On the Absolute Quadratic Complex and its Application to Autocalibration

Jean Ponce 1 Kenton Mc Henry 1 Théodore Papadopoulo 2 Monique Teillaud 3, * Bill Triggs 4
* Corresponding author
2 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
3 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
4 LEAR - Learning and recognition in vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : This article introduces the absolute quadratic complex formed by all lines that intersect the absolute conic. If ω denotes the 3 × 3 symmetric matrix representing the image of that conic under the action of a camera with projection matrix P, it is shown that ω ≈ P~Ω_P~T where V is the 3 × 6 line projection matrix associated with P and Ω_ is a 6 × 6 symmetric matrix of rank 3 representing the absolute quadratic complex. This simple relation between a camera's intrinsic parameters, its projection matrix expressed in a projective coordinate frame, and the metric upgrade separating this frame from a metric one - as respectively captured by the matrices ω, P~ and Ω_ - provides a new framework for autocalibration, particularly well suited to typical digital cameras with rectangular or square pixels since the skew and aspect ratio are decoupled from the other intrinsic parameters in ω.
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Jean Ponce, Kenton Mc Henry, Théodore Papadopoulo, Monique Teillaud, Bill Triggs. On the Absolute Quadratic Complex and its Application to Autocalibration. IEEE Conference on Computer Vision & Pattern Recognition (CPRV '05), Jun 2005, San Diego, United States. pp.780--787, ⟨10.1109/CVPR.2005.256⟩. ⟨inria-00548505⟩

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