Self calibration of focal length and rotation parameters using cross ratio

This paper presents a simple method for the calibration of a focal length and rotation parameters of a camera. We assume that the remaining calibration parameters of the camera change so little that they are considered fixed constants during a visual task. The employed vision system comprises a pan/tilt mechanism and a single camera, which is a typical setup for mobile robot navigation. The calibration process is performed by making use of vanishing points obtained from a rectangular pattern with an unknown size. Determination of vanishing points relies on a viewpoint invariant property in perspective transform-cross ratio. Focal length calibration is carried out by inner product of two vanishing point vectors. The rotation parameters are also estimated by projecting the image plane on the Gaussian sphere and extracting the surface normal vector of the calibration object. Possible errors in the calibrated parameters are studied by simulation and a preliminary result is presented