Acta Optica Sinica, Volume. 42, Issue 16, 1612004(2022)
Camera Parameter Calibration Based on Directional Layered Target
Figures & Tables(16)
Fig. 2. Results of camera calibration by using target with different sizes. (a) Focal length; (b) horizontal coordinates of principal points
Fig. 4. Results of camera calibration with complete and incomplete targets. (a) Focal length; (b) horizontal coordinates of principal points
Fig. 8. Identification and matching of directional targets. (a) Sketch of combined coordinate system; (b) marker map of target matching on axis
Fig. 9. Target matching for partial target deficiency. (a) Experimental picture I; (b) matching result of experimental picture I; (c) experimental picture II; (d) matching result of experimental picture II
Fig. 10. Experimental pictures of camera calibration. (a) Small view (groups 1 and 2); (b) large view (groups 3 and 4)
Fig. 11. Distributions of reprojection error. (a) Group 1; (b) group 2; (c) group 3; (d) group 4
Table 1. Standard error of calibration results of camera parameters under different target sizes
View tableTable 1. Standard error of calibration results of camera parameters under different target sizes
Proportion of target in camera field Focal length
fx /mm
Focal length
fy /mm
Horizontal coordinate of principal point /pixel Vertical coordinate of principal point /pixel 1/16 0.3196 0.3097 45.0250 46.0966 1/8 0.1644 0.1645 24.8408 24.9445 1/4 0.0720 0.0718 11.5732 11.6927 1/2 0.0370 0.0371 5.3656 5.7319
Table 2. Standard error of calibration results of camera parameters under different number of targets
View tableTable 2. Standard error of calibration results of camera parameters under different number of targets
Number of targets Focal length
fx /mm
Focal length
fy /mm
Horizontal coordinate of principal point /pixel Vertical coordinate of principal point /pixel 3×3 0.1268 0.1267 18.2767 18.4984 5×5 0.0769 0.0774 14.2790 13.9455 7×7 0.0398 0.0390 11.1139 10.7524 9×9 0.0317 0.0313 10.1562 9.9529
Table 3. Standard error of calibration results of camera parameters for complete and incomplete targets
View tableTable 3. Standard error of calibration results of camera parameters for complete and incomplete targets
Target Focal length
fx /mm
Focal length
fy /mm
Horizontal coordinate of principal point /pixel Vertical coordinate of principal point /pixel Complete target 0.0424 0.0426 10.2133 10.3020 Incomplete target 0.0450 0.0454 10.1544 10.5856
Table 4. Results of camera parameter calibration
View tableTable 4. Results of camera parameter calibration
Group No. Focal
length /mm
Principal point
（u0，v0）（unit：pixel）
Radical distortion coefficient Tangential distortion coefficient Reprojection
error /pixel
k1 k2 p1 p2 1 53.25 （1315.2，993.7） -0.065 -3.244 0.001 0 0.076 2 53.37 （1317.1，990.1） -0.064 -3.266 0.001 0 0.073 3 52.57 （1328.0，995.0） 0.170 -3.437 0.001 0 0.108 4 51.33 （1317.5，991.2） 0.177 -3.122 0.001 0 0.072
Table 5. Results of camera calibration and measurement
View tableTable 5. Results of camera calibration and measurement
Target Focal
length /mm
Principal
point（u0，v0）（unit：pixel）
Radical distortion
coefficient
Tangential distortion
coefficient
Reprojection
error /pixel
Measuring
error /mm
k1 k2 p1 p2 I 16.50 （788.0，485.3） -0.505 -11.851 -0.002 0.001 0.208 0.009 II 16.56 （791.3，477.6） -0.533 -10.044 -0.002 0 0.200 0.008 I 34.48 （816.6，453.4） 3.036 -867.384 0.008 0.015 0.832 0.054 II 32.16 （768.2，494.6） 0.734 -189.812 -0.001 0.011 0.217 0.008
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Min Zhao, Xiaogang Li, Zepeng Su, Lingjian Zhu. Camera Parameter Calibration Based on Directional Layered Target[J]. Acta Optica Sinica, 2022, 42(16): 1612004
Paper Information
Category: Instrumentation, Measurement and Metrology
Received: Jan. 17, 2022
Accepted: Mar. 24, 2022
Published Online: Aug. 4, 2022
The Author Email: Zhao Min (zhaomin1973@xaut.edu.cn)
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