  Polynomial and rational functions are the number one choice when it comes to
modeling of radial distortion of lenses. However, several extrapolation and
numerical issues may arise while using these functions that have not been
covered by the literature much so far. In this paper, we identify these
problems and show how to deal with them by enforcing nonnegativity of certain
polynomials. Further, we show how to model these nonnegativities using
polynomial matrix inequalities (PMI) and how to estimate the radial distortion
parameters subject to PMI constraints using semidefinite programming (SDP).
Finally, we suggest several approaches on how to incorporate the proposed
method into the overall camera calibration procedure.
