BIOLOGICALLY MOTIVATED OSCILLATORY NETWORK MODEL FOR DYNAMICAL IMAGE SEGMENTATION

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BIOLOGICALLY MOTIVATED OSCILLATORY NETWORK MODEL
FOR DYNAMICAL IMAGE SEGMENTATION

• Margarita Kuzmina, Eduard Manykin
• Keldysh Institute of Applied Mathematics RAS,
• RRC Kurchatov Institute

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Motivations

• Synchronous cortical oscillations, experimentally
  discovered in the brain visual
  cortices of cat and monkey (1988-1989)
• Evidence on exploitation of synchronization and
  resonance in functioning of brain structures,
  different of the visual cortex
  (olfactory bulb and cortex, hippocampus,
  thalamo-cortical system, spinal cord, neocortex).
  

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3D oscillatory network (model of VC)

• neural oscillator is network processing unit
• network architecture imitates columnar structure
  of VC
• network performance consists in synchronization
  of network assemblies (clusters) of dynamically
  coupled oscillators it
  imitates self-organized collective behavior of
  orientation-selective (simple) cells of VC in
  preattentive stage of image processing
• 3D network is a tunable network. The whole set
  of network parameters consists of 3D array
  of receptive field orientations (internal
  network parameters) and 2D array
  of image characteristics - pixel
  brightness values and elementary bar
  orientations. The parameters provide tuning of
  both internal dynamics of network
  oscillators and self-organized dynamical network
  coupling.

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Single network oscillator

• The oscillator model is based on biologically
  motivated model of neural oscillator, formed by a
  pair of interconnected cortical neurons, that was
  designed by Z.Li in 1998.
• It is a relaxational, or limit cycle oscillator
  with dynamics, parametrically dependent on

Oscillator state is specified by a pair of
real-valued variables ODE system, governing
oscillator dynamics, is written for
The oscillator is capable to demonstrate either
activity state (stable oscillations) or
silence (quickly damping oscillations).
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Dynamical connections in 3D network
of all oscillator states.
The network state is defined by 3D array
Network dynamics is governed by the system of
ODE
Here functions
define internal oscillator dynamics, and the
terms
specify network
coupling. Dynamical coupling is designed in the
form
The values
defining the strength of network connections, are
constructed in the form of product of three
nonlinear functions, dependent
on oscillator activities, receptive field
orientations and spatial distance
between oscillator pair in the network.
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Dynamical connections in 3D network
The network connectivity rule can be written as
where
and
are limit cycle radii for oscillators with
indices

and
are RF orientations for these
and
oscillators,
are radius-vectors defining their spatial
locations.
and
In accordance with construction of nonlinear
functions
any
pair of network oscillators is proved to be
connected under combination
of the conditions
a) both oscillators are active
b) they possess close receptive field
orientations
c) they are separated by a distance not
exceeding the prescribed radius
of spatial interaction.
Otherwise dynamical connection is absent.
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2D reduced network model
2D network is a limit version of 3D oscillatory
network. The network oscillators are located
in 2D spatial lattice being in one-to-one
correspondence with image pixel array.
Single oscillator dynamics is tunable only by
pixel
brightness

network
connectivity rule includes the cofactor
, dependent
.
on elementary bar orientations, instead of
cofactor
2D network provides both brightness image
segmentation and solving of some texture
segmentation tasks, including contour
integration.

In problems of brightness image segmentation the
network performance is improved via simple
method of network coupling adjustment, providing
synchronization control. Synchronized clusters
arise successfully, starting from the one,
corresponding to the brightest image fragment.
At final stage of performance the oscillatory
network is decomposed into a set of internally
synchronized, but mutually desynchronized
clusters, corresponding to all image fragments.

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Stages of 2D oscillatory network performance
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Image versions in the process of 2D network
performance
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Texture segmentation
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Current 2D model modifications
The following 2D model modifications have been
designed and are currently under code
implementation. A) Modifications in
oscillator dynamics 1) Replacement of former
arbitrary oscillator frequency distribution
by frequences
, dependent on pixel brightness
2) Design of new version of oscillator dynamics,
providing arbitrary monotonic dependence of
oscillator activity (limit cycle size ) on
pixel brightness
B) Modification of network connectivity rule
1) Design of modified cofactor ,
providing higher segmentation accuracy 2)
Replacement of former network coupling adjustment
by more efficient discrete-time process of
successive image fragment selection.
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Image versions in the case of oscillator
frequences dependent on pixel
brightness
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Conclusive remarks
The following advantages of the dynamical image
segmentatiom method can be marked
parallel and automatic performance (similar to
that inherent in VC )
convenient successive image fragment selection
informative and flexibly controllable
visualization of image decomposition into the
set of fragments
The following directions of further model
extension look like possible a) extension
to real-time segmentation of moving images
b) development of active vision approaches.
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