On the Absolute Quadratic Complex and Its Application to Autocalibration

Abstract

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/.