• Open Access

Statistical Thermodynamics of Natural Images

Greg J. Stephens, Thierry Mora, Gašper Tkačik, and William Bialek
Phys. Rev. Lett. 110, 018701 – Published 2 January 2013

Abstract

The scale invariance of natural images suggests an analogy to the statistical mechanics of physical systems at a critical point. Here we examine the distribution of pixels in small image patches and show how to construct the corresponding thermodynamics. We find evidence for criticality in a diverging specific heat, which corresponds to large fluctuations in how “surprising” we find individual images, and in the quantitative form of the entropy vs energy. We identify special image configurations as local energy minima and show that average patches within each basin are interpretable as lines and edges in all orientations.

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  • Received 31 January 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.018701

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Greg J. Stephens*, Thierry Mora, Gašper Tkačik, and William Bialek

  • Joseph Henry Laboratories of Physics and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA

  • *Present address: Department of Physics and Astronomy, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands and Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, Okinawa, Japan.
  • Present address: Laboratoire de physique statistique, UMR8550, CNRS and École normale supérieure, 24, rue Lhomond, 75005 Paris, France.
  • Present address: Institute of Science and Technology Austria, Am Campus 1, A-3400 Klosterneuburg, Austria.

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Issue

Vol. 110, Iss. 1 — 4 January 2013

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