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Pattern generation using likelihood inference for cellular automata.

Radu V Craiu1, Thomas C M Lee

  • 1Department of Statistics, University of Toronto, ON, Canada.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 13, 2006
PubMed
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We developed likelihood-based methods to estimate rules for cellular automata, enabling the regeneration of complex patterns from observed data. This approach works even with noisy data, offering a new way to understand these discrete dynamical systems.

Area of Science:

  • Computational Science
  • Dynamical Systems Theory
  • Pattern Recognition

Background:

  • Cellular automata (CA) are discrete dynamical systems known for generating complex patterns from simple rules.
  • Existing methods for rule inference often struggle with noisy data or specific pattern types.

Purpose of the Study:

  • To develop and present likelihood-based methods for estimating the rules of cellular automata.
  • To enable the accurate regeneration of observed regular patterns, even under noisy conditions.

Main Methods:

  • Formulation of a likelihood-based approach for rule estimation in cellular automata.
  • Equivalence to estimating the local map of a stochastic cellular automaton for noisy data.
  • Direct computation of maximum likelihood estimates for regular binary patterns.

Related Experiment Videos

  • Utilizing the minimum description length principle for model selection.

    • Main Results:

    • Demonstrated the effectiveness of the likelihood-based method in regenerating patterns from binary images.
    • Showcased the method's robustness in the presence of noise.
    • Validated the approach through illustrative examples.

    Conclusions:

    • Likelihood-based methods provide a powerful framework for inferring cellular automaton rules.
    • The proposed approach is suitable for regenerating observed patterns and handling noisy data.
    • This work contributes to a deeper understanding and application of cellular automata in pattern generation and analysis.