International Joint Conference on Neural Networks – IJCNN 2009 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
Outline Visual Selection Chaotic Phase Synchronization Model Description Computer Simulations Artificial images Real-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 | |< t M as 1 2 [PIK01, ROS96]
Chaotic Phase Synchronization Two coupled Rössler oscillators: = ( ) x y z k x x 1,2 1,2 1,2 1,2 2,1 1,2 1,2 = y x ay 1,2 1,2 1,2 = ( ) z b z x c 1,2 1,2 1,2 = 0.98 = 1.02 2 2 = A x y 1 2 [ROS96, OSI97]
Model Description Two dimensional network of Rössler Oscillators: = , x y z k x x , , , , , , , i j i j i j i j i j i j i j = , y x ay , , , , i j i j i j i j = ( ). z b z x c [1 1 ] , , , i j i j i j , i j 2 2 min ( ) C C = ( ) x x x , i j i , j i 1, j 1; i , j i 1, j 1 i , j = , ( ) x x , i j max ( ) C i 1, j ; i , j i 1, j i , j ( ) x x 1, 1; , 1, 1 , i j i j i j i j ( ) x x d d = | | , C F F i , j 1; i , j i , j 1 i , j , , i j i j avg ( ) x x , 1; , , 1 , i j i j i j i j d ( ) x x i 1, j 1; i , j i 1, j 1 i , j = = j M i N 1 ( ) x x 1, ; , 1, , i j i j i j i j d d = . F F ( ) x x , avg i j i 1, j 1; i , j i 1, j 1 i , j . N M = 1 = 1 i j 1, ( , ) ( , ) , if oscillator i j is coupled to p q = i , j ; p , q 0, . otherwise
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.
Computer Simulations ARTIFICIAL IMAGES
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
Computer Simulations REAL-WORLD IMAGES
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-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 on 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.
International Joint Conference on Neural Networks – IJCNN 2009 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
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