• Acta Optica Sinica
  • Vol. 42, Issue 19, 1912003 (2022)
Zhenzhen Huang1, Xiaomei Huang2, Lianyu Zheng3, Kejian Liu4, Tao Peng1, and Zhijiang Zhang1、*
Author Affiliations
  • 1Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200444, China
  • 2Shanghai Institute of Astronautical Systems Engineering, Shanghai 201108, China
  • 3Shanghai Satellite Engineering Research Institute, Shanghai 200240, China
  • 4Shanghai Aerospace Electronics Research Institute, Shanghai 201108, China
  • show less
    DOI: 10.3788/AOS202242.1912003 Cite this Article Set citation alerts
    Zhenzhen Huang, Xiaomei Huang, Lianyu Zheng, Kejian Liu, Tao Peng, Zhijiang Zhang. Camera Calibration Method for Concentric Circle Eccentricity Error Compensation Iteration[J]. Acta Optica Sinica, 2022, 42(19): 1912003 Copy Citation Text show less
    Concentric circle eccentricity error model and geometric constraint model diagram. (a) Mathematical model of concentric circle eccentricity error; (b) geometric constraint mathematical model
    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
    Geometric constraint models of distance OC¯ and concentric circle center. (a) Geometric constraint relation between distance OC¯ and θ; (b) geometric constraint relation of coordinates near center of concentric circle projection
    Fig. 2. Geometric constraint models of distance OC¯ and concentric circle center. (a) Geometric constraint relation between distance OC¯ and θ; (b) geometric constraint relation of coordinates near center of concentric circle projection
    Pseudo-code of camera iterative calibration algorithm based on concentric circle center eccentricity error
    Fig. 3. Pseudo-code of camera iterative calibration algorithm based on concentric circle center eccentricity error
    Comparison of concentric circle eccentricity error compensation
    Fig. 4. Comparison of concentric circle eccentricity error compensation
    Compensation results of eccentricity error for boundary points after adding noise
    Fig. 5. Compensation results of eccentricity error for boundary points after adding noise
    Concentric circle calibration plate pattern
    Fig. 6. Concentric circle calibration plate pattern
    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. 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
    Camera calibration of concentric planar target
    Fig. 8. Camera calibration of concentric planar target
    Accuracy verification experiment of binocular system. (a) Binocular experimental measurement system; (b) benchmark ruler measurement; (c) binocular system calibration image
    Fig. 9. Accuracy verification experiment of binocular system. (a) Binocular experimental measurement system; (b) benchmark ruler measurement; (c) binocular system calibration image
    Error between measured data and standard data of ruler length
    Fig. 10. Error between measured data and standard data of ruler length
    ParameterZhang5Ours
    Focal lengthfx1462.41851464.8232
    fy1460.59651464.3652
    Principal pointu01235.95621239.1695
    v01042.69181039.2509
    Distortionk10.016600.01285
    k20.017900.00208
    p1-0.00021-0.00092
    p20.000420.00098
    k3-0.00015-0.00020
    RMS0.090.03
    UncertaintyUfx1.08600.5230
    Ufy1.08600.4890
    Uu00.60300.1560
    Uv00.78200.1860
    Uk10.00450.0023
    Uk20.00740.0030
    Up10.00130.0010
    Up20.00110.0009
    Uk30.00650.0060
    Table 1. Camera inner parameters, reprojection error, and uncertainty obtained by two methods
    ParameterBefore compensationAfter compensation
    Left cameraRight cameraLeft cameraLeft camera
    fx1462.1281459.7041463.0011459.795
    fy1461.7651459.6101462.7331460.001
    u01238.6851232.0311237.2311232.050
    v01040.9921047.5041035.3281047.042
    k10.011340.008900.009800.00330
    k2-0.000820.013300.012000.04180
    p10.000000263-0.000630000-0.001000000-0.000620000
    p20.0009000.0017640.0004000.002200
    k3-0.01510-0.02700-0.03300-0.06400
    RMS0.12560.13470.03210.0286
    R[0.001843 0.942010 -0.001980][0.005220 0.939200 -0.003200]
    T[-460.1710 -0.7764 228.6040][-459.2620 -0.7932 227.5350]
    RMS0.15320.0426
    Table 2. Correction results of binocular camera calibration parameters
    MethodZhang's methodYang's methodProposed method
    Mean0.11720.08280.0239
    RMS0.12400.07790.0268
    Maximum0.19560.13600.0450
    Table 3. Statistical results of error between measurement data and standard length of base ruler
    Zhenzhen Huang, Xiaomei Huang, Lianyu Zheng, Kejian Liu, Tao Peng, Zhijiang Zhang. Camera Calibration Method for Concentric Circle Eccentricity Error Compensation Iteration[J]. Acta Optica Sinica, 2022, 42(19): 1912003
    Download Citation