Chaotic Phase Synchronization for Visual Selection Fabricio A. - - PowerPoint PPT Presentation

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Chaotic Phase Synchronization for Visual Selection Fabricio A. - - PowerPoint PPT Presentation

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International Joint Conference on Neural Networks IJCNN 2009 Chaotic Phase Synchronization for Visual Selection Fabricio A. Breve fabricio@icmc.usp.br Liang Zhao zhao@icmc.usp.br Marcos G. Quiles quiles@icmc.usp.br Elbert E. N.

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SLIDE 1

Chaotic Phase Synchronization for Visual Selection

Fabricio A. Breve¹ fabricio@icmc.usp.br Liang Zhao¹ zhao@icmc.usp.br Marcos G. Quiles¹ quiles@icmc.usp.br Elbert E. N. Macau² elbert@lac.inpe.br

¹ Department of Computer Science, Institute of Mathematics and Computer Science, University of São Paulo, São Carlos-SP, Brazil ² National Institute for Space Research, São José dos Campos-SP, Brazil

International Joint Conference on Neural Networks – IJCNN 2009

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Outline

 Visual Selection  Chaotic Phase Synchronization  Model Description  Computer Simulations

Artificial images Real-world images

 Conclusions

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SLIDE 3

Visual Selection

 Capacity developed by living systems to

select just relevant environmental information

Identifies the region of the visual input that will

reach awareness level (focus of attention) while irrelevant information is suppressed

[FRI01, KIM07, BUI06, NIE94, SHI07, TSO92, ITT01, CAR04]

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Chaotic Phase Synchronization

 Two oscillators are called phase

synchronized if their phase difference is kept bounded while their amplitudes may be completely uncorrelated

M |< |

2 1

  

  t

as

[PIK01, ROS96]

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SLIDE 5

Chaotic Phase Synchronization

 Two coupled Rössler oscillators:

) ( =

1,2 2,1 1,2 1,2 1,2 1,2

x x k z y x     

1,2 1,2 1,2 1,2 =

ay x y    ) ( =

1,2 1,2 1,2

c x z b z   

2 2

= y x A 

[ROS96, OSI97]

0.98 =

1

 1.02 =

2

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SLIDE 6

Model Description

 Two dimensional network of Rössler Oscillators:

, =

, , , , , , , j i j i j i j i j i j i j i

x x k z y x

 

         , =

, , , , j i j i j i j i

ay x y    ). ( =

, , ,

c x z b z

j i j i j i

  

  

    

) ( =

, 1 1, , 1; 1, , j i j i j i j i j i

x x x   

 

) (

, 1, , ; 1, j i j i j i j i

x x   

   

) (

, 1 1, , 1; 1, j i j i j i j i

x x   

 

) (

, 1 , , 1; , j i j i j i j i

x x   

 

) (

, 1 , , 1; , j i j i j i j i

x x   

   

) (

, 1 1, , 1; 1, j i j i j i j i

x x   

 

) (

, 1, , ; 1, j i j i j i j i

x x  ) (

, 1 1, , 1; 1, j i j i j i j i

x x 

   

   . 0, , ) , ( ) , ( 1, =

, ; ,

  • therwise

q p to coupled is j i

  • scillator

if

q p j i

, ) ( max ) ( min =

, ,

C C C

j i j i

  

, | | =

, , 

      

d avg d j i d j i

F F C

. . 1 =

, = 1 = = 1 = d j i M j j N i i d avg

F M N F

 

] 2 1 2 [1

,

       

j i

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SLIDE 7

Model Description

 Oscillators which corresponds to pixels with:

 higher contrast

 Negative coupling strength tends to zero  They will be synchronized in phase

 lower contrast

 Negative coupling strength is higher  They will repel each other.

 After some time, only the oscillators corresponding

to the salient object will remain with their trajectories synchronized in phase while the other

  • bjects will have trajectories with different phases.
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SLIDE 8

ARTIFICIAL IMAGES

Computer Simulations

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SLIDE 9

Artificial Image with high contrast

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Artificial Image with high contrast

1.0 = 

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SLIDE 11

Artificial Image with low contrast

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SLIDE 12

Artificial Image with low contrast

1.0 = 

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SLIDE 13

Artificial Image with low contrast

4.0 = 

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SLIDE 14

REAL-WORLD IMAGES

Computer Simulations

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SLIDE 15
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Real-world Image: Bird

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SLIDE 17
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Real-world Image: Dog

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SLIDE 19
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Real-world Image: Flower

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Conclusions

 The proposed model can be applied to object

selection

 Chaotic Phase Synchronization

 Used to discriminate the salient object from the visual

input while keeping the non-salient, or less salient,

  • bjects unsynchronized

 Main Advantages:

 Robustness

  • Requires small coupling strength

 Biological inspiration

  • Observed in nonidentical systems
  • Believed to be the key mechanism for neural integration

in brain [VAR01]

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Acknowledgements

 This work was supported by the State of

São Paulo Research Foundation (FAPESP) and the Brazilian National Council of Technological and Scientific Development (CNPq)

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References

[FRI01] P. Fries, J. H. Reynolds, A. E. Rorie, and R. Desimone, “Modulation of oscillatory neuronal synchronization by selective visual attention,” Science, vol. 291, no. 5508, pp. 1560–1563, 2001.

[KIM07] Y. J. Kim, M. Grabowecky, K. A. Paller, K. Muthu, and S. Suzuki, “Attention induces synchronization-based response gain in steady-state visual evoked potentials,” Nature Neuroscience,

  • vol. 10, no. 1, p.117–125, 2007.

[BUI06] C. Buia and P. Tiesinga, “Attentional modulation of firing rate and synchrony in a model cortical network,” Journal of Computational Neuroscience, vol. 20, pp. 247–264, 2006.

[NIE94] E. Niebur and C. Koch, “A model for neuronal implementation of selective visual attention based

  • n temporal correlation among neurons,” Journal of Computational Neuroscience, vol. 1, pp. 141–158,

1994.

[SHI07] F. Shic and B. Scassellati, “A behavioral analysis of computational models of visual attention,” International Journal of Computer Vision, vol. 73, no. 2, pp. 159–177, 2007.

[TSO92] J. K. Tsotsos, “On the relative complexity of active vs. passive visual search,” International Journal of Computer Vision, vol. 7, pp. 127–141, 1992.

[ITT01] L. Itti and C. Koch, “Computational modelling of visual attention,” Nature Reviews Neuroscience,

  • vol. 2, pp. 194–203, 2001.

[CAR04] L. Carota, G. Indiveri, and V. Dante, “A softwarehardware selective attention system,” Neurocomputing, vol. 58-60, pp. 647–653, 2004.

[PIK01] A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A universal concept in nonlinear

  • sciences. Cambridge University Press, 2001.

[ROS96] M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phisical Review Letters, vol. 76, no. 7, pp. 1804–1807, March 1996.,

[OSI97] G. V. Osipov, A. S. Pikovsky, M. G. Rosenblum, and J. Kurths, “Phase synchronization effects in a lattice of nonidentical r¨ossler oscillators,” Phys. Rev. E, vol. 55, no. 3, pp. 2353–2361, Mar 1997.

[VAR01] F. Varela, J.-P. Lachaux, E. Rodriguez, and J. Martinerie, “The brainweb: Phase synchronization and large-scale integration,” Nature Reviews Neuroscience, vol. 2, pp. 229–239, April 2001.

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Chaotic Phase Synchronization for Visual Selection

Fabricio A. Breve¹ fabricio@icmc.usp.br Liang Zhao¹ zhao@icmc.usp.br Marcos G. Quiles¹ quiles@icmc.usp.br Elbert E. N. Macau² elbert@lac.inpe.br

¹ Department of Computer Science, Institute of Mathematics and Computer Science, University of São Paulo, São Carlos-SP, Brazil ² National Institute for Space Research, São José dos Campos-SP, Brazil

International Joint Conference on Neural Networks – IJCNN 2009