







Concept of graph cut
Hard and smooth constrains
Min cut/Max flow
Extensive of Graph cut


Interactive segmentation
Related work
Grab cut
Paint Selection
Unsupervise graph cut
Conclusion
Reference
Unsupervise graph cut
19


Automatic object segmentation with salient color
model
Saliency Map:
K
F ( x)   k f k ( x)
k 1
 xF , if F ( x)   F

x   xB , if F ( x)   B
x ,
 U
Unsupervise graph cut
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Saliency map
Unsupervise graph cut
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
Segmentation
Hard constrains


D( , , X )   H ( , x, )
x
H ( , x, )  (1   x )  Pr ob( x |  F )   x  Pr ob( x |  B )
 K-means is employed to model distribution
Pr ob( x |  F )  1/ min dis( x, F )
Pr ob( x |  B )  1/ min dis( x, B )
min dis( x,F )  min{| x  tF1 |2 ,...,| x  tFC |2}
Unsupervise graph cut
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
Smoothness constrains
B( , X )
  ( x ,  x ' ) exp( 
x x 'N ( x )

if ( x   x ' ) then   1
else   0

  arg min E( , , X )

| x  x ' |2 )
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Outline
24

Introduction



Graph cut







Concept of graph cut
Hard and smooth constrains
Min cut/Max flow
Extensive of Graph cut


Interactive segmentation
Related work
Grab cut
Paint Selection
Unsupervise graph cut
Conclusion
Reference
Conclusion
25



Interactive segmentation
Graph cut is fast, robust segmentation
It consider not only difference between source to
node, but also link of node to node.
Reference
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1.
2.
3.
4.
Lecture slide from Dr. Y.Y. Chuang.
Y. Boyjov, “An Experimental Comparison of MinCut/Max-Flow Algorithms for Energy Minimization
in Vision”, PAMI 2002.
J. Liu, J. Sun, H.Y. Shum, ”Paint Selection”, sigraph
2007.
C.C. Kao, J.H. Lai, S.Y. Chien,“Automatic Object
Segmentation With Salient Color Model”, IEEE
2011.
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Q&A