Author Affiliations
School of Mechanical and Precision Instrument Engineering, Xi′an University of Technology, Xi′an710048, Shaanxi , Chinashow less
Fig. 1. Pinhole imaging model
Fig. 2. Results of camera calibration by using target with different sizes. (a) Focal length; (b) horizontal coordinates of principal points
Fig. 3. Results of focal length calibration by using different number of targets
Fig. 4. Results of camera calibration with complete and incomplete targets. (a) Focal length; (b) horizontal coordinates of principal points
Fig. 5. Directional layered target
Fig. 6. Flow chart of target recognition and matching algorithm
Fig. 7. Numbering sequence of targets
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
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 |
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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 |
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Table 1. Standard error of calibration results of camera parameters under different target sizes
Number of targets | Focal length fx /mm | Focal length fy /mm | Horizontal coordinate of principal point /pixel | Vertical coordinate of principal point /pixel |
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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 |
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Table 2. Standard error of calibration results of camera parameters under different number of targets
Target | Focal length fx /mm | Focal length fy /mm | Horizontal coordinate of principal point /pixel | Vertical coordinate of principal point /pixel |
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Complete target | 0.0424 | 0.0426 | 10.2133 | 10.3020 | Incomplete target | 0.0450 | 0.0454 | 10.1544 | 10.5856 |
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Table 3. Standard error of calibration results of camera parameters for complete and incomplete targets
Group No. | Focal length /mm | Principal point (u0,v0)(unit:pixel) | Radical distortion coefficient | Tangential distortion coefficient | Reprojection error /pixel |
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k1 | k2 | p1 | p2 |
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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 |
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Table 4. Results of camera parameter calibration
Target | Focal length /mm | Principal point(u0,v0)(unit:pixel) | Radical distortion coefficient | Tangential distortion coefficient | Reprojection error /pixel | Measuring error /mm |
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k1 | k2 | p1 | p2 |
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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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Table 5. Results of camera calibration and measurement