On the absolute quadratic complex and its application to autocalibration

• Published in: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) Vol. 1; pp. 780 - 787 vol. 1
• Main Authors: Ponce, J., McHenry, K., Papadopoulo, T., Teillaud, M., Triggs, B.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2005
• Subjects: Calibration; Digital cameras; Geometry; Image reconstruction; Iterative algorithms; Iterative methods; Layout; Physics computing; Surface reconstruction; Symmetric matrices
• ISBN: 0769523722; 9780769523729
• ISSN: 1063-6919; 1063-6919
• DOI: 10.1109/CVPR.2005.256

This article introduces the absolute quadratic complex formed by all lines that intersect the absolute conic. If /spl omega/ denotes the 3 /spl times/ 3 symmetric matrix representing the image of that conic under the action of a camera with projection matrix P, it is shown that /spl omega/ /spl ap/ P/sup ~//spl Omega//sub /spl I.bar//P/sup ~T/ where V is the 3 /spl times/ 6 line projection matrix associated with P and /spl Omega//sub /spl I.bar// is a 6 /spl times/ 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 /spl omega/, P/sup ~/ and /spl Omega//sub /spl I.bar// - 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 /spl omega/.