Chaotic Phase Synchronization for Visual Selection

Fabricio A. Breve¹ fabricio@icmc.usp.brLiang Zhao¹ zhao@icmc.usp.brMarcos G. Quiles¹ quiles@icmc.usp.brElbert 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

Outline

Visual Selection Chaotic Phase Synchronization Model Description Computer Simulations

Artificial imagesReal-world images

Conclusions

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]

Chaotic Phase Synchronization

Two oscillators are called phase synchronized if their phase difference is kept bounded while their amplitudes may be completely uncorrelated

M|<| 21 tas

[PIK01, ROS96]

Chaotic Phase Synchronization Two coupled Rössler oscillators:

)(= 1,22,11,21,21,21,2 xxkzyx 1,21,21,21,2 = ayxy )(= 1,21,21,2 cxzbz

22= yxA [ROS96, OSI97] 0.98=1 1.02=2

Model Description Two dimensional network of Rössler Oscillators:

,= ,,,,,,, jijijijijijiji xxkzyx ,= ,,,, jijijiji ayxy

).(= ,,, cxzbz jijiji

)(= ,11,,1;1,, jijijijiji xxx

)( ,1,,;1, jijijiji xx )( ,11,,1;1, jijijiji xx

)( ,1,,1;, jijijiji xx )( ,1,,1;, jijijiji xx

)( ,11,,1;1, jijijiji xx )( ,1,,;1, jijijiji xx)( ,11,,1;1, jijijiji xx

.0,,),(),(1,

=,;, otherwiseqptocoupledisjioscillatorif

qpji

,)(max)(min

= ,, C

CC jiji

,||= ,,

d

avgdji

dji FFC

..1= ,

=

1=

=

1=

dji

Mj

j

Ni

i

davg F

MNF

]2

12

[1,

ji

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 objects will have trajectories with different phases.

ARTIFICIAL IMAGESComputer Simulations

Artificial Image with high contrast

Artificial Image with high contrast

1.0=

Artificial Image with low contrast

Artificial Image with low contrast

1.0=

Artificial Image with low contrast

4.0=

REAL-WORLD IMAGESComputer Simulations

Real-world Image: Bird

Real-world Image: Dog

Real-world Image: Flower

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, objects 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]

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)

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-

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[NIE94] E. Niebur and C. Koch, “A model for neuronal implementation of selective visual attention based on temporal correlation among neurons,” Journal of Computational Neuroscience, vol. 1, pp. 141–158, 1994.

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[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.

Chaotic Phase Synchronization for Visual Selection

Fabricio A. Breve¹ fabricio@icmc.usp.brLiang Zhao¹ zhao@icmc.usp.brMarcos G. Quiles¹ quiles@icmc.usp.brElbert 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