Minimal Solvers for Relative Pose with a Single Unknown Radial Distortion

Abstract:
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 Gr¨obner 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.