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Ronda Prieto, José Ignacio and Valdés Morales, Antonio
(2012)
*Calibración euclídea a partir de longitudes de segmentos.*
In
Contribuciones matemáticas en honor a Juan Tarrés.
UCM, Madrid, pp. 343-374.
ISBN 978-84-695-4421-1

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## Abstract

We address the problem of the recovery of Euclidean structure of a projectively distorted n-dimensional space from the knowledge of the, possibly diverse, lenghts of a set of segments. This problem is relevant, in particular, for Euclidean reconstruction with uncalibrated cameras, extending previously known results in the affine setting. The key concept is the Quadric of Segments (QoS), defined in a higher-dimensional space by the set of segments of a fixed lenght, from which Euclidean structure can be obtained in closed form. We have intended to make a thorough study of the properties of the QoS, including the determination of the minimum number of segments of arbitrary length that determine it and its relationship with the standard geometric objects associated to the Euclidean structure of space. Explicit formulas are given to obtain the dual absolute quadric and the absolute quadratic complex from the QoS. Experiments with real and synthetic images evaluate the performance of the techniques.

Item Type: | Book Section |
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Uncontrolled Keywords: | Calibración de cámaras; Actualización euclídea; Reconstrucción 3D |

Subjects: | Sciences > Mathematics > Geometry Sciences > Mathematics > Topology |

ID Code: | 17400 |

Deposited On: | 12 Dec 2012 12:55 |

Last Modified: | 09 Sep 2020 08:10 |

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