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Towards effective information content assessment: Analytical derivation of information loss in the reconstruction of random fields with model uncertainty

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  • Cherkasov, Aleksei
  • Gerke, Kirill M.
  • Khlyupin, Aleksey

Abstract

Structures are abundant in both natural and human-made environments and usually studied in the form of images or scattering patterns. To characterize structures a huge variety of descriptors is available spanning from porosity to radial and correlation functions. In addition to morphological structural analysis, such descriptors are necessary for stochastic reconstructions, stationarity and representativity analysis. The most important characteristic of any such descriptor is its information content — or its ability to describe the structure at hand. For example, from crystallography it is well known that experimentally measurable S2 correlation function lacks necessary information content to describe majority of structures. The information content of this function can be assessed using Monte-Carlo methods only for very small 2D images due to computational expenses. Some indirect quantitative approaches for this and other correlation function were also proposed. Yet, to date no methodology to obtain information content for arbitrary 2/3D image is available. In this work, we make a step towards developing a general framework to perform such computations analytically. We show, that one can assess the entropy of a perturbed random field and that stochastic perturbation of fields’ correlation function decreases its information content. In addition to analytical expression, we demonstrate that different regions of correlation function are in different extent informative and sensitive for perturbation. Proposed model bridges the gap between descriptor-based heterogeneous media reconstruction and information theory and opens way for computationally effective way to compute information content of any descriptor as applied to arbitrary structure.

Suggested Citation

  • Cherkasov, Aleksei & Gerke, Kirill M. & Khlyupin, Aleksey, 2024. "Towards effective information content assessment: Analytical derivation of information loss in the reconstruction of random fields with model uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
  • Handle: RePEc:eee:phsmap:v:633:y:2024:i:c:s037843712300955x
    DOI: 10.1016/j.physa.2023.129400
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    References listed on IDEAS

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    1. Postnicov, Vasily & Karsanina, Marina V. & Khlyupin, Aleksey & Gerke, Kirill M., 2023. "The 2- and 3-point surface correlation functions calculations: From novel exact continuous approach to improving methodology for discrete images," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 628(C).
    2. Volker Springel & Carlos S. Frenk & Simon D. M. White, 2006. "The large-scale structure of the Universe," Nature, Nature, vol. 440(7088), pages 1137-1144, April.
    3. Marina V Karsanina & Kirill M Gerke & Elena B Skvortsova & Dirk Mallants, 2015. "Universal Spatial Correlation Functions for Describing and Reconstructing Soil Microstructure," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-26, May.
    4. Karsanina, Marina V. & Gerke, Kirill M., 2023. "Stochastic (re)constructions of non-stationary material structures: Using ensemble averaged correlation functions and non-uniform phase distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    5. Uche, O.U. & Stillinger, F.H. & Torquato, S., 2006. "On the realizability of pair correlation functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 21-36.
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    1. Karsanina, Marina V. & Gerke, Kirill M., 2023. "Stochastic (re)constructions of non-stationary material structures: Using ensemble averaged correlation functions and non-uniform phase distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
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