Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion

In this paper, we study the problems of estimating relative pose between two cameras in the presence of radial distortion. Specifically, we consider minimal problems where one of the cameras has no or known radial distortion. There are three useful cases for this setup with a single unknown distortion: (i) fundamental matrix estimation where the two cameras are uncalibrated, (ii) essential matrix estimation for a partially calibrated camera pair, (iii) essential matrix estimation for one calibrated camera and one camera with unknown focal length. We study the parameterization of these three problems and derive fast polynomial solvers based on Gröbner basis methods. We demonstrate the numerical stability of the solvers on synthetic data. The minimal solvers have also been applied to real imagery with convincing results.