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GRAPH CUT

Chien-chi Chen

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Outline Introduction

Interactive segmentation Related work

Graph cut Concept of graph cut Hard and smooth constrains Min cut/Max flow

Extensive of Graph cut Grab cut Paint Selection

Unsupervise graph cut Conclusion Reference

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Outline Introduction

Demo Related work

Graph cut Concept of grap hcut Hard and smooth constrains Min cut/Max flow

Extensive of Graph cut Grab cut Paint Selection

Unsupervise graph cut Conclusion Reference

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Interactive Segmentation

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Related Work

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

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Outline Introduction

Demo Related work

Graph cut Concept of graph cut Hard and smooth constrains Min cut/Max flow

Extensive of Graph cut Grab cut Paint Selection

Unsupervise graph cut Conclusion Reference

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Concept of graph cut

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

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Labeling as a graph problem Each pixel = node Add two nodes F & B Labeling: link each pixel to either F or B

F

B

Desired result

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Data term

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

B

F

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Smoothness term

Add an edge between each neighbor pair Weight = smoothness term

B

F

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Energy function Labeling: one value per pixel, F or B Energy(labeling) = hard + smoothness

Will be minimized

Hard: for each pixel Probability that this color belongs to F (resp. B)

Smoothness (aka regularization): per neighboring pixel pair Penalty for having different label Penalty is downweighted if the two

pixel colors are very different

One labeling(ok, not best)

Data

Smoothness

( ) ( ) ( )E A R A B A

( ) ( )p pp all

R A R A

{ , }{ , }

( ) ( , )p q p qp q N

B A B A A

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Min cut

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/MaxFlowStart.htm

B

F

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Outline Introduction

Demo Related work

Graph cut Concept of graph cut Hard and smooth constrains Min cut/Max flow

Extensive of Graph cut Grab cut Paint Selection

Unsupervise graph cut Conclusion Reference

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Extensive of Graph cut

Grab cut E(φ,S,x, λ) = Ecol(φ,S,x) + Ecol(,S,x, λ) :Gaussian

mixture model

22, .

1( , , ) ( ) exp{ || || }

2coh i j i j

i jadjE S x S S x x

( , , ) ( , , )col n nn

E S x D S x

Image

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Extensive of Graph cut

Paint selection

B- user brush, F- existing selection F’- new selection, U- backgroundR-dilated box, L- local foreground, dF-frontal foreground

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Extensive of Graph cut

E(X)= Hard constrains

Using L(local foreground) to build GMM Background model is randomly sampling a

number (1200 points)from background to build GMM

( )fp

( )bp ( ) (1 )

( )

( ) (1 ) | ( )

d p p

Bd p p

f b Bd p p p p p

E x x K p S

E x x K p S

E x x L x L p U S S

,( ) ( ) ( , )d p c p q

p p qE X E x E x x

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Extensive of Graph cut

Smoothness constrains

Adding frontal forground

1

2 1

( , ) | | ( || || )

0.05, (|| || )

c p q p q p q

p q

E x x x x I I

I I

( ) (1 ) d p pE x x K p S F

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Outline Introduction

Interactive segmentation Related work

Graph cut Concept of graph cut Hard and smooth constrains Min cut/Max flow

Extensive of Graph cut Grab cut Paint Selection

Unsupervise graph cut Conclusion Reference

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Unsupervise graph cut

Automatic object segmentation with salient color model

Saliency Map: 1

( ) ( )K

k kk

F x f x

, ( )

, ( )

,

F F

B B

U

x if F x

x x if F x

x

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Unsupervise graph cut

Saliency map

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Unsupervise graph cut Segmentation Hard constrains

K-means is employed to model distribution

( , , ) ( , , )x

D X H x

( , , ) (1 ) Pr ( | ) Pr ( | )x F x BH x ob x ob x

Pr ( | ) 1/ min ( , )

Pr ( | ) 1/ min ( , )F F

B B

ob x dis x

ob x dis x

1 2 2min ( , ) min{| | ,...,| | }CF F Fdis x x t x t

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Unsupervise graph cut

Smoothness constrains

2'

' ( )( , ) ( , ) exp( | ' | )x x

x x N xB X x x

'( ) 1

0x xif then

else

arg min ( , , )E X

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Outline Introduction

Interactive segmentation Related work

Graph cut Concept of graph cut Hard and smooth constrains Min cut/Max flow

Extensive of Graph cut Grab cut Paint Selection

Unsupervise graph cut Conclusion Reference

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Conclusion

Interactive segmentation Graph cut is fast, robust segmentation It consider not only difference between

source to node, but also link of node to node.

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Reference

1. Lecture slide from Dr. Y.Y. Chuang.2. Y. Boyjov, “An Experimental Comparison

of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision”, PAMI 2002.

3. J. Liu, J. Sun, H.Y. Shum, ”Paint Selection”, sigraph 2007.

4. C.C. Kao, J.H. Lai, S.Y. Chien,“Automatic Object Segmentation With Salient Color Model”, IEEE 2011.

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Q&A