Abderrahim Labbi

Gray-Level Object Segmentation with a Network of FitzHugh-Nagumo Oscillators

In this paper we adopt a temporal coding approach to neuronal modeling of the visual cortex, using oscillations. We propose a hierarchy of three processing modules corresponding to different levels of representation. The first layer encodes the input image (stimulus) into an array of units, while the second layer consists of a network of FitzHugh-Nagumo oscillators. The dynamical behaviour of the coupled oscillators is rigorously investigated and a stimulus-driven synchronization theorem is derived. However, this module reveals itself insufficient to correctly encode and segregate different objects when they have similar gray-levels in the input image. Therefore, a third layer connected in a feedback loop with the oscillators is added. This ensures synchronization (resp. desynchronization) of neuron ensembles representing the same (resp. a different) object. Simulation results are presented using synthetic as well as real and noisy gray-level images.

ASYMPTOTIC SYNCHRONIZATION IN NETWORKS OF LOCALLY CONNECTED OSCILLATORS

In this paper, we describe the asymptotic behavior of a network of locally connected oscillators. The main result concerns asymptotic synchronization. The presented study is stated in the framework of neuronal modeling of visual object segmentation using oscillatory correlation. The practical motivations of the synchronization analysis are based on neurophysiological experiments which led to the assumptions that existence of temporal coding schemes in the brain by which neurons, with oscillatory dynamics, coding for the same coherent object synchronize their activities, while neurons coding for different objects oscillate with nonzero phase lags. The oscillator model considered is the FitzHugh–Nagumo neuron model. We restrict our study to the mathematical analysis of a network of such neurons. We firstly show the motivations and suitability of choosing FitzHugh–Nagumo oscillator, mainly for stimulus coding purposes, and then we give sufficient conditions on the coupling parameters which guarantee asymptotic synchronization of oscillators receiving the same external stimulation (input). We have used networks of such oscillators to design a layered architecture for object segmentation in gray-level images. Due to space limitations, description of this architecture and simulation results are briefly referred to by the end of the paper.

Rate and Temporal Coding with a Neural Oscillator

A neural oscillator capable of processing graded inputs is studied. The oscillator has two functional modes controlled by an external signal and codes information either by the amplitude of its oscillations or by the coordinates of its fixed point. Excitatory and inhibitory connections between coupled oscillators control their phase relations. Simulations and theoretical analyses show that any desired phase relation can be induced by an appropriate choice of connections. The capabilities of the oscillator model are demonstrated in an architecture for gray-level image segmentation.

Asymptotic Behavior of a Neural Network with Dynamic External Input

In this paper we show how a recurrent neural network, of shunting type, receiving changing input can be used for pattern classification or association. An important feature of the proposed network is its ability to continuously process environmental (external) input. Such ability is very useful if one is to design a real-time reactive system in an unexpectedly changing environment. We firstly state sufficient conditions under which the network dynamics is convergent to stable punctual attractors. Therefore, we show that relaxing the condition on symmetry of connectivity and making a local quadratic approximation of the dynamics can lead the network into an oscillatory mode. The corresponding limit cycles are shown to be stable. Application of the network with punctual attractor dynamics to navigation in a changing environment is pointed out but is not in the scope of this paper.

A variational approach to associative memory

The purpose of this paper is to show how fundamental results from variational approximation theory can be exploited to design recurrent associative memory networks. We begin by stating the problem of learning a set of given patterns with an associative memory network as a hypersurface construction problem, then we show that the associated approximation problem is well-posed. Characterizing and determining such a solution will lead us to introduce the desired associative memory network which can be viewed as a recurrent radial basis function (RBF) network which has as many attractor states as there are fundamental patterns (no spurious memories). Subject classification: AMS(MOS) 65F10, 65B05.