Author Affiliations
1National Key Laboratory of Fundamental Science on Synthetic Vision, Sichuan University, Chengdu , Sichuan 610065, China2College of Computer Science, Sichuan University, Chengdu , Sichuan 610065, Chinashow less
Fig. 1. Camera imaging model
Fig. 2. Simulation vision system based on absolute phase calibration method
Fig. 3. 22 simulated poses in the camera's view
Fig. 4. Part of the simulated images
Fig. 5. Simulated results. (a) Pixel error in direction; (b) pixel error in direction
Fig. 6. Absolute error at different noise levels. (a)(d)(g) Absolute error of checkerboard calibration method; (b)(e)(h) absolute error of circle calibration method; (c)(d)(g) absolute error of APT calibration method
Fig. 7. Absolute error at different fuzzy levels. (a)(d)(g) Absolute error of checkerboard calibration method; (b)(e)(h) absolute error of circle calibration method; (c)(d)(g) absolute error of APT calibration method
Fig. 8. APT experimental device
Fig. 9. Part calibration images and part feature points. (a)(c)(e) In-focus images; (b)(d)(f) out-of-focus images
Fig. 10. Target poses in the camera's view. (a) 16 poses under in-focus condition; (b) 14 poses under out-of-focus condition
Fig. 11. Re-projection errors of three calibration methods under in-focus condition. (a) Checkerboard calibration method; (b) circle calibration method; (c) APT calibration method
Fig. 12. Re-projection errors of three calibration methods when the target is far away from the effective working distance of the camera. (a) Checkerboard calibration method; (b) circle calibration method; (c) APT calibration method
Fig. 13. Column charts of world coordinate difference before and after optimization. (a)(d) Checkerboard calibration method under in-focus condition and out-of-focus condition; (b)(e) circle calibration method under in-focus condition and out-of-focus condition; (c)(f) APT calibration method under in-focus condition and out-of-focus condition
Parameter | fu /pixel | fv /pixel | u0 /pixel | v0 /pixel | tx /mm | ty /mm | tz/mm |
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Ground truth | 1455 | 1455 | 1024 | 540 | 0 | 0 | 650 | Absolute error | 0.0036 | 0.0037 | 0.0003 | 0.00056 | 0.03477 | 0.02785 | 0.0283 |
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Table 1. Systematic errors of visual simulation system and calibration software
Parameter | Checkerboard | Circle | APT |
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fu /pixel | 2605.92 | 2606.92 | 2603.82 | fv /pixel | 2606.03 | 2607.11 | 2603.74 | u0 /pixel | 648.82 | 647.13 | 648.38 | v0 /pixel | 511.21 | 510.75 | 511.68 | k1 | -0.03199 | -0.04702 | -0.05360 | k2 | 0.01309 | 0.4687 | 0.58223 | p1 | 0.00044 | 0.00016 | 0.00021 | p2 | 0.00086 | 0.00062 | 0.00085 | tx | 0.02901 | 0.073178 | 0.10481 | ty | 3.84972 | 3.13728 | 3.87875 | tz | 1001.60622 | 1094.46671 | 1095.71075 | θx | 0.02898 | 0.06827 | 0.02897 | θy | 0.043195 | -0.45406 | 0.04366 | θz | -0.003219 | 0.047016 | -0.003272 | Re-project_error /pixel | 0.03366 | 0.02840 | 0.02262 |
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Table 2. Calibration results of the camera
Parameter | Checkerboard | Circle | APT |
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fu /pixel | 2650.70 | 2637.38 | 2641.39 | fv /pixel | 2649.46 | 2636.90 | 2640.65 | u0 /pixel | 627.04 | 624.25 | 622.55 | v0 /pixel | 501.50 | 502.06 | 505.19 | k1 | -0.06195 | -0.00610 | -0.04133 | k2 | 0.86519 | -0.19245 | 0.17647 | p1 | 0.00030 | 0.00027 | 0.00014 | p2 | 0.00211 | -0.00137 | -0.00202 | tx | 5.76005 | 6.69944 | 5.47052 | ty | -24.34501 | -24.12537 | -23.96307 | tz | 1305.40317 | 1303.11704 | 1301.76072 | θx | -0.00512 | -0.0027632 | -0.12287 | θy | 0.081087 | 0.079357 | -0.00606 | θz | 0.0029841 | 0.0028501 | 0.0028776 | Re-project_error /pixel | 0.04641 | 0.03371 | 0.01393 |
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Table 3. Calibration results when the target is far away from the effective working distance of the camera