The Absolute Line Quadric and Camera Autocalibration

Valdés Morales, Antonio and Ronda Prieto, José Ignacio and Gallego Bonet, Guillermo (2006). The Absolute Line Quadric and Camera Autocalibration. "International Journal of Computer Vision", v. 66 (n. 3); pp. 283-303. ISSN 0920-5691.


Title: The Absolute Line Quadric and Camera Autocalibration
  • Valdés Morales, Antonio
  • Ronda Prieto, José Ignacio
  • Gallego Bonet, Guillermo
Item Type: Article
Título de Revista/Publicación: International Journal of Computer Vision
Date: March 2006
Volume: 66
Freetext Keywords: Camera autocalibration, Euclidean upgrading, Three-dimensional reconstruction, Algebraic geometry, Space lines, Square pixels, Known Pixel Shape, Absolute Line Quadric, Absolute Quadratic Complex, Grassmannian, Dual Absolute Quadric
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Señales, Sistemas y Radiocomunicaciones
UPM's Research Group:
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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We introduce a geometrical object providing the same information as the absolute conic: the absolute line quadric (ALQ). After the introduction of the necessary exterior algebra and Grassmannian geometry tools, we analyze the Grassmannian of lines of P^3 from both the projective and Euclidean points of view. The exterior algebra setting allows then to introduce the ALQ as a quadric arising very naturally from the dual absolute quadric. We fully characterize the ALQ and provide clean relationships to solve the inverse problem, i.e., recovering the Euclidean structure of space from the ALQ. Finally we show how the ALQ turns out to be particularly suitable to address the Euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters, providing new linear and non-linear algorithms for this problem. We also provide experimental results showing the good performance of the techniques.

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Item ID: 10422
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Deposited by: Dr Guillermo Gallego Bonet
Deposited on: 02 Mar 2012 08:50
Last Modified: 29 May 2015 10:52
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