The impact of radial distortion on the self-calibration of rotating cameras

Recent methods of automatically calibrating the intrinsic parameters of cameras undergoing pure rotation are based on the infinite homography constraint, and have been found to be sensitive to radial distortion in the imagery. This paper develops a straightforward argument based on geometrical optics to show that increasing pin-cushion radial distortion will produce a gently worsening underestimate of the lens' focal length, whereas increasing barrel radial distortion will produce a more sharply increasing overestimate followed by failure of the calibration. A second geometrical argument uses the approximation of a barrel-distorted image to a spherical projection to estimate the degree of distortion at which breakdown is likely to occur. The predictions are verified experimentally using data from real scenes with varying degrees of distortion and noise added. The paper also considers four methods of correcting the radial distortion within self-calibration. The first method pre-calibrates the distortion as a function of focal length, but the remainder assume no such prior knowledge. Although these prior-less methods are successful to an extent, everyday scenes are unlikely to provide image feature data of sufficient density and quality to make them fully viable.