### Abstract

Given a set of point correspondences in an uncalibrated image pair, we can estimate the fundamental matrix, which can be used in calculating several geometric properties of the images. Among the several existing estimation methods, nonlinear methods can yield accurate results if an approximation to the true solution is given, whereas linear methods are inaccurate but no prior knowledge about the solution is required. Usually a linear method is employed to initialize a nonlinear method, but this sometimes results in failure when the linear approximation is far from the true solution. We herein describe an alternative, or complementary, method for the initialization. The proposed method minimizes the algebraic error, making sure that the results have the rank-2 property, which is neglected in the conventional linear method. Although an approximation is still required in order to obtain a feasible algorithm, the method still outperforms the conventional linear 8-point method, and is even comparable to Sampson error minimization.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 1215-1224 |

Number of pages | 10 |

Volume | 4319 LNCS |

DOIs | |

Publication status | Published - 2006 |

Event | 1st Pacific Rim Symposium on Image and Video Technology, PSIVT 2006 - Hsinchu, Taiwan, Province of China Duration: Dec 10 2006 → Dec 13 2006 |

### 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 | 4319 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 1st Pacific Rim Symposium on Image and Video Technology, PSIVT 2006 |
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Country | Taiwan, Province of China |

City | Hsinchu |

Period | 12/10/06 → 12/13/06 |

### Fingerprint

### Keywords

- Epipole estimation
- Fundamental matrix
- Polynomial equation
- Resultant

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 4319 LNCS, pp. 1215-1224). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4319 LNCS). https://doi.org/10.1007/11949534-123