Fig. 1. Main flow of camera calibration
Fig. 2. Coordinate transformation of camera imaging
Fig. 3. Improved calibration process of camera
Fig. 4. Calibration images at different positions
Fig. 5. Calibration image after corner extraction
Fig. 6. Optimization results of two PSO algorithms
Fig. 7. Position relationship between actual corner and reprojection corner
Fig. 8. Reprojection error of different calibration methods. (a) Calibration toolbox; (b) Zhang calibration method; (c) proposed method
Fig. 9. Search performance comparison of four intelligent optimization algorithms
Parameter | fx | fy | u0 | v0 | k1, k2, k3, | p1, p2 |
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Value | 10214.33 | 10214.33 | 643.25 | 482.52 | 0 | 0 |
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Table 1. Linear solution of camera internal parameters
Parameter | Number of iterations |
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100 | 200 | 300 | 400 |
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fx | 10208.04 | 10209.09 | 10207.78 | 10208.23 | fy | 10205.38 | 1.020538 | 10204.89 | 10204.25 | u0 | 644.51 | 644.46 | 645.0140 | 644.72 | v0 | 482.76 | 482.22 | 486.280 | 481.77 | k1 | -7.72 | -5.4735 | -4.1863 | -3.3107 | k2 | 0.1996 | -2.0780 | -0.4304 | 0.2064 | k3 | -5.2160 | -4.9430 | -4.6964 | -4.5130 | p1 | -0.0862 | -0.0254 | -0.0261 | 0.0006 | p2 | 0.1197 | 0.0821 | 0.0643 | 0.0632 | Fitness | 0.4200 | 0.3852 | 0.3534 | 0.3195 |
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Table 2. Results of PSO with different iterations
Parameter | Number of iterations |
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100 | 200 | 300 | 400 |
---|
fx | 10214.35 | 10214.31 | 10214.31 | 10218.25 | fy | 10219.29 | 10216.50 | 10216.34 | 10217.61 | u0 | 645.5413 | 645.4992 | 645.5005 | 645.4854 | v0 | 481.3720 | 481.4797 | 481.4860 | 481.4947 | k1 | -0.1778 | -0.1897 | -0.1681 | -0.3372 | k2 | -4.4974 | -4.4636 | -4.4629 | -4.3837 | k3 | -8.0918 | -7.3946 | -7.5034 | -9.3731 | p1 | 0.0042 | 0.0011 | 0.0010 | 0.00002 | p2 | 0.0005 | 0..0022 | 0.0017 | 0.0017 | Fitness | 0.0460 | 0.0372 | 0.0370 | 0.0368 |
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Table 3. Results of DWAMPSO with different iterations
Algorithm | Optimal fitness | Worst fitness |
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DE | 0.2152 | 0.3033 | GA | 0.1572 | 0.2389 | PSO | 0.3195 | 0.4075 | DWAMPSO | 0.0368 | 0.1694 |
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Table 4. Fitness results of different algorithms
Algorithm | Fitness | 1 | 0.8 | 0.6 | 0.4 | 0.2 |
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GD | Iteration number | 36 | 43 | 109 | 186 | | Running time /s | 38.9057 | 46.1268 | 117.1337 | 197.2784 | | DE | Iteration number | 184 | 202 | 246 | 278 | | Running time /s | 156.2791 | 171.8147 | 210.1576 | 239.0557 | | GA | Iteration number | 43 | 125 | 169 | 268 | 351 | Running time /s | 44.7721 | 129.5620 | 176.4058 | 280.4783 | 368.7568 | PSO | Iteration number | 47 | 82 | 87 | 147 | | Running time /s | 40.9787 | 73.1574 | 77.9820 | 142.2541 | | DWAMPSO | Iteration number | 12 | 12 | 13 | 41 | 54 | Running time /s | 11.6289 | 11.6289 | 12.5381 | 38.0881 | 50.2417 |
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Table 5. Convergence rate of different algorithms