Stable radial distortion calibration by polynomial matrix inequalities programming

TL;DR

This paper introduces a novel method for radial distortion calibration that enforces polynomial nonnegativity constraints using polynomial matrix inequalities and semidefinite programming, improving accuracy and robustness.

Contribution

It presents a new approach to radial distortion calibration by modeling nonnegativity constraints with PMI and solving via SDP, addressing extrapolation and numerical issues.

Findings

Enhanced calibration accuracy with PMI constraints

Robustness against extrapolation issues

Integration into camera calibration workflows

Abstract

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.