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Neural-Network Model for Compensation of Lens Distortion in Camera Calibration

Abstract

Camera calibration for machine vision is critical in three-dimensional (3-D) measurement systems based on a digital light processing (DLP) projector and a camera. The Z-height of the measurement point is calculated using the phase value observed by the camera when a fringe pattern is scanned from a projection onto an object. On the other hand, the X and Y coordinates are obtained from the camera coordinates using a transformation matrix, and the mathematical model for lens distortion is additionally used. However, the errors for x and y coordinates are 10 times larger than the z-height error in an experiment. This is because the lens distortion is not sufficiently compensated in the mathematical model considering only the position from the lens center. Therefore, the neural network (NN) model that considers the measurement distance in addition to the position is proposed in this paper. Experiments were conducted on a 100 × 100 mm2 area, and a maximum error of 0.5 mm is observed for the mathematical model. However, when the NN model considering the height of the object is used, the error is reduced by 60% to 0.2 mm.

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References

  1. Chen, F., Brown, G. M., and Song, M., “Overview of Three-Dimensional Shape Measurement Using Optical Methods,” Optical Engineering. Vol. 39, No. 1, pp. 10–22, 2000.

    Article  Google Scholar 

  2. Takeda, M. and Mutoh, K., “Fourier Transform Profilometry for the Automatic Measurement of 3-D Object Shapes,” Applied Optics, Vol. 22, No. 24, pp. 3977–3982, 1983.

    Article  Google Scholar 

  3. Sansoni, G., Carocci, M., and Rodella, R., “3D Vision Based on the Combination of Gray Code and Phase Shift Light Projection,” Applied Optics, Vol. 38, No. 31, pp. 6565–6573, 1999.

    Article  Google Scholar 

  4. Tian, A., Jiang, Z., and Huang, Y., “A Flexible New Three-Dimensional Measurement Technique by Projected Fringe Pattern,” Optics & Laser Technology, Vol. 38, pp. 585–589, 2006.

    Article  Google Scholar 

  5. Du, H. and Wang, Z., “Three-Dimensional Shape Measurement with an Arbitrarily Arranged Fringe Projection Profilometry System,” Optics Letters, Vol. 32, No. 16, pp. 2438–2440, 2007.

    Article  Google Scholar 

  6. Huang, L., Chua, P., and Asundi, A., “Least-Squares Calibration Method for Fringe Projection Profilometry Considering Camera Lens Distortion,” Applied Optics, Vol. 49, No. 9, pp. 1539–1548, 2010.

    Article  Google Scholar 

  7. Liu, H., Su, W. H., Reichard, K., and Yin, S., “Calibration-Based Phase-Shifting Projected Fringe Profilometry for Accurate Absolute 3D Surface Profile Measurement,” Optics Communications, Vol. 216, pp. 65–80, 2003.

    Article  Google Scholar 

  8. Guo, H., He, H., Yu, Y., and Chen, M., “Least-Squares Calibration Method for Fringe Projection Profilometry,” Optical Engineering, Vol. 44, No. 3, pp. 033603–1–9, 2005.

    Article  Google Scholar 

  9. Jia, P., Kofman, J., and English, C., “Comparison of Linear and Nonlinear Calibration Methods for Phase-Measuring Profilometry,” Optical Engineering, Vol. 46, Paper No. 043601, 2007.

  10. Li, W., Fang, S., and Duan, S., “3D Shape Measurement Based on Structured Light Projection Applying Polynomial Interpolation Technique,” Optik, Vol. 124, No. 1, pp. 20–27, 2013.

    Article  Google Scholar 

  11. Chung, B., “Improved Least-Squares Method for Phase-to-Height Relationship in Fringe Projection Profilometry,” Journal of European Optical Society-RP, Vol. 12, No. 11, pp. 1–11, 2016.

    Google Scholar 

  12. Tsai, R., “A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Camera and Lenses,” IEEE Journal of Robotics and Automation, Vol. 3, No. 4, pp. 323–344, 1987.

    Article  Google Scholar 

  13. Weng, J., Cohen, P., and Herniou, M., “Camera Calibration with Distortion Model and Accuracy Evaluation,” IEEE Transactions on Pattern and Machine Intelligence, Vol. 14, No. 10, pp. 965–980, 1992.

    Article  Google Scholar 

  14. Wei, G. and Song, M., “Implicit and Explicit Camera Calibration: Theory and Experiments,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 16, No. 5, pp. 469–480, 1994.

    Article  Google Scholar 

  15. Zhang, Z., “Flexible Camera Calibration by Viewing a Plane from Unknown Orientations,” Proc. of IEEE International Conference on Computer Vision, pp. 666–673, 1999.

    Chapter  Google Scholar 

  16. Zhang, Z., “A Flexible New Technique for Camera Calibration,” IEEE Trans. on Pattern and Machine Intelligence, Vol. 22, No. 11, pp. 1330–1334, 2000.

    Article  Google Scholar 

  17. Li, B., Karpinsky, N., and Zhang, S., “Novel Calibration Method for Structured Light System with an Out-of-Focus Projector,” Applied Optics, Vol. 53, No. 16, pp. 3415–3426, 2014.

    Article  Google Scholar 

  18. Ganotra, D., Joseph, J., and Singh, K., “Profilometry for the Measurement of Three-Dimensional Object Shape Using Radial Basis Function, and Multi-layer Perceptron Neural Networks,” Optics Communications, Vol. 209, pp. 291–301, 2002.

    Article  Google Scholar 

  19. Yan, T., Wen, C., Xian, S., and Li, X., “Neural Network Applied to Reconstruction of Complex Objects Based on Fringe Projection,” Optics Communications, Vol. 278, pp. 274–278, 2007.

    Article  Google Scholar 

  20. Chung, B., “Neural Network Model for Phase-Height Relationship of Each Image Pixel in 3D Shape Measurement by Machine Vision,” Optica Applicata, Vol. 44, No. 4, pp. 587–599, 2014.

    Google Scholar 

  21. Wasser, P., “Neural Computing: Theory and Practice,” New York: Van Nostrand Reinhold, pp. 43–59, 1989.

    Google Scholar 

  22. Beale, M, Hagan, M., and Demuth, H, “Neural Network Toolbox, User’s Guide,” Mathworks, pp. 3.1–30, 2017.

    Google Scholar 

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Correspondence to Byeong-Mook Chung.

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Chung, BM. Neural-Network Model for Compensation of Lens Distortion in Camera Calibration. Int. J. Precis. Eng. Manuf. 19, 959–966 (2018). https://doi.org/10.1007/s12541-018-0113-0

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  • DOI: https://doi.org/10.1007/s12541-018-0113-0

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