A Unified Approach to Extrinsic Calibration between a Camera and a Laser Range Finder using Point-Plane Constraints

This paper deals with the extrinsic calibration problem between a camera and a 2D or 3D laser range finder. While various solutions have been previously proposed, the ge- ometry of the problem is not well described, and minimal conditions and degenerate configurations are not well es- tablished. We show that the various constraints used in the previously proposed methods can all be modelled as point-plane constraints, a problem that has already received some attention in the field of robot kinematics. By doing so, the extrinsic calibration problem can be expressed as a system of quadratic polynomials, and solved in a uni- fied manner using methods developed for the kinematics point-plane constraints problem. Furthermore, using ana- lytical results obtained in algebraic geometry, the minimal conditions and degenerate configurations for the extrinsic calibration problem can be established. Lastly, we pro- pose to minimize the “line-of-sight” errors, which directly models the noise in the laser range finder measurements, giving a maximum likelihood estimate of the calibration parameters.