  This paper presents a novel method for fully automatic and convenient
extrinsic calibration of a 3D LiDAR and a panoramic camera with a normally
printed chessboard. The proposed method is based on the 3D corner estimation of
the chessboard from the sparse point cloud generated by one frame scan of the
LiDAR. To estimate the corners, we formulate a full-scale model of the
chessboard and fit it to the segmented 3D points of the chessboard. The model
is fitted by optimizing the cost function under constraints of correlation
between the reflectance intensity of laser and the color of the chessboard's
patterns. Powell's method is introduced for resolving the discontinuity problem
in optimization. The corners of the fitted model are considered as the 3D
corners of the chessboard. Once the corners of the chessboard in the 3D point
cloud are estimated, the extrinsic calibration of the two sensors is converted
to a 3D-2D matching problem. The corresponding 3D-2D points are used to
calculate the absolute pose of the two sensors with Unified Perspective-n-Point
(UPnP). Further, the calculated parameters are regarded as initial values and
are refined using the Levenberg-Marquardt method. The performance of the
proposed corner detection method from the 3D point cloud is evaluated using
simulations. The results of experiments, conducted on a Velodyne HDL-32e LiDAR
and a Ladybug3 camera under the proposed re-projection error metric,
qualitatively and quantitatively demonstrate the accuracy and stability of the
final extrinsic calibration parameters.
