Author Affiliations
1Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200444, China2Shanghai Institute of Astronautical Systems Engineering, Shanghai 201108, China3Shanghai Satellite Engineering Research Institute, Shanghai 200240, China4Shanghai Aerospace Electronics Research Institute, Shanghai 201108, Chinashow less
Fig. 1. Concentric circle eccentricity error model and geometric constraint model diagram. (a) Mathematical model of concentric circle eccentricity error; (b) geometric constraint mathematical model
Fig. 2. Geometric constraint models of distance and concentric circle center. (a) Geometric constraint relation between distance and ; (b) geometric constraint relation of coordinates near center of concentric circle projection
Fig. 3. Pseudo-code of camera iterative calibration algorithm based on concentric circle center eccentricity error
Fig. 4. Comparison of concentric circle eccentricity error compensation
Fig. 5. Compensation results of eccentricity error for boundary points after adding noise
Fig. 6. Concentric circle calibration plate pattern
Fig. 7. Camera calibration of concentric planar target. (a)-(d) Concentric circle target patterns collected; (e) sub-pixel detection effect of concentric circle edge; (f) ordering of concentric circle feature points
Fig. 8. Camera calibration of concentric planar target
Fig. 9. Accuracy verification experiment of binocular system. (a) Binocular experimental measurement system; (b) benchmark ruler measurement; (c) binocular system calibration image
Fig. 10. Error between measured data and standard data of ruler length
Parameter | Zhang[5] | Ours |
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Focal length | | 1462.4185 | 1464.8232 | | 1460.5965 | 1464.3652 | Principal point | | 1235.9562 | 1239.1695 | | 1042.6918 | 1039.2509 | Distortion | | 0.01660 | 0.01285 | | 0.01790 | 0.00208 | | -0.00021 | -0.00092 | | 0.00042 | 0.00098 | | -0.00015 | -0.00020 | | 0.09 | 0.03 | Uncertainty | | 1.0860 | 0.5230 | | 1.0860 | 0.4890 | | 0.6030 | 0.1560 | | 0.7820 | 0.1860 | | 0.0045 | 0.0023 | | 0.0074 | 0.0030 | | 0.0013 | 0.0010 | | 0.0011 | 0.0009 | | 0.0065 | 0.0060 |
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Table 1. Camera inner parameters, reprojection error, and uncertainty obtained by two methods
Parameter | Before compensation | After compensation |
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| | | |
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| 1462.128 | 1459.704 | 1463.001 | 1459.795 | | 1461.765 | 1459.610 | 1462.733 | 1460.001 | | 1238.685 | 1232.031 | 1237.231 | 1232.050 | | 1040.992 | 1047.504 | 1035.328 | 1047.042 | | 0.01134 | 0.00890 | 0.00980 | 0.00330 | | -0.00082 | 0.01330 | 0.01200 | 0.04180 | | 0.000000263 | -0.000630000 | -0.001000000 | -0.000620000 | | 0.000900 | 0.001764 | 0.000400 | 0.002200 | | -0.01510 | -0.02700 | -0.03300 | -0.06400 | RMS | 0.1256 | 0.1347 | 0.0321 | 0.0286 | R | [0.001843 0.942010 -0.001980] | [0.005220 0.939200 -0.003200] | | [-460.1710 -0.7764 228.6040] | [-459.2620 -0.7932 227.5350] | RMS | 0.1532 | 0.0426 |
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Table 2. Correction results of binocular camera calibration parameters
Method | Zhang's method | Yang's method | Proposed method |
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Mean | 0.1172 | 0.0828 | 0.0239 | RMS | 0.1240 | 0.0779 | 0.0268 | Maximum | 0.1956 | 0.1360 | 0.0450 |
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Table 3. Statistical results of error between measurement data and standard length of base ruler