### Abstract

In this paper we study the learnability of a mixture of lines model which is of great importance in machine vision, computer graphics, and computer aided design applications. The mixture of lines is a partially-probabilistic model for an image composed of line-segments. Observations are generated by choosing one of the lines at random and picking a point at random from the chosen line. Each point is contaminated with some noise whose distribution is unknown, but which is bounded in magnitude. Our goal is to discover efficiently and rather accurately the line-segments that generated the noisy observations. We describe and analyze an efficient probably approximately correct (PAC) algorithm for solving the problem. Our algorithm combines techniques from planar geometry with simple large deviation tools and is simple to implement.

Original language | English (US) |
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Title of host publication | Algorithmic Learning Theory - 13th International Conference, ALT 2002, Proceedings |

Editors | Nicolò Cesa-Bianchi, Masayuki Numao, Rüdiger Reischuk |

Publisher | Springer Verlag |

Pages | 351-364 |

Number of pages | 14 |

ISBN (Print) | 3540001700, 9783540001706 |

State | Published - Jan 1 2002 |

Externally published | Yes |

Event | 13th International Conference on Algorithmic Learning Theory, ALT 2002 - Lübeck, Germany Duration: Nov 24 2002 → Nov 26 2002 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2533 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 13th International Conference on Algorithmic Learning Theory, ALT 2002 |
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Country | Germany |

City | Lübeck |

Period | 11/24/02 → 11/26/02 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithmic Learning Theory - 13th International Conference, ALT 2002, Proceedings*(pp. 351-364). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2533). Springer Verlag.