Point correspondence validation under unknown radial distortion

Abstract

Standard two-view epipolar geometry assumes that images are taken using pinhole cameras. Real cameras, however, approximate ideal pinhole cameras using lenses and apertures. This leads to radial distortion effects in images that are not characterisable by the standard epipolar geometry model. The existence of radial distortion severely impacts the efficacy of point correspondence validation based on the epipolar constraint. Many previous works deal with radial distortion by augment- ing the epipolar geometry model (with additional parameters such as distortion coefficients and centre of distortion) to enable the modelling of radial distortion effects. Indirectly, this assumes that an accurate model of the radial distortion is known. In this paper, we take a different approach: we view radial distortion as a violation to the basic epipolar geometry equation. Instead of striving to model radial distortion, we adjust the epipolar geometry to account for the distortion effects. This adjustment is performed via moving least squares (MLS) surface approxi- mation, which we extend to allow for projective estimation. We also combine M-estimators with MLS to allow robust matching of interest points under severe radial distortion. Compared to previous works, our method is much simpler and involves just solving linear subproblems. It also exhibits a higher tolerance in cases where the exact model of radial distortion is unknown.