COUPLED DIFFUSION MAPS IN NEURAL MASSES
Image analysis and scene segmentation usually have to cope with the problem
of binding different features in a global unifying percept.
Biological approaches to computer vision and image processing have
evidenced the advantages of a delocalized representation of information
through feature maps which mix topological contiguity with proximity
in the feature space. By example, the peculiar dispositions of
orientation-selective cells can be understood in terms of
dimension-reducing mappings which translate neighborhood relations in the
orientation-subspace in spatial neighborhood relations on the
. Thus, cortical maps are not only a repository of
information about the features present in the image, but
are the substrate on which to organize a locally based set of excitatory
and inhibitory interconnections among features.
The overall functionality of these systems will depend
both on their structural schemata and on the "physics" of
the interaction processes.
In this framework, the spreading
of features on the cortical surface poses, at some point, the problem of a global coding
that encourages grouping processes among visual fetaures that belongs to a
common object, and dissociates those features that belongs to
distinct objects, though they be equally close together in the cortical
After recent observations that synchronous oscillations in different
regions of visual cortex reflect global properties of the stimulus,
several cooperative neural networks have been proposed in which
global properties of the image can be read in the
correlated activity of neural populations
Usually such cooperative oscillating systems are based on:
(i) non-linear self-catalyzing action with a delayed negative feedback,
or (ii) cooperative-competive action between two populations acting through
cross-coupled non-linear delay differential equations.
In this paper we have analyzed the computational capabilities of
continuous-distributed coupled diffusion maps governed by
laterally-reacting non linear equations.
Coupled diffusion maps can be interpreted as a phenomenological model for
the processes that take place in the cortical surface.
Such systems are based on (i) linear spatial diffusion components, and (ii)
non-linear reaction components. The former allow for a weighted averaging
on the input signal over a region of a certain extent (the receptive field),
and, through anisotropic diffusion coefficients, lead to continuous
distributions of oriented receptive fields similar to real orientation maps
The latter ignite cooperative processes. Specifically, activation in a
point of the network sets in motion a local excitatory diffusion process
and a spatially displaced inhibitory reaction through lateral clustered
coupling. The non-linear competition between the two processes leads to a
macroscopic organized dynamic behaviour that, under appropriate input
conditions, results in oscillations.
Superimposed dynamic coupling between localized portions of the
orientation map, characterized by similar response properties, impose a
coherence and the whole system evolves throught different configurations of
coherent states each representing features related to common textured
Hence, diffusive-reacting processes allow the systems to show phasic
transitions from disordered states to ordered states or from one ordered
state to a different one, and long-range connections synchronize such
transitions on how coherent features are in the image.
Averaging the pattern of activity over a window comparable in size with
those of a complete set of orientations (hypercolumn) we gain istantaneous
global perception supporting segmentation.
Experiments conducted with artificial and natural textures validated the
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