On the absolute quadratic complex and its application to autocalibration

J. Ponce, K. McHenry, T. Papadopoulo, M. Teillaud, B. Triggs

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 ℘, it is shown that ω ≈ P̄ΩP̄T, where ℘̄ is the 3×6 line projection matrix associated with ℘, 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, ℘̄, 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.

Original languageEnglish (US)
Title of host publicationProceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
PublisherIEEE Computer Society
Pages780-787
Number of pages8
ISBN (Print)0769523722, 9780769523729
DOIs
StatePublished - 2005
Event2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005 - San Diego, CA, United States
Duration: Jun 20 2005Jun 25 2005

Publication series

NameProceedings - 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
VolumeI

Other

Other2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005
Country/TerritoryUnited States
CitySan Diego, CA
Period6/20/056/25/05

ASJC Scopus subject areas

  • Engineering(all)

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