### 抜粋

The representation of objects in images as tree structures is of great interest to vision, as they can represent articulated objects such as people as well as other structured objects like arteries in human bodies, roads, circuit board patterns, etc. Tree structures are often related to the symmetry axis representation of shapes, which captures their local symmetries. Algorithms have been introduced to detect (i) open contours in images in quadratic time (ii) closed contours in images in cubic time, and (in) tree structures from contours in quadratic time. The algorithms are based on dynamic programming and Single Source Shortest Path algorithms. However, in this paper, we show that the problem of finding tree structures in images in a principled manner is a much harder problem. We argue that the optimization problem of finding tree structures in images is essentially equivalent to a variant of the Steiner Tree problem, which is NP-hard. Nevertheless, an approximate polynomial-time algorithm for this problem exists: we apply a fast implementation of the Goemans-Williamson approximate algorithm to the problem of finding a tree representation after an image is transformed by a local symmetry mapping. Examples of extracting tree structures from images illustrate the idea and applicability of the approximate method.

元の言語 | English |
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ホスト出版物のタイトル | Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005 |

ページ | 1132-1139 |

ページ数 | 8 |

DOI | |

出版物ステータス | Published - 2005 12 1 |

外部発表 | Yes |

イベント | Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005 - Beijing, China 継続期間: 2005 10 17 → 2005 10 20 |

### 出版物シリーズ

名前 | Proceedings of the IEEE International Conference on Computer Vision |
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巻 | II |

### Conference

Conference | Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005 |
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国 | China |

市 | Beijing |

期間 | 05/10/17 → 05/10/20 |

### ASJC Scopus subject areas

- Software
- Computer Vision and Pattern Recognition

## フィンガープリント Finding tree structures by grouping symmetries' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*Proceedings - 10th IEEE International Conference on Computer Vision, ICCV 2005*(pp. 1132-1139). [1544848] (Proceedings of the IEEE International Conference on Computer Vision; 巻数 II). https://doi.org/10.1109/ICCV.2005.100