Open AccessOpen Access


Phase Error Compensation of Three-Dimensional Reconstruction Combined with Hilbert Transform

Tao Zhang1,*, Jie Shen1, Shaoen Wu2

1 School of Mechanical Engineering, North China University of Water Conservancy and Hydroelectric Power, Zhengzhou, 450045, China
2 Department of Computer Science, Ball State University, Muncie, 47306, IN, USA

* Corresponding Author: Tao Zhang. Email:

Computers, Materials & Continua 2021, 68(3), 3121-3131.


Nonlinear response is an important factor affecting the accuracy of three-dimensional image measurement based on the fringe structured light method. A phase compensation algorithm combined with a Hilbert transform is proposed to reduce the phase error caused by the nonlinear response of a digital projector in the three-dimensional measurement system of fringe structured light. According to the analysis of the influence of Gamma distortion on the phase calculation, the algorithm establishes the relationship model between phase error and harmonic coefficient, introduces phase shift to the signal, and keeps the signal amplitude constant while filtering out the DC component. The phase error is converted to the transform domain, and compared with the numeric value in the space domain. The algorithm is combined with a spiral phase function to optimize the Hilbert transform, so as to eliminate external noise, enhance the image quality, and get an accurate phase value. Experimental results show that the proposed method can effectively improve the accuracy and speed of phase measurement. By performing phase error compensation for free-form surface objects, the phase error is reduced by about 26%, and about 27% of the image reconstruction time is saved, which further demonstrates the feasibility and effectiveness of the method.


Cite This Article

T. Zhang, J. Shen and S. Wu, "Phase error compensation of three-dimensional reconstruction combined with hilbert transform," Computers, Materials & Continua, vol. 68, no.3, pp. 3121–3131, 2021.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 1249


  • 1019


  • 0


Share Link

WeChat scan