### Abstract

Many problems in computer vision, image processing, and computer graphics can be put into labeling problems [1]. In such a problem, an undirected graph is given as an abstraction of locations and their neighborhood structure, along with a set of labels. Then, the solutions to the problem is identified with labelings, or assignments of a label to each vertex in the graph. The problem is then to find the best labeling according to the criteria in the problem's requirements. An energy is a translation of the criteria into a function that evaluates how good the given labeling is, so that smaller energy for a labeling means a better corresponding solution to the problem. Thus, the problem becomes an “energy minimization problem”. This separates the problem and the technique to solve it in a useful way by formulating the problem as an energy, it tends to make the problem more clearly defined, and also, once the problem is translated into an energy minimization problem, it can be solved using general algorithms.

Original language | English |
---|---|

Title of host publication | Image Processing and Analysis with Graphs |

Subtitle of host publication | Theory and Practice |

Publisher | CRC Press |

Pages | 25-64 |

Number of pages | 40 |

ISBN (Electronic) | 9781439855089 |

ISBN (Print) | 9781315217284 |

DOIs | |

Publication status | Published - 2012 Jan 1 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Engineering(all)

### Cite this

*Image Processing and Analysis with Graphs: Theory and Practice*(pp. 25-64). CRC Press. https://doi.org/10.1201/b12281

**Graph cuts-combinatorial optimization in vision.** / Ishikawa, Hiroshi.

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

*Image Processing and Analysis with Graphs: Theory and Practice.*CRC Press, pp. 25-64. https://doi.org/10.1201/b12281

}

TY - CHAP

T1 - Graph cuts-combinatorial optimization in vision

AU - Ishikawa, Hiroshi

PY - 2012/1/1

Y1 - 2012/1/1

N2 - Many problems in computer vision, image processing, and computer graphics can be put into labeling problems [1]. In such a problem, an undirected graph is given as an abstraction of locations and their neighborhood structure, along with a set of labels. Then, the solutions to the problem is identified with labelings, or assignments of a label to each vertex in the graph. The problem is then to find the best labeling according to the criteria in the problem's requirements. An energy is a translation of the criteria into a function that evaluates how good the given labeling is, so that smaller energy for a labeling means a better corresponding solution to the problem. Thus, the problem becomes an “energy minimization problem”. This separates the problem and the technique to solve it in a useful way by formulating the problem as an energy, it tends to make the problem more clearly defined, and also, once the problem is translated into an energy minimization problem, it can be solved using general algorithms.

AB - Many problems in computer vision, image processing, and computer graphics can be put into labeling problems [1]. In such a problem, an undirected graph is given as an abstraction of locations and their neighborhood structure, along with a set of labels. Then, the solutions to the problem is identified with labelings, or assignments of a label to each vertex in the graph. The problem is then to find the best labeling according to the criteria in the problem's requirements. An energy is a translation of the criteria into a function that evaluates how good the given labeling is, so that smaller energy for a labeling means a better corresponding solution to the problem. Thus, the problem becomes an “energy minimization problem”. This separates the problem and the technique to solve it in a useful way by formulating the problem as an energy, it tends to make the problem more clearly defined, and also, once the problem is translated into an energy minimization problem, it can be solved using general algorithms.

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U2 - 10.1201/b12281

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SP - 25

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BT - Image Processing and Analysis with Graphs

PB - CRC Press

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