Author Affiliations
1State Key Laboratory of Astronautic Dynamics, Xi′an 710043, Shaanxi, China2Xian Satellite Control Center, Xi′an 710043, Shaanxi, China3China Academy of Space Technology (Xi′an), Xi′an 710000, Shaanxi, China4College of Aeronautics and Astronautics, National University of Defense Technology, Changsha 410073, Hunan, Chinashow less
Fig. 1. Imaging model of central perspective projection
Fig. 2. Correlation coefficient between translation component and equivalent focal length of camera varying with focal length. (a) Translation component in x direction; (b) translation component in y direction
Fig. 3. Standard concentric semi-circular cooperative template
Fig. 4. Cooperative concentric semi-elliptical template after projective transformation
Fig. 5. Perspective projection imaging model of 3D lines
Fig. 6. Flow chart of calibration algorithm
Fig. 7. RMS of relative error of calibration parameters of camera (f=20 mm) under different number of calibration views. (a) Fx; (b) Cx
Fig. 8. RMS of relative error of calibration parameters of camera (f=20 mm) under different noise level. (a) Fx; (b) Cx
Fig. 9. RMS of relative error of calibration parameters of camera (f=100 mm) under different number of calibration views. (a) Fx; (b) Cx
Fig. 10. RMS of relative error of calibration parameters of camera (f=100 mm) under different noise level. (a) Fx; (b) Cx
Fig. 11. RMS of relative error of camera calibration parameters under different focal lengths. (a) Fx; (b) Cx
Fig. 12. Detection results of concentric elliptical template
Fig. 13. Typical reconstruction results of stereo telephoto camera plane template. (a) Reconstructed 3D checkerboard points and fitted plane; (b) error distribution of reconstructed plane
Method | Zhang’s checkerborads | Zhang | ConC | ML-RML | NML-RNML |
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Cond | 24.4512 | 27.8839 | 31.5621 | 25.7813 | 24.3749 | Fx | 10201.9479 | 10278.1560 | 9878.3110 | 10277.8873 | 10214.9767 | Fy | 10152.2879 | 10237.8088 | 9844.5762 | 10242.7139 | 10163.7846 | Cx | 1212.2449 | 1188.0651 | 1239.5327 | 1255.4521 | 1212.6460 | Cy | 1071.7819 | 999.1277 | 1274.9569 | 1057.1832 | 1094.4985 | k1 | -0.2650 | -0.2380 | | -0.2760 | -0.2698 | k2 | -0.9880 | -2.2153 | | 0.3085 | -1.3301 | k3 | 0.0046 | 0.0040 | | 0.0041 | 0.0050 | k4 | -0.0022 | -0.0018 | | -0.0019 | -0.0028 | RMS /pixel | 0.1875 | 0.2071 | | 0.2064 | 0.1793 |
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Table 1. Results of different calibration algorithms under condition of 35 mm focal length
Methods | Zhang’s checkerborads | Zhang | ConC | ML-RML | NML-RNML |
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Cond | 24352.7465 | 26486.3694 | 25456.2581 | 89.7586 | 28.1650 | Fx | 22506.5159 | 20634.8147 | 28410.4990 | 21131.5526 | 20981.3379 | Fy | 22471.8806 | 20544.4192 | 28374.5081 | 21128.8873 | 20867.2976 | Cx | 1055.5585 | 1213.2326 | 1693.0702 | 1284.2126 | 1267.5908 | Cy | 494.1133 | 467.6265 | 595.6751 | 380.3522 | 428.9498 | k1 | 0.2890 | 0.2366 | | 0.0469 | 0.1575 | k2 | 25.8882 | -14.4427 | | -3.4698 | 8.7873 | RMS /pixel | 0.1594 | 0.1651 | | 0.1628 | 0.1605 |
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Table 2. Results of different calibration algorithms under the condition of 75 mm focal length
Method | Zhang’s checkerborads | Zhang | RML | RNML |
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RMS /mm | 0.0243 | 0.0239 | 0.0191 | 0.0190 |
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Table 3. RMS of off-plane displacements reconstructed by output parameters of different calibration methods