On the Absolute Quadratic Complex and Its Application to Autocalibration

This article introduces the absolute quadratic complex formed by all lines that intersect the absolute conic. If 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 PP T , where P is the 3?6 line projection matrix associated with P, and 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 , P, and --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 .

• Type: Conference
• Year: 2005
• Where: CVPR
• Authors: Jean Ponce, Kenton McHenry, Théodore Papadopoulo, Monique Teillaud, Bill Triggs
• Keywords: Absolute Quadratic Complex, Computer Vision, CVPR 2005, Intrinsic Parameters, Line Projection Matrix, Projection Matrix, Symmetric Matrix