Normalized Cuts and Image Segmentation - Final Project | GEOG 8, Study Guides, Projects, Research of Geography

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ECE 278 Final project

Normalized Cuts Normalized Cuts

andand Image SegmentationImage Segmentation

Baris Sumengen

Jelena Tešic

Vision Research Lab

Electrical and Computer engineering

June 8, 2000

Outline

n Introduction

n Graph Partitioning

n Grouping Algorithm

n Experiments

n Results

n Related Approaches

n Conclusion

June 8, 2000

Graph Partitioning

n Dissimilarity measure between two sets of

graph G=(V, E),

n Minimum cut Optimal bi-partitioning

n Clustering method (Wu, Leathy, PAMI

1. that favors outliers

n Different cost function proposed:

,

u A v B

cut A B w u v

∈ ∈

= (^) ∑

A ∪ B = V A , ∩ B = ∅

cut A B cut A B

Ncut A B

asso A V asso B V

,

( , ) ( , )

u A t V

asso A V w u t

∈ ∈

= (^) ∑

June 8, 2000

Optimal Partitioning

i (^) j

d = ∑ W i j

n N – number of nodes in the graph V

n W – NxN symmetrical matrix with elements W(i,j)

n D:

n x – indication vector:

n Final result:

with the condition:

D = d i a g ( d 1 , d 2 ..., dN )

xi = { +1, V i ( ) ∈ A −1, V i ( ) ∉ A }

min ( ) min

T

x y T

y D W y

Ncut x

y Dy

i

i

x^ i

i

x i

d

y

d

T

N

d

y

d

M

June 8, 2000

The Grouping Algorithm

n Use spatial proximity term and feature similarity terms to

calculate weighted coefficients W(i,j)

n Summarize information in W and D

n Find an approximate solution for the second smallest

eigenvalue of the system

n Bipartition the graph by finding the best splitting point

n Check the stability of the cut and decide on the current

partition status

n Stop the recursion if Ncut exceeds certain limit

( D − W y ) = λDy

June 8, 2000

Experiments

n Different parameter values and feature desriptors

2

( , ) ,

i j i j

I X

F F X X

i j

W i j e e X X r

σ σ

− − − −

= ∗ − <

1

( ), intensity

( ) , sin( ), cos( ),color

* ,..., * , texture n

I i

F i v v s h v s h i

I f I f i



 = 





g g g g

June 8, 2000

5 10 15 20 25 30

2 4 6 8 10 12 14 16 18 20 5 10 15 20 25 30

2 4 6 8 10 12 14 16 18 20 5 10 15 20 25 30

2 4 6 8 10 12 14 16 18 20

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2 4 6 8 10 12 14 16 18 20

5 10 15 20 25 30

2 4 6 8 10 12 14 16 18 20 5 10 15 20 25 30

2 4 6 8 10 12 14 16 18 20

5 10 15 20 25 30

2 4 6 8 10 12 14 16 18 20 5 10 15 20 25 30

2 4 6 8 10 12 14 16 18 20

June 8, 2000

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