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

1 Scopus citations

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
EditorsKohei Arai, Supriya Kapoor
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
ISSN (Electronic)2194-5365

Conference

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

Keywords

  • Inpainting
  • Ising model
  • MAP interpolation
  • Odd bonds

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)

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  • Cite this

    Reyes, M. G., Neuhoff, D. L., & Pappas, T. N. (2020). MAP Interpolation of an Ising Image Block. In K. Arai, & S. Kapoor (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