Calibration methods for a camera with a tilted lens and a three-dimensional laser scanner in the Scheimpflug condition

Mingwei Shao

doi:10.1364/JOSAA.391906

Journal of the Optical Society of America A
Vol. 37,
Issue 7,
pp. 1076-1082
(2020)
•https://doi.org/10.1364/JOSAA.391906

Calibration methods for a camera with a tilted lens and a three-dimensional laser scanner in the Scheimpflug condition

Mingwei Shao

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Mingwei Shao, "Calibration methods for a camera with a tilted lens and a three-dimensional laser scanner in the Scheimpflug condition," J. Opt. Soc. Am. A 37, 1076-1082 (2020)

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Abstract

A three-dimensional laser scanner has been designed and widely utilized in many fields. The lens plane is tilted according to the Scheimpflug condition and the optical axis is not perpendicular to the charge-coupled device plane. In this case, depth of view can be extended significantly. In this paper, analytical models for a camera with a tilted lens and a laser scanner meeting the Scheimpflug condition are presented. Based on these models, a calibration procedure is detailed. We propose a simple calibration method to determine the intrinsic parameters of a Scheimpflug camera. Meanwhile, two calibration methods for a laser scanner in the Scheimpflug condition are detailed. According to the obtained intrinsic parameters, the laser scanner can be calibrated directly. Moreover, a simple calibration for a three-dimensional laser scanner without the help of a precise positioning system is described. Experimental results show the effectiveness and high measurement accuracy of our calibration methods.

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Equations (20)

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Item	Distortion-Free	Distortion-Rectified
( $f_{x}, f_{y}$ )	(2963.96,2971.21)	(2949.73,2966.51)
( $u_{0}, v_{0}$ ) (pixel)	(621.39, 405.11)	(601.90, 390.17)
( $α, β$ ) (degree)	(8.11,262.31)	(8.05,269.91)
( $m_{11}, m_{12}, m_{13}$ )	(−0.134, −0.140, −0.981)	(−0.002, −0.140, −0.990)
( $m_{21}, m_{22}, m_{23}$ )	(0.000,0.990, −0.141)	(0.000,0.990, −0.140)
( $m_{31}, m_{32}, m_{33}$ )	(0.991, −0.019, −0.133)	(1.000, −0.000, −0.002)
( $t_{x}, t_{y}, t_{z}$ ) (mm)	(−79.213,11.199,120.774)	(−78.199,10.237,119.072)
( $k_{1}, k_{2}$ )	(0.00,0.00)	(−0.2451, −0.3607)
Reprojection error	0.089	0.008

Item	1	2	3	4	5	6	7	8	9	10	RMS
dMea1 (mm)	11.970	12.047	12.046	11.999	12.030	11.964	11.992	12.042	12.029	12.046	0.035
Error 1	−0.030	0.047	0.046	0.001	0.030	−0.036	−0.008	0.042	0.029	0.046
dMea1 (mm)	12.040	12.007	12.021	11.954	12.040	12.048	12.033	12.002	11.957	12.047	0.036
Error 1	0.040	0.007	0.021	−0.046	0.040	0.048	0.033	0.002	−0.043	0.047

Item	Distortion-Free	Distortion-Rectified
( $f_{x}, f_{y}$ )	(2963.96,2971.21)	(2949.73,2966.51)
( $u_{0}, v_{0}$ ) (pixel)	(621.39, 405.11)	(601.90, 390.17)
( $α, β$ ) (degree)	(8.11,262.31)	(8.05,269.91)
( $m_{11}, m_{12}, m_{13}$ )	(−0.134, −0.140, −0.981)	(−0.002, −0.140, −0.990)
( $m_{21}, m_{22}, m_{23}$ )	(0.000,0.990, −0.141)	(0.000,0.990, −0.140)
( $m_{31}, m_{32}, m_{33}$ )	(0.991, −0.019, −0.133)	(1.000, −0.000, −0.002)
( $t_{x}, t_{y}, t_{z}$ ) (mm)	(−79.213,11.199,120.774)	(−78.199,10.237,119.072)
( $k_{1}, k_{2}$ )	(0.00,0.00)	(−0.2451, −0.3607)
Reprojection error	0.089	0.008

Item	1	2	3	4	5	6	7	8	9	10	RMS
dMea1 (mm)	11.970	12.047	12.046	11.999	12.030	11.964	11.992	12.042	12.029	12.046	0.035
Error 1	−0.030	0.047	0.046	0.001	0.030	−0.036	−0.008	0.042	0.029	0.046
dMea1 (mm)	12.040	12.007	12.021	11.954	12.040	12.048	12.033	12.002	11.957	12.047	0.036
Error 1	0.040	0.007	0.021	−0.046	0.040	0.048	0.033	0.002	−0.043	0.047

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Equations (20)

Journal of the Optical Society of America A