Margarita Kuzmina

Tunable Oscillatory Network for Visual Image Segmentation

Recurrent oscillatory network with tunable oscillator dynamics and nonlocal dynamical interaction has been designed. Two versions of the network model have been suggested: 3D oscillatory network of columnar architecture that reflects some image processing features inherent in the brain visual cortex, and 2D version of the model, obtained from the 3D network by proper reduction. The developed image segmentation algorithm is based on cluster synchronization of the reduced network that is controlled by means of interaction adaptation method. Our approach provides successive separation of synchronized clusters and final decomposition of the network into a set of mutually desynchronized clusters corresponding to image fragments with different levels of brightness. The algorithm demonstrates the ability of automatic gray-level image segmentation with accurate edge detection. It also demonstrates noise reduction ability.

Macrodynamic approach for oscillatory networks

The system of coupled oscillators, interacting via arbitrary symmetric matrix of connections, is studied from a viewpoint of associative memory modelling. A self-consistent field approach which consists in operating with a finite number of macrovariables (appropriate inner products which can be regarded as order parameters) is used. A system of dynamic equations of oscillatory network being rewritten in terms of macrovariables has a form of independent equations. Being completed by functional equations for order parameters, this system provides a self-consistent description of the oscillatory network. In particular, the approach can be used as an instrument for studying the dependence of the number of network phase locked states on the frequency distribution and the architecture of connections. The abilities of this approach are demonstrated in the case of a network with all-to-all uniform connections.

Oscillatory Network for Synchronization-Based Adaptive Image Segmentation

Oscillatory network model with controllable oscillator dynamics and self-organized dynamical coupling has been created for synchronization-based image processing. The model was previously obtained via reduction from a biologically motivated oscillatory model of the brain primary visual cortex. The reduced network model performance consists in network relaxation into the state of synchronization. The set of internally synchronized but mutually desynchronized network ensembles (clusters), arising at final synchronization state, corresponds to full set of image fragments. New model developments, presented in the paper, include: a) the advanced version of single oscillator dynamics, admitting introduction of arbitrary continuous dependence of oscillator limit cycle size on pixel brightness; b) new principle of network coupling, permitting to raise image segmentation accuracy and to control network noise reduction. A capability of selective image segmentation (extraction of image fragment subset of a priori prescribed brightness levels) is also inherent to current model version.

Recurrent Associative Memory Network of Nonlinear Coupled Oscillators

The recurrent associative memory networks with complex-valued Hebbian matrices of connections are designed from interacting limit-cycle oscillators. These oscillatory networks have peculiarities and advantages as compared to Hoplield neural network model. In particular, the class of networks with high memory characteristics (the capacity close to 1, low extraneous memory) exists. At zero values of oscillator frequencies the designed networks are closely related to the known “clock” neural networks (networks from complex-valued neurons). Pattern recognition of colored images and recognition of objects with complicated topological structure look quite natural in the context of such models. Exact solutions have been obtained for a few types of the networks considered, in particular, for homogeneous closes chains.

Exact solutions and modeling of associative memory in oscillatory networks

This paper is devoted to the study of associative memory in the networks of N coupled nonlinear oscillators interacting via complex-valued weights. Exact solutions relating to the structure of attractors have been obtained. The complete solution to the systems of two oscillators and the structural portrait of the governing dynamical system have been obtained. It is shown that homogeneous closed chains of oscillators play important role in the context of phase associative memory problems. Qualitative description of the memory in the closed chains of N oscillators is given for arbitrary N, and rigorous solutions for N <EQ 6 are illustrated. The networks considered admit electronic, nonlinear optical and optoelectronic implementations. The background of some of them is under development.

Pattern Formation in Locally Connected Oscillatory Networks

The subject of our study is a class of networks consisting of locally connected nonlinear oscillators. In spatially continual limit these oscillatory networks can be considered as oscillatory media governed by a system of reaction-diffusion equations. Formation of spatio-temporal patterns in nonlinear active media (wave trains, standing waves, targets and shock structures, spiral waves, stripe patterns, cluster states ) is the subject of interest in physical, chemical, biological problems.

Polarized Radiative Transfer in Optically Active Light Scattering Media

The disperse media composed of non-spherical particles (say, dust aerosols layers, and ice crystal clouds) can appear both optically isotropic and optically anisotropic, depending on local optical characteristics of turbid medium in question and also on the orientation of particles.

A model of pulsed oscillator network and the perspectives of its application to the problems of information routing in wireless sensor networks

Development of performance principles of wireless sensor networks (WSN) and the methods of information routing in the networks, providing a capability of self-organized and automatic style of the WSN network work, is currently of substantial interest. The attraction of associated model of pulsed oscillator networks seems to be helpful for the design of adaptive synchronization-based information routing in the WSN. An oscillatory network model with pulsed oscillator dynamics and pulsed oscillator interaction is proposed. The initial version of information transfer in the WSN with the help of synchronization of an associated oscillatory network is discussed.

Image Processing via Synchronization in a Self-Organizing Oscillatory Network

We develop a biologically inspired method of image processing based on synchronization-based performance of an oscillatory network with controllable self-organized coupling. The oscillatory network, obtained from a previously designed biologically motivated oscillatory neural network model of the brain’s visual cortex, provides automatic, adaptive, and active image segmentation. Being tuned by an image to be processed, the network dynamics realizes network decomposition into a set of synchronized ensembles of oscillators, corresponding to image decomposition into the required set of image fragments. The current network model version provides: (a) full segmentation of real grey-level and colored images; and (b) selective image segmentation (extraction of a subset of image fragments with brightness values contained inside a given arbitrary brightness interval).

Oscillatory neural network for adaptive dynamical image processing

We develop a biologically motivated oscillatory network model and related dynamical synchronization-based method of image segmentation. The first version of successive segmentation algorithm was based on coupling adaptation in the oscillatory network. New model developments, presented in the paper, include: 1) a modified version of single oscillator dynamics; 2) new network connectivity rule. These modifications permit to significantly improve the oscillatory method capabilities, providing image processing with significantly larger pixel array sizes and ensuring higher segmentation accuracy. In addition the improved network model allows to perform selective image segmentation tasks (extraction of prescribed subset of image fragments). New method capabilities have been demonstrated in computer experiments