---
_id: '2914'
abstract:
- lang: eng
  text: 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.
acknowledgement: "This work was supported in part by NSF Grants No. IIS-0613435, No.
  IBN-0344678, and No. PHY-0957573, by NIH Grant No. T32 MH065214, by the Human Frontier
  Science Program, and by the Swartz Foundation.\r\nCC BY 3.0\r\n"
article_number: '018701'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Greg
  full_name: Stephens, Greg
  last_name: Stephens
- first_name: Thierry
  full_name: Mora, Thierry
  last_name: Mora
- first_name: Gasper
  full_name: Tkacik, Gasper
  id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
  last_name: Tkacik
  orcid: 0000-0002-6699-1455
- first_name: William
  full_name: Bialek, William
  last_name: Bialek
citation:
  ama: Stephens G, Mora T, Tkačik G, Bialek W. Statistical thermodynamics of natural
    images. <i>Physical Review Letters</i>. 2013;110(1). doi:<a href="https://doi.org/10.1103/PhysRevLett.110.018701">10.1103/PhysRevLett.110.018701</a>
  apa: Stephens, G., Mora, T., Tkačik, G., &#38; Bialek, W. (2013). Statistical thermodynamics
    of natural images. <i>Physical Review Letters</i>. American Physical Society.
    <a href="https://doi.org/10.1103/PhysRevLett.110.018701">https://doi.org/10.1103/PhysRevLett.110.018701</a>
  chicago: Stephens, Greg, Thierry Mora, Gašper Tkačik, and William Bialek. “Statistical
    Thermodynamics of Natural Images.” <i>Physical Review Letters</i>. American Physical
    Society, 2013. <a href="https://doi.org/10.1103/PhysRevLett.110.018701">https://doi.org/10.1103/PhysRevLett.110.018701</a>.
  ieee: G. Stephens, T. Mora, G. Tkačik, and W. Bialek, “Statistical thermodynamics
    of natural images,” <i>Physical Review Letters</i>, vol. 110, no. 1. American
    Physical Society, 2013.
  ista: Stephens G, Mora T, Tkačik G, Bialek W. 2013. Statistical thermodynamics of
    natural images. Physical Review Letters. 110(1), 018701.
  mla: Stephens, Greg, et al. “Statistical Thermodynamics of Natural Images.” <i>Physical
    Review Letters</i>, vol. 110, no. 1, 018701, American Physical Society, 2013,
    doi:<a href="https://doi.org/10.1103/PhysRevLett.110.018701">10.1103/PhysRevLett.110.018701</a>.
  short: G. Stephens, T. Mora, G. Tkačik, W. Bialek, Physical Review Letters 110 (2013).
date_created: 2018-12-11T12:00:19Z
date_published: 2013-01-02T00:00:00Z
date_updated: 2025-09-29T13:29:28Z
day: '02'
ddc:
- '530'
department:
- _id: GaTk
doi: 10.1103/PhysRevLett.110.018701
external_id:
  arxiv:
  - '0806.2694'
  isi:
  - '000313006100058'
file:
- access_level: open_access
  checksum: 72bfbc2094c4680e8a8a6bed668cd06d
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:18:44Z
  date_updated: 2020-07-14T12:45:53Z
  file_id: '5366'
  file_name: IST-2016-401-v1+1_1281.full.pdf
  file_size: 416965
  relation: main_file
file_date_updated: 2020-07-14T12:45:53Z
has_accepted_license: '1'
intvolume: '       110'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
publication: Physical Review Letters
publication_status: published
publisher: American Physical Society
publist_id: '3829'
pubrep_id: '401'
quality_controlled: '1'
status: public
title: Statistical thermodynamics of natural images
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 110
year: '2013'
...