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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...
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Shearlet-based measures of entropy and complexity for two-dimensional patterns.

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New methods quantify spatial entropy and complexity in 2D patterns using shearlet transforms. This approach helps analyze order and randomness in diverse imaging data, textures, and surfaces.

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Area of Science:

  • Image analysis
  • Information theory
  • Computational mathematics

Background:

  • Quantifying spatial complexity and entropy in 2D patterns is crucial for understanding image data.
  • Existing methods may lack the multiscale and directional analysis needed for complex patterns.

Purpose of the Study:

  • To introduce novel spatial entropy and complexity measures for 2D patterns.
  • To develop a method capable of local and global complexity mapping in inhomogeneous patterns.

Main Methods:

  • Utilizing directional multiscale coefficients from the fast finite shearlet transform.
  • Employing Shannon entropy and Jensen-Shannon divergence for complexity and entropy estimation.
  • Building the approach on the statistical notion of disequilibrium.

Main Results:

  • The proposed measures provide both local and global estimates of spatial entropy and complexity.
  • The algorithm successfully maps complexity variations within inhomogeneous patterns.
  • Validation demonstrated effectiveness on decaying periodic patterns and Ising surfaces near criticality.

Conclusions:

  • The developed algorithm offers a robust tool for analyzing 2D imaging data, textures, and surfaces.
  • It enables a deeper understanding of the order and randomness inherent in various spatial patterns.
  • This method has broad applicability in fields requiring spatial data characterization.