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Entropy estimation in bidimensional sequences.

F N M de Sousa Filho1, V G Pereira de Sá1, E Brigatti2

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Block entropy methods offer superior entropy estimation for bidimensional sequences compared to compression techniques that lose dimensional correlations. Block entropies provide the best asymptotic entropy estimation.

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Area of Science:

  • Information Theory
  • Image Analysis
  • Data Science

Background:

  • Entropy estimation is crucial for analyzing complex data.
  • Bidimensional sequences, common in natural systems, present unique challenges for entropy estimation.
  • Existing methods often struggle with high-dimensional correlations.

Purpose of the Study:

  • To evaluate entropy estimation methods for bidimensional sequences.
  • To introduce a diverse dataset of natural images for validation.
  • To identify robust and accurate entropy estimation techniques.

Main Methods:

  • Comparison of block entropy methods and compression-based approaches.
  • Utilizing a validation dataset of images from natural systems with long-range correlations.
  • Analyzing the impact of dimensionality reduction in compression methods.

Main Results:

  • One-dimensional projection-based compression methods yield poor entropy estimates due to lost correlations.
  • Compression methods without dimensionality reduction show improved performance.
  • Traditional block entropies demonstrate the fastest convergence and best asymptotic entropy estimation.

Conclusions:

  • Block entropy methods are more effective for bidimensional sequence entropy estimation than projected compression methods.
  • Specific compression techniques can be repurposed for automatic symmetry detection in images.
  • Accurate entropy estimation requires methods that preserve data dimensionality.