A Minimal Solution for the Extrinsic Calibration of a Camera and a Laser-Rangefinder

Abstract

This paper presents a new algorithm for the extrinsic calibration of a perspective camera and an invisible 2D laser-rangefinder (LRF). The calibration is achieved by freely moving a checkerboard pattern in order to obtain plane poses in camera coordinates and depth readings in the LRF reference frame. The problem of estimating the rigid displacement between the two sensors is formulated as one of registering a set of planes and lines in the 3D space. It is proven for the first time that the alignment of three plane-line correspondences has at most eight solutions that can be determined by solving a standard p3p problem and a linear system of equations. This leads to a minimal closed-form solution for the extrinsic calibration that can be used as hypothesis generator in a RANSAC paradigm. Our calibration approach is validated through simulation and real experiments that show the superiority with respect to the current state-of-the-art method requiring a minimum of five input planes.

UCalMiCeL – UNIFIED INTRINSIC AND EXTRINSIC CALIBRATION OF A MULTI-CAMERA-SYSTEM AND A LASERSCANNER

“…This procedure was developed to calibrate line laserscanners to a single camera with a generic camera model, including pinhole, fisheye and omnidirectional cameras. The calibration in Urban and Jutzi (2017) is an extension to The Robust Automatic Detection in Laser Of Calibration Chessboards (RADLOCC) toolbox (Zhang and Pless, 2004) and the minimal approach of registering a set of lines to a set of planes (Vasconcelos et al, 2012). These algorithms treat the calibration of a line laserscanner w.r.t.…”

“…Thereby, the pose of the camera can be estimated from a single image. For practical reasons, the calibration methods which are mostly used deal with planar checkerboards like they are commonly utilized for intrinsic camera calibrations (Zhang and Pless, 2004;Zhou, 2014;Tulsuk et al, 2014;Vasconcelos et al, 2012). In contrast, the usage of scene corners avoids the need for special calibration objects (GomezOjeda et al, 2015) which offers potential to be extended to a self-calibration technique.…”

“…Like the calibration procedure proposed by Zhang and Pless (2004) and Vasconcelos et al (2012) our calibration requires a plane whose pose can be estimated from the images, e.g. a checkerboard.…”

“…In the next step of the procedure, all laserscanner points which correspond to the calibration plane are searched in the assigned observation. Finally, the approximate transformation matrixM C i L is estimated basically by using random sample consensus (RANSAC) like in the minimal approach of registering a set of lines to a set of planes (Vasconcelos et al, 2012).…”

“…While capturing, we stay for some seconds in the individual positions to eliminate remaining errors in the synchronization of the cameras and the laserscanner as well as to increase the accuracy of the distance measurements of the laserscanner by averaging five consecutive observations. To ensure that the minimal solution described by Vasconcelos et al (2012) estimates a correct pose of the scanner w.r.t. the cameras, a set of well distributed laserscanner segments with varying orientations is needed.…”