Fast Approximate Energy Minimization via Graph Cuts M.S. Student, Hee-Jong Hong May 29, 2013.

Fast Approximate Energy Min-imization via Graph Cuts

M.S. Student, Hee-Jong HongMay 29, 2013

2

Introduction

Previous Works

Proposed Method

Experiment

Conclusion

Contents

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

3

Local Method

– Sum of Squared Differences

– Sum of Absolute Differences

– Zero-mean Normalized Cross-Correlation

Global Method

– Dynamic Programming (One Dimensional Problem)

– Graph Cuts (Every Epipolar Line)

Introduction

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

4

Global Optimization

Introduction

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

Sum Of Local Energy Sum Of Global Energy

(a)

(b)

0

4

0 + K/2 + K/2 = K

V(a,b) = V(b,c) = K/2

V(a,c) = K

(d)

4 + 0 + 0 = 4

Dynamic Programming

Introduction

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

5

1 2 3 41

2

3

4

Disparity

A Image Row

Energy Minimization

Introduction

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

6

Another global approach to improve qual-ity of correspondences

Assumption: disparities vary (mostly) smoothly

Minimize energy function:Edata+lEsmoothness

Edata: how well does disparity match data

Esmoothness: how well does disparity matchthat of neighbors – regularization

Energy Definition in Stereo

Introduction

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

7

),(),(),,( ydxyxdyxD JI

similar)something(or

d2 and d1 labels with pixelsadjacentofcost

21

21 ),(

dd

ddV

)2,2(),1,1(

2,21,1),(

, ),(),,(})({yxyxneighbors

yxyxyx

yx ddVdyxDdE

Max Flow / Min Cut

Previous Works

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

8

“source”

A graph with two terminals

S T

“sink”

Previous Works

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

Labeling– For each pixel, either the F or G edge has to be cut– Only one edge label per pixel can be cut (otherwise

could be added

B

F

Proposed Method

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

Swap Move & Expansion Move

𝜶− 𝜷𝑺𝒘𝒂𝒑Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

𝜶− 𝜷𝑺𝒘𝒂𝒑Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

𝜶−𝑬𝒙𝒑𝒂𝒏𝒔𝒊𝒐𝒏Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

𝜶−𝑬𝒙𝒑𝒂𝒏𝒔𝒊𝒐𝒏Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

Move

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

Energy Definition

– Data Term :

– Smoothness Term : Static Cues (Weighted Potts)

Experiment

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

16

Static Cues

Experiment

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

17

Potts

Static Cues

0?1?unkown

Give Higher Smoothness Factor to Continues Intensity

1Pixel Move

Experiment

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

18

Swap Move

Expansion Move

Experiment

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

19

Normalized Corr

&

Annealling

Expansion Move

&

Swap Move

Experiment

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

20

Conclusion

Visual Object Tracking using Adaptive Correlation Filters [CVPR 2010]

21

Performs well on a variety of computer vision prob-

lems

– Image Restoration, Stereo, and Motion

Very Faster than Annealing

22

Thank you!