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 Application of Nonlinear Dynamics to Image Recognition


Research Mentor(s)

Shaheen M. Hoque
Raytheon Systems Company
Visiting Research Mentor
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Dr. Sanza T. Kazadi
Jisan Research Institute
JRI Research Mentor
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A stable non-linear dynamic system has three kinds of attractors:

  • Point attractor
  • Periodic attractor (limit cycle)
  • Strange attractor

Among these three attractors, the strange attractor displays some interesting behaviors. Strange attractors are results of non-linear dynamics behaving chaotically. Some interesting characteristics of chaos are presented below:

  • Chaos results from a deterministic process.
  • Chaos happens only in non-linear systems.
  • Chaos happens in feedback systems.
  • Chaos is entirely self-generated.
  • Chaos can usually pass all statistical test for randomness.
  • The Fourier spectrum is "broad" but with some periodicities.
  • Chaos includes one or more types order.
  • Chaos can have large number of symmetry, including scale symmetry.
  • The phase space trajectories may have some fractal properties.
  • Fractals can be scale invariant.
  • Details of the chaotic behavior are hypersensitive to changes in initial conditions. Chaotic trajectories never repeat, and they never cross each other.
  • The ranges of the variables have finite bounds. The state trajectories are bounded in phase space. The region where the trajectories are bounded is called the attractor for the system.

Characteristic No. 7, 8, and 9 suggest that chaotic dynamics are capable of producing complex structures. Since the state trajectories never repeat, yet they are bounded to the attractor in the phase space, chaotic dynamics can create infinite variety within a bound. So, it seems that if we can identify the attractor associated with the apple trees we will be able to identify an apple tree. Therefore, it seems feasible that chaotic dynamics can be used to solve recognition problem. We are investigating this possibility.



We describe a nonlinear system capable of use as a recognition system. This system is composed of a set of coupled oscillators, connected by linear springs. Images are overlaid on the system by altering the masses and spring constants of the oscillators, thereby modifying the detailed behavior of the system. Signatures extracted from the system using FFT of the individual oscillator positions show coherance, relative continuity, and translational and rotational invariance. These properties are discussed in the context of the eventual use of this system as a general identification system.

S. Hoque, S. Kazadi, A. Li, W. Chen, and E. Sadun. Identification of Shapes Using a Nonlinear Dynamic System . Lecture Notes in Computer Science , 2095, pp.236-245, 2001. (Postscript) (PDF)

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