MAP Interpolation of an Ising Image Block

  • Matthew G. ReyesEmail author
  • David L. Neuhoff
  • Thrasyvoulos N. Pappas
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 943)


This paper considers the problem of finding the set of MAP reconstructions of an \(N\times N\) 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.


Inpainting MAP interpolation Ising model Odd bonds 


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Matthew G. Reyes
    • 1
    Email author
  • David L. Neuhoff
    • 2
  • Thrasyvoulos N. Pappas
    • 3
  1. 1.Independent Researcher and ConsultantAnn ArborUSA
  2. 2.University of MichiganAnn ArborUSA
  3. 3.Northwestern UniversityEvanstonUSA

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