MAP Interpolation of an Ising Image Block

Matthew G. Reyes*, David L. Neuhoff, Thrasyvoulos N Pappas

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper considers the problem of finding the set of MAP reconstructions of an N× N block conditioned on a boundary configuration consisting of 1 or 2 alternating runs of black and white in a uniform Ising model with no external field. It shows that when the boundary contains a single run, the set of minimum odd bond reconstructions are described by simple paths connecting the endpoints of either the black or white run. When the boundary consists of 2 runs, the set of minimum odd bond reconstructions are formed in one or more of the following ways: by simple paths connecting the endpoints of the two black runs; by simple paths connecting the two white runs; or by three simple paths connecting one of the boundary odd bonds to each of the other three. The paper provides a closed form solution for determining all minimum odd bond reconstructions for a 2-run boundary.

Original languageEnglish (US)
Title of host publicationAdvances in Computer Vision - Proceedings of the 2019 Computer Vision Conference CVC
EditorsSupriya Kapoor, Kohei Arai
PublisherSpringer Verlag
Pages237-256
Number of pages20
ISBN (Print)9783030177942
DOIs
StatePublished - Jan 1 2020
EventComputer Vision Conference, CVC 2019 - Las Vegas, United States
Duration: Apr 25 2019Apr 26 2019

Publication series

NameAdvances in Intelligent Systems and Computing
Volume943
ISSN (Print)2194-5357

Conference

ConferenceComputer Vision Conference, CVC 2019
CountryUnited States
CityLas Vegas
Period4/25/194/26/19

Fingerprint

Ising model
Interpolation

Keywords

  • Inpainting
  • Ising model
  • MAP interpolation
  • Odd bonds

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)

Cite this

Reyes, M. G., Neuhoff, D. L., & Pappas, T. N. (2020). MAP Interpolation of an Ising Image Block. In S. Kapoor, & K. Arai (Eds.), Advances in Computer Vision - Proceedings of the 2019 Computer Vision Conference CVC (pp. 237-256). (Advances in Intelligent Systems and Computing; Vol. 943). Springer Verlag. https://doi.org/10.1007/978-3-030-17795-9_17
Reyes, Matthew G. ; Neuhoff, David L. ; Pappas, Thrasyvoulos N. / MAP Interpolation of an Ising Image Block. Advances in Computer Vision - Proceedings of the 2019 Computer Vision Conference CVC. editor / Supriya Kapoor ; Kohei Arai. Springer Verlag, 2020. pp. 237-256 (Advances in Intelligent Systems and Computing).
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Reyes, MG, Neuhoff, DL & Pappas, TN 2020, MAP Interpolation of an Ising Image Block. in S Kapoor & K Arai (eds), Advances in Computer Vision - Proceedings of the 2019 Computer Vision Conference CVC. Advances in Intelligent Systems and Computing, vol. 943, Springer Verlag, pp. 237-256, Computer Vision Conference, CVC 2019, Las Vegas, United States, 4/25/19. https://doi.org/10.1007/978-3-030-17795-9_17

MAP Interpolation of an Ising Image Block. / Reyes, Matthew G.; Neuhoff, David L.; Pappas, Thrasyvoulos N.

Advances in Computer Vision - Proceedings of the 2019 Computer Vision Conference CVC. ed. / Supriya Kapoor; Kohei Arai. Springer Verlag, 2020. p. 237-256 (Advances in Intelligent Systems and Computing; Vol. 943).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - This paper considers the problem of finding the set of MAP reconstructions of an N× N block conditioned on a boundary configuration consisting of 1 or 2 alternating runs of black and white in a uniform Ising model with no external field. It shows that when the boundary contains a single run, the set of minimum odd bond reconstructions are described by simple paths connecting the endpoints of either the black or white run. When the boundary consists of 2 runs, the set of minimum odd bond reconstructions are formed in one or more of the following ways: by simple paths connecting the endpoints of the two black runs; by simple paths connecting the two white runs; or by three simple paths connecting one of the boundary odd bonds to each of the other three. The paper provides a closed form solution for determining all minimum odd bond reconstructions for a 2-run boundary.

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Reyes MG, Neuhoff DL, Pappas TN. MAP Interpolation of an Ising Image Block. In Kapoor S, Arai K, editors, Advances in Computer Vision - Proceedings of the 2019 Computer Vision Conference CVC. Springer Verlag. 2020. p. 237-256. (Advances in Intelligent Systems and Computing). https://doi.org/10.1007/978-3-030-17795-9_17