### 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 language | English (US) |
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Title of host publication | Advances in Computer Vision - Proceedings of the 2019 Computer Vision Conference CVC |

Editors | Kohei Arai, Supriya Kapoor |

Publisher | Springer Verlag |

Pages | 237-256 |

Number of pages | 20 |

ISBN (Print) | 9783030177942 |

DOIs | |

State | Published - Jan 1 2020 |

Event | Computer Vision Conference, CVC 2019 - Las Vegas, United States Duration: Apr 25 2019 → Apr 26 2019 |

### Publication series

Name | Advances in Intelligent Systems and Computing |
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Volume | 943 |

ISSN (Print) | 2194-5357 |

ISSN (Electronic) | 2194-5365 |

### Conference

Conference | Computer Vision Conference, CVC 2019 |
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Country | United States |

City | Las Vegas |

Period | 4/25/19 → 4/26/19 |

### Fingerprint

### Keywords

- Inpainting
- Ising model
- MAP interpolation
- Odd bonds

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science(all)

### Cite this

*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

}

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - MAP Interpolation of an Ising Image Block

AU - Reyes, Matthew G.

AU - Neuhoff, David L.

AU - Pappas, Thrasyvoulos N

PY - 2020/1/1

Y1 - 2020/1/1

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.

AB - 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.

KW - Inpainting

KW - Ising model

KW - MAP interpolation

KW - Odd bonds

UR - http://www.scopus.com/inward/record.url?scp=85065499556&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065499556&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-17795-9_17

DO - 10.1007/978-3-030-17795-9_17

M3 - Conference contribution

SN - 9783030177942

T3 - Advances in Intelligent Systems and Computing

SP - 237

EP - 256

BT - Advances in Computer Vision - Proceedings of the 2019 Computer Vision Conference CVC

A2 - Arai, Kohei

A2 - Kapoor, Supriya

PB - Springer Verlag

ER -