Camera-Projector Calibration Methods with Compensation of Geometric Distortions in Fringe Projection Profilometry: A Comparative Study

Métodos de calibración cámara-proyector con compensación de distorsiones geométricas en perfilometría por proyección de franjas: un estudio comparativo

By: R. Vargas, A. G. Marrugo, J. Pineda, J. Meneses, L. Romero

Main Information

Vol.51-N3 / 2018 - Ordinario
Image Processing and Imaging Techniques
Research Paper
Fringe projection, stereo-vision, lens geometric distortions, polynomial calibration.

Proyección de franjas, visión estéreo, distorsiones geométricas, calibración polinomial.
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The calibration methods most used in fringe projection profilometry are based on models of least squares adjustment and stereo vision techniques. However, the geometric distortions of the projector and camera lenses introduce imprecision in certain regions of the 3D reconstruction. In this paper, we perform a comparative study between the second order polynomial adjustment method and the stereo calibration method applying lens distortion compensation. The experimental results show that in the stereo calibration the incidence of the distortions in the 3D reconstruction is significant. In contrast, in the proposed polynomial calibration, reconstruction errors are associated with the calibrated volume, typically low within the calibration volume.

Los métodos de calibración más usados en perfilometría por proyección de franjas están basados en modelos de ajustes por mínimos cuadrados y técnicas de visión estéreo. Sin embargo, las distorsiones geométricas de los lentes del proyector y de la cámara introducen imprecisión en ciertas regiones de la reconstrucción 3D. En este trabajo realizamos un estudio comparativo entre el método de ajuste polinomial de segundo orden y el método de calibración estéreo aplicando compensación de distorsiones. Los resultados experimentales muestran que en la calibración estéreo la incidencia de las distorsiones en la reconstrucción 3D es significativa. En cambio, en la calibración polinomial propuesta, los errores de reconstrucción están asociados al volumen calibrado.


[1] L. Felipe-Sesé, F. A. Díaz, and P. Siegmann, "Integration of Fringe Projection and 2D Digital Image Correlation for the measurement of 3D displacements and strains," Opt. Pura Apl., 50, pp. 25-35,(2017).

[2] S. S. Gorthi and P. Rastogi, "Fringe projection techniques: whither we are?," Opt. Lasers Eng., 48, pp.133-140, (2010).

[3] A. Hanafi, T. Gharbi, and J.-Y. Cornu, "In vivo measurement of lower back deformations with Fourier transform profilometry.," Appl. Opt,. 44, pp. 2266-2273, (2005).

[4] J. Barrios, M. Morón, C. Barrios, R. Contreras, A. González, and J. Meneses, "Three-dimensional scanning of the cornea by using a structured light module," Opt. Pura y Apl., 50, pp. 351-357, (2017).

[5] Q. Guo, Y. Ruan, J. Xi, L. Song, X. Zhu, Y. Yu, and J. Tong, "3D shape measurement of moving object with FFT-based spatial matching," Opt Laser Technol, 100, pp. 325-331, (2018).

[6] L. Huang, P. S. K. Chua, and A. Asundi, "Least-squares calibration method for fringe projection profilometry considering camera lens distortion.," Appl. Opt., 49, pp. 1539-1548, (2010).

[7] M. Takeda and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3-D object shapes.," Appl. Opt., 22, p. 3977, (1983).

[8] A.-S. Poulin-Girard, S. Thibault, and D. Laurendeau, "Influence of camera calibration conditions on the accuracy of 3D reconstruction," Opt Express, 24, p. 2678, (2016).

[9] Y. Wen, S. Li, H. Cheng, X. Su, and Q. Zhang, "Universal calculation formula and calibration method in Fourier transform profilometry.," Appl. Opt., 49, pp. 6563-6569, (2010).

[10] J. Lu, R. Mo, H. Sun, and Z. Chang, "Flexible calibration of phase-to-height conversion in fringe projection profilometry," Appl. Opt., 55, p. 6381, (2016).

[11] S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng., 45, 083601, (2006).

[12] P. Stavroulakis, D. Sims-Waterhouse, S. Piano, and R. Leach, "Flexible decoupled camera and projector fringe projection system using inertial sensors," Opt. Eng. 56, no. 10, pp. 1-6, (2017).

[13] H. Liu, W.-H. Su, K. Reichard, and S. Yin, "Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement," Optics Commun., 216, pp. 65-80, (2003).

[14] X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, "Calibration of fringe projection profilometry using an inaccurate 2D reference target," Opt. Lasers Eng., 89, pp. 131-137, (2017).

[15] Y. Yin, X. Peng, A. Li, X. Liu, and B. Z. Gao, "Calibration of fringe projection profilometry with bundle adjustment strategy.," Opt. Lett, 37, pp. 542-544, (2012).

[16] D. Acevedo and J. Meneses, "Global positioning system of an object using high resolution stereo vision," Opt. Pura y Apl., 45, pp. 307-313 (2012).

[17] W. Zhang, W. Li, L. Yu, H. Luo, H. Zhao, and H. Xia, "Sub-pixel projector calibration method for fringe projection profilometry," Opt Express, 25, p. 19158, (2017).

[18] Z. Huang, J. Xi, Y. Yu, and Q. Guo, "Accurate projector calibration based on a new point-to-point mapping relationship between the camera and projector images," Appl. Opt., 54, pp. 347-356, (2015).

[19] S. Zhang, High-Speed 3D Imaging with Digital Fringe Projection Techniques. CRC Press, (2016).

[20] J.-Y. Bouguet, "Camera calibration toolbox for Matlab," , (2004)

[21] Z. Zhang, "A flexible new technique for camera calibration," IEEE Trans. Pattern Anal. Mach. Intell., 22, pp. 1330-1334, (2000).