Border Figure Detection Using a Phase Oscillator Network with Dynamical Coupling

Oscillator networks have been developed in order to perform specific tasks related to image processing. Here we analytically investigate the existence of synchronism in a pair of phase oscillators that are short-range dynamically coupled. Then, we use these analytical results to design a network able of detecting border of black-and-white figures. Each unit composing this network is a pair of such phase oscillators and is assigned to a pixel in the image. The couplings among the units forming the network are also dynamical. Border detection emerges from the network activity.

[1]  E. Niebur,et al.  Growth patterns in the developing brain detected by using continuum mechanical tensor maps , 2022 .

[2]  Luiz Henrique Alves Monteiro,et al.  Symmetry Detection Using Global-Locally Coupled Maps , 2002, ICANN.

[3]  F. Skinner,et al.  Phase‐coupled oscillator models can predict hippocampal inhibitory synaptic connections , 2001, The European journal of neuroscience.

[4]  E. M. Pinches,et al.  The role of synchrony and oscillations in the motor output , 1999, Experimental Brain Research.

[5]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[6]  Yukio Hayashi,et al.  Oscillatory neural network and learning of continuously transformed patterns , 1994, Neural Networks.

[7]  F. Varela,et al.  Perception's shadow: long-distance synchronization of human brain activity , 1999, Nature.

[8]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[9]  Liang Zhao,et al.  A network of dynamically coupled chaotic maps for scene segmentation , 2001, IEEE Trans. Neural Networks.

[10]  José Roberto Castilho Piqueira,et al.  Models for Master-Slave Clock Distribution Networks with Third-Order Phase-Locked Loops , 2007 .

[11]  Frank C. Hoppensteadt,et al.  Pattern recognition via synchronization in phase-locked loop neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[12]  E. Capaldi,et al.  The organization of behavior. , 1992, Journal of applied behavior analysis.

[13]  Eugene M. Izhikevich,et al.  Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory , 1999, IEEE Trans. Neural Networks.

[14]  Lev S Tsimring,et al.  Plasticity and learning in a network of coupled phase oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  J. Kirkpatrick,et al.  Automated border detection on contrast enhanced echocardiographic images. , 2005, International journal of cardiology.

[16]  José Roberto Castilho Piqueira,et al.  Bifurcation analysis for third-order phase-locked loops , 2004, IEEE Signal Processing Letters.

[17]  José Roberto Castilho Piqueira,et al.  Synchronous state in a fully connected phase-locked loop network , 2006 .

[18]  Alessandro Sarti,et al.  Binding and segmentation of multiple objects through neural oscillators inhibited by contour information , 2003, Biological Cybernetics.

[19]  José Roberto Castilho Piqueira,et al.  Computing with phase locked loops: choosing gains and delays , 2003, IEEE Trans. Neural Networks.

[20]  DeLiang Wang,et al.  Emergent synchrony in locally coupled neural oscillators , 1995, IEEE Trans. Neural Networks.

[21]  W. Singer,et al.  Temporal coding in the visual cortex: new vistas on integration in the nervous system , 1992, Trends in Neurosciences.

[22]  Gjlles Aubert,et al.  Mathematical problems in image processing , 2001 .

[23]  R M Borisyuk,et al.  Memorizing and recalling spatial-temporal patterns in an oscillator model of the hippocampus. , 1998, Bio Systems.

[24]  Roman Borisyuk,et al.  Dynamics of neural networks with a central element , 1999, Neural Networks.

[25]  José Roberto Castilho Piqueira,et al.  Global and partial synchronism in phase-locked loop networks , 2003, IEEE Trans. Neural Networks.

[26]  Bijoy K. Ghosh,et al.  Bio-Inspired Networks of Visual Sensors, Neurons, and Oscillators , 2007, Proceedings of the IEEE.

[27]  José Roberto Castilho Piqueira,et al.  Estimating the critical number of slave nodes in a single-chain PLL network , 2003, IEEE Communications Letters.

[28]  P. Holmes,et al.  The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model , 1982, Journal of mathematical biology.

[29]  M. Just,et al.  Cortical activation and synchronization during sentence comprehension in high-functioning autism: evidence of underconnectivity. , 2004, Brain : a journal of neurology.

[30]  Stephen Wolfram,et al.  Theory and Applications of Cellular Automata , 1986 .

[31]  P. Holmes,et al.  Simple models for excitable and oscillatory neural networks , 1998, Journal of mathematical biology.