Overconstrained Linear Estimation of Radial Distortion and Multi-View Geometry

Abstract

This paper introduces a new method for simultaneous estimation of lens distortion and multi-view geometry using only point correspondences. The new technique has significant advantages over the current state-of-the art in that it makes more effective use of correspondences arising from any number of views. Multi-view geometry in the presence of lens distortion can be expressed as a set of point correspondence constraints that are quadratic in the unknown distortion parameter. Previous work has demonstrated how the system can be solved efficiently as a quadratic eigenvalue problem by operating on the normal equations of the system. Although this approach is appropriate for situations in which only a minimal set of matchpoints are available, it does not take full advantage of extra correspondences in overconstrained situations, resulting in significant bias and many potential solutions. The new technique directly operates on the initial constraint equations and solves the quadratic eigenvalue problem in the case of rectangular matrices. The method is shown to contain significantly less bias on both controlled and real-world data and, in the case of a moving camera where additional views serve to constrain the number of solutions, an accurate estimate of both geometry and distortion is achieved.