• Acta Optica Sinica
  • Vol. 39, Issue 4, 0415001 (2019)
Yanming Quan1、*, Zhenbo Qin1、2, Weishi Li2, and Rui Zhang2
Author Affiliations
  • 1 School of Mechanical & Automotive Engineering, South China University of Technology, Guangzhou, Guangdong 510640, China;
  • 2 Intelligent Measurement Team, Guangdong Academy, Hefei University of Technology, Foshan, Guangdong 528137, China
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    DOI: 10.3788/AOS201939.0415001 Cite this Article Set citation alerts
    Yanming Quan, Zhenbo Qin, Weishi Li, Rui Zhang. Multi-Camera Calibration of One-Dimensional Calibration Objects Based on Normalization Algorithm[J]. Acta Optica Sinica, 2019, 39(4): 0415001 Copy Citation Text show less
    Schematic of pinhole imaging
    Fig. 1. Schematic of pinhole imaging
    Schematic of simulation
    Fig. 2. Schematic of simulation
    Intrinsic parameters from original and normalized data. (a) Relative error of αk; (b) relative error of βk; (c) relative error of uk; (d) relative error of vk
    Fig. 3. Intrinsic parameters from original and normalized data. (a) Relative error of αk; (b) relative error of βk; (c) relative error of uk; (d) relative error of vk
    Extrinsic parameters from original and normalized data. (a) Maximum relative error of Euler angle; (b) relative error of translation vector
    Fig. 4. Extrinsic parameters from original and normalized data. (a) Maximum relative error of Euler angle; (b) relative error of translation vector
    Effect of normalization on condition number
    Fig. 5. Effect of normalization on condition number
    Calibration stick
    Fig. 6. Calibration stick
    Images sampled by camera set. (a) Calibration stick; (b) calibration board
    Fig. 7. Images sampled by camera set. (a) Calibration stick; (b) calibration board
    Cameraαkβkukvk
    0765762385293
    1763768410305
    2760755403307
    Table 1. Intrinsic parameters of three simulation cameras
    MethodCameraαkβkukvkskCondition number
    Proposed methodLeft4880.354833.771018.661009.89-2.114.71×107
    Right4868.554823.981023.671001.172.00
    Method in Ref. [10]Left4591.124675.97801.731194.257.182.93×1019
    Right4565.624658.49979.901185.772.72
    Two-dimensional (2D) methodLeft4640.624643.98984.201003.200
    Right4628.864630.32977.771042.680
    Table 2. Results of calibration
    MethodDifference /mmStandard deviation /mm
    ABBCCDABBCCD
    Proposed method0.19-0.10-0.020.400.720.53
    Method in Ref. [10]0.240.220.191.082.625.33
    2D method0.210.03-0.180.661.101.33
    Table 3. Results of length measurement
    Yanming Quan, Zhenbo Qin, Weishi Li, Rui Zhang. Multi-Camera Calibration of One-Dimensional Calibration Objects Based on Normalization Algorithm[J]. Acta Optica Sinica, 2019, 39(4): 0415001
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