Abstract

A Lambertian surface is a kind of very important assumption in shape from shading (SFS), which is widely used in many measurement cases. In this paper, a novel scaled SFS method is developed to measure the shape of a Lambertian surface with dimensions. In which, a more accurate light source model is investigated under the illumination of a simple point light source, the relationship between surface depth map and the recorded image grayscale is established by introducing the camera matrix into the model. Together with the constraints of brightness, smoothness and integrability, the surface shape with dimensions can be obtained by analyzing only one image using the scaled SFS method. The algorithm simulations show a perfect matching between the simulated structures and the results, the rebuilding root mean square error (RMSE) is below 0.6mm. Further experiment is performed by measuring a PVC tube internal surface, the overall measurement error lies below 2%.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. M. T. E. Melegy, A. S. Abdelrahim, and A. A. Farag, “Better Shading for Better Shape Recovery,” In CVPR, 2307–2312 (2014)
  2. D. Roxo, N. Gonçalves, and J. P. Barreto, “Perspective shape from shading for wide-fov near-lighting endoscopes,” in Iberian Conference on Pattern Recognition and Image Analysis, Springer, Berlin, Heidelberg (2013), pp. 21–30.
    [Crossref]
  3. H. Tang, L. Yan, and P. Gao, “A modified SFS algorithm based on stereo images for the three-dimension reconstruction of Urban buildings,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. IV-390.
    [Crossref]
  4. G. D. Martino, A. D. Simone, A. Iodice, D. Riccio, and G. Ruello, “SAR Shape from Shading in suburban areas,” In Urban Remote Sensing Event (JURSE) (2015), pp. 1–4.
  5. L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
    [Crossref]
  6. Y. Sun, J. Dong, M. Jian, and L. Qi, “Fast 3D face reconstruction based on uncalibrated photometric stereo,” Multimedia Tools Appl. 74(11), 3635–3650 (2015).
    [Crossref]
  7. L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
    [Crossref]
  8. J. Hou, “A novel cloud surface shape estimation method based on SFS,” in Proceedings of IEEE Conference on Computer Science and Network Technology (IEEE, 2016 5th), pp. 80–83.
    [Crossref]
  9. Y. Zhang and J. Peng, “Surface shape estimation of textureless area using shape from shading for Landsat imagery,” in Remote Sensing of the Atmosphere, Clouds, and Precipitation V (2014), Vol. 9259, p. 92591S.
  10. L. Min, D. Li, and S. Dong, “3D Surface Roughness Measurement Based on SFS Method,” in Proceedings of IEEE Conference on Intelligent Human-Machine Systems and Cybernetics (IEEE, 2016 8th), Vol. 2, pp. 484–488.
    [Crossref]
  11. J. Wu, P. L. Rosin, X. Sun, and R. R. Martin, “Improving shape from shading with interactive tabu search,” J. Comput. Sci. Technol. 31(3), 450–462 (2016).
    [Crossref]
  12. H. Bingwei, C. Zhipeng, L. Dongyi, and Z. Xiaolong, “Research on reconstruction method for unknown objects through incorporating SFS algorithm and active vision technology,” PhChin. J. Sci. Instrum. 4, 002 (2012).
  13. X. Huang, M. Walton, G. Bearman, and O. Cossairt, “Near light correction for image relighting and 3D shape recovery,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2015),pp. 215–222.
    [Crossref]
  14. Y. C. Ju, A. Bruhn, and M. Breuß, “Variational perspective shape from shading,” in International Conference on Scale Space and Variational Methods in Computer Vision, Springer, Cham, Heidelberg (2015), pp. 538–550.
  15. J. Ackermann, S. Fuhrmann, and M. Goesele, “Geometric Point Light Source Calibration,” in VMV (2013), pp. 161–168.
  16. T. Aoto, T. Taketomi, T. Sato, Y. Mukaigawa, and N. Yokoya, “Position estimation of near point light sources using a clear hollow sphere,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2012), Vol. 1, pp. 3721–3724.
  17. A. Giachetti, C. Daffara, C. Reghelin, E. Gobbetti, and R. Pintus, “Light calibration and quality assessment methods for Reflectance Transformation Imaging applied to artworks’ analysis,” in Optics for Arts, Architecture, and Archaeology V (2015), Vol. 9527, p. 95270B.
  18. H. L. Shen and Y. Cheng, “Calibrating light sources by using a planar mirror,” J. Electron. Imaging 20(1), 013002 (2011).
    [Crossref]
  19. J. Ma, P. Zhao, and B. Gong, “A shape-from-shading method based on surface reflectance component estimation,” in Proceedings of IEEE Conference on Fuzzy Systems and Knowledge Discovery (IEEE, 2012 9th), pp. 1690–1693.
    [Crossref]
  20. J. Wang, F. H. Wu, X. L. Li, and J. C. Wang, “Smoothing of SFS Reconstructed Surface Based on Genetic Algorithm,” Key Eng. Mater. 579, 877–884 (2014).
  21. T. S. F. Haines and R. C. Wilson, “Combining shape-from-shading and stereo using Gaussian-Markov random fields,” in Proceedings of IEEE Conference on Pattern Recognition (IEEE, ICPR, 2008), pp. 1–4.
    [Crossref]
  22. M. G. H. Mostafa, S. M. Yamany, and A. A. Farag, “Integrating stereo and shape from shading,” in Proceedings of IEEE Conference on Image Processing (IEEE, 1999), Vol. 3, pp. 130–134.
  23. A. Tankus, A. N. Sochen, and Y. Yeshurun, “Shape-from-shading under perspective projection,” Int. J. Comput. Vis. 60(1), 21–43 (2005).

2018 (1)

L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
[Crossref]

2016 (1)

J. Wu, P. L. Rosin, X. Sun, and R. R. Martin, “Improving shape from shading with interactive tabu search,” J. Comput. Sci. Technol. 31(3), 450–462 (2016).
[Crossref]

2015 (1)

Y. Sun, J. Dong, M. Jian, and L. Qi, “Fast 3D face reconstruction based on uncalibrated photometric stereo,” Multimedia Tools Appl. 74(11), 3635–3650 (2015).
[Crossref]

2014 (1)

J. Wang, F. H. Wu, X. L. Li, and J. C. Wang, “Smoothing of SFS Reconstructed Surface Based on Genetic Algorithm,” Key Eng. Mater. 579, 877–884 (2014).

2012 (1)

H. Bingwei, C. Zhipeng, L. Dongyi, and Z. Xiaolong, “Research on reconstruction method for unknown objects through incorporating SFS algorithm and active vision technology,” PhChin. J. Sci. Instrum. 4, 002 (2012).

2011 (1)

H. L. Shen and Y. Cheng, “Calibrating light sources by using a planar mirror,” J. Electron. Imaging 20(1), 013002 (2011).
[Crossref]

2005 (1)

A. Tankus, A. N. Sochen, and Y. Yeshurun, “Shape-from-shading under perspective projection,” Int. J. Comput. Vis. 60(1), 21–43 (2005).

Aoto, T.

T. Aoto, T. Taketomi, T. Sato, Y. Mukaigawa, and N. Yokoya, “Position estimation of near point light sources using a clear hollow sphere,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2012), Vol. 1, pp. 3721–3724.

Bearman, G.

X. Huang, M. Walton, G. Bearman, and O. Cossairt, “Near light correction for image relighting and 3D shape recovery,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2015),pp. 215–222.
[Crossref]

Bingwei, H.

H. Bingwei, C. Zhipeng, L. Dongyi, and Z. Xiaolong, “Research on reconstruction method for unknown objects through incorporating SFS algorithm and active vision technology,” PhChin. J. Sci. Instrum. 4, 002 (2012).

Cheng, Y.

H. L. Shen and Y. Cheng, “Calibrating light sources by using a planar mirror,” J. Electron. Imaging 20(1), 013002 (2011).
[Crossref]

Cossairt, O.

X. Huang, M. Walton, G. Bearman, and O. Cossairt, “Near light correction for image relighting and 3D shape recovery,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2015),pp. 215–222.
[Crossref]

Dong, J.

Y. Sun, J. Dong, M. Jian, and L. Qi, “Fast 3D face reconstruction based on uncalibrated photometric stereo,” Multimedia Tools Appl. 74(11), 3635–3650 (2015).
[Crossref]

L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
[Crossref]

Dongyi, L.

H. Bingwei, C. Zhipeng, L. Dongyi, and Z. Xiaolong, “Research on reconstruction method for unknown objects through incorporating SFS algorithm and active vision technology,” PhChin. J. Sci. Instrum. 4, 002 (2012).

Fan, J.

L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
[Crossref]

Fang, Z.

L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
[Crossref]

Farag, A. A.

M. G. H. Mostafa, S. M. Yamany, and A. A. Farag, “Integrating stereo and shape from shading,” in Proceedings of IEEE Conference on Image Processing (IEEE, 1999), Vol. 3, pp. 130–134.

Gao, P.

H. Tang, L. Yan, and P. Gao, “A modified SFS algorithm based on stereo images for the three-dimension reconstruction of Urban buildings,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. IV-390.
[Crossref]

Gong, B.

J. Ma, P. Zhao, and B. Gong, “A shape-from-shading method based on surface reflectance component estimation,” in Proceedings of IEEE Conference on Fuzzy Systems and Knowledge Discovery (IEEE, 2012 9th), pp. 1690–1693.
[Crossref]

Guang, J.

L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
[Crossref]

He, X.

L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
[Crossref]

Hou, J.

J. Hou, “A novel cloud surface shape estimation method based on SFS,” in Proceedings of IEEE Conference on Computer Science and Network Technology (IEEE, 2016 5th), pp. 80–83.
[Crossref]

Hou, T.

L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
[Crossref]

Huang, X.

X. Huang, M. Walton, G. Bearman, and O. Cossairt, “Near light correction for image relighting and 3D shape recovery,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2015),pp. 215–222.
[Crossref]

Jian, M.

Y. Sun, J. Dong, M. Jian, and L. Qi, “Fast 3D face reconstruction based on uncalibrated photometric stereo,” Multimedia Tools Appl. 74(11), 3635–3650 (2015).
[Crossref]

Li, C.

L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
[Crossref]

Li, E.

L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
[Crossref]

Li, X. L.

J. Wang, F. H. Wu, X. L. Li, and J. C. Wang, “Smoothing of SFS Reconstructed Surface Based on Genetic Algorithm,” Key Eng. Mater. 579, 877–884 (2014).

Li, Y.

L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
[Crossref]

Liang, Z.

L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
[Crossref]

Long, T.

L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
[Crossref]

Ma, J.

J. Ma, P. Zhao, and B. Gong, “A shape-from-shading method based on surface reflectance component estimation,” in Proceedings of IEEE Conference on Fuzzy Systems and Knowledge Discovery (IEEE, 2012 9th), pp. 1690–1693.
[Crossref]

Mao, Y.

L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
[Crossref]

Martin, R. R.

J. Wu, P. L. Rosin, X. Sun, and R. R. Martin, “Improving shape from shading with interactive tabu search,” J. Comput. Sci. Technol. 31(3), 450–462 (2016).
[Crossref]

Mostafa, M. G. H.

M. G. H. Mostafa, S. M. Yamany, and A. A. Farag, “Integrating stereo and shape from shading,” in Proceedings of IEEE Conference on Image Processing (IEEE, 1999), Vol. 3, pp. 130–134.

Mukaigawa, Y.

T. Aoto, T. Taketomi, T. Sato, Y. Mukaigawa, and N. Yokoya, “Position estimation of near point light sources using a clear hollow sphere,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2012), Vol. 1, pp. 3721–3724.

Qi, L.

Y. Sun, J. Dong, M. Jian, and L. Qi, “Fast 3D face reconstruction based on uncalibrated photometric stereo,” Multimedia Tools Appl. 74(11), 3635–3650 (2015).
[Crossref]

Rosin, P. L.

J. Wu, P. L. Rosin, X. Sun, and R. R. Martin, “Improving shape from shading with interactive tabu search,” J. Comput. Sci. Technol. 31(3), 450–462 (2016).
[Crossref]

Sato, T.

T. Aoto, T. Taketomi, T. Sato, Y. Mukaigawa, and N. Yokoya, “Position estimation of near point light sources using a clear hollow sphere,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2012), Vol. 1, pp. 3721–3724.

Shen, H. L.

H. L. Shen and Y. Cheng, “Calibrating light sources by using a planar mirror,” J. Electron. Imaging 20(1), 013002 (2011).
[Crossref]

Sochen, A. N.

A. Tankus, A. N. Sochen, and Y. Yeshurun, “Shape-from-shading under perspective projection,” Int. J. Comput. Vis. 60(1), 21–43 (2005).

Sun, X.

J. Wu, P. L. Rosin, X. Sun, and R. R. Martin, “Improving shape from shading with interactive tabu search,” J. Comput. Sci. Technol. 31(3), 450–462 (2016).
[Crossref]

Sun, Y.

Y. Sun, J. Dong, M. Jian, and L. Qi, “Fast 3D face reconstruction based on uncalibrated photometric stereo,” Multimedia Tools Appl. 74(11), 3635–3650 (2015).
[Crossref]

Taketomi, T.

T. Aoto, T. Taketomi, T. Sato, Y. Mukaigawa, and N. Yokoya, “Position estimation of near point light sources using a clear hollow sphere,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2012), Vol. 1, pp. 3721–3724.

Tang, H.

H. Tang, L. Yan, and P. Gao, “A modified SFS algorithm based on stereo images for the three-dimension reconstruction of Urban buildings,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. IV-390.
[Crossref]

Tankus, A.

A. Tankus, A. N. Sochen, and Y. Yeshurun, “Shape-from-shading under perspective projection,” Int. J. Comput. Vis. 60(1), 21–43 (2005).

Walton, M.

X. Huang, M. Walton, G. Bearman, and O. Cossairt, “Near light correction for image relighting and 3D shape recovery,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2015),pp. 215–222.
[Crossref]

Wang, J.

J. Wang, F. H. Wu, X. L. Li, and J. C. Wang, “Smoothing of SFS Reconstructed Surface Based on Genetic Algorithm,” Key Eng. Mater. 579, 877–884 (2014).

Wang, J. C.

J. Wang, F. H. Wu, X. L. Li, and J. C. Wang, “Smoothing of SFS Reconstructed Surface Based on Genetic Algorithm,” Key Eng. Mater. 579, 877–884 (2014).

Wu, F. H.

J. Wang, F. H. Wu, X. L. Li, and J. C. Wang, “Smoothing of SFS Reconstructed Surface Based on Genetic Algorithm,” Key Eng. Mater. 579, 877–884 (2014).

Wu, J.

J. Wu, P. L. Rosin, X. Sun, and R. R. Martin, “Improving shape from shading with interactive tabu search,” J. Comput. Sci. Technol. 31(3), 450–462 (2016).
[Crossref]

Xiaolong, Z.

H. Bingwei, C. Zhipeng, L. Dongyi, and Z. Xiaolong, “Research on reconstruction method for unknown objects through incorporating SFS algorithm and active vision technology,” PhChin. J. Sci. Instrum. 4, 002 (2012).

Xue, Y.

L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
[Crossref]

Yamany, S. M.

M. G. H. Mostafa, S. M. Yamany, and A. A. Farag, “Integrating stereo and shape from shading,” in Proceedings of IEEE Conference on Image Processing (IEEE, 1999), Vol. 3, pp. 130–134.

Yan, L.

H. Tang, L. Yan, and P. Gao, “A modified SFS algorithm based on stereo images for the three-dimension reconstruction of Urban buildings,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. IV-390.
[Crossref]

Yang, L.

L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
[Crossref]

L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
[Crossref]

Yeshurun, Y.

A. Tankus, A. N. Sochen, and Y. Yeshurun, “Shape-from-shading under perspective projection,” Int. J. Comput. Vis. 60(1), 21–43 (2005).

Yokoya, N.

T. Aoto, T. Taketomi, T. Sato, Y. Mukaigawa, and N. Yokoya, “Position estimation of near point light sources using a clear hollow sphere,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2012), Vol. 1, pp. 3721–3724.

Zhao, P.

J. Ma, P. Zhao, and B. Gong, “A shape-from-shading method based on surface reflectance component estimation,” in Proceedings of IEEE Conference on Fuzzy Systems and Knowledge Discovery (IEEE, 2012 9th), pp. 1690–1693.
[Crossref]

Zhipeng, C.

H. Bingwei, C. Zhipeng, L. Dongyi, and Z. Xiaolong, “Research on reconstruction method for unknown objects through incorporating SFS algorithm and active vision technology,” PhChin. J. Sci. Instrum. 4, 002 (2012).

Int. J. Adv. Manuf. Technol. (1)

L. Yang, E. Li, T. Long, J. Fan, Y. Mao, Z. Fang, and Z. Liang, “A welding quality detection method for arc welding robot based on 3D reconstruction with SFS algorithm,” Int. J. Adv. Manuf. Technol. 94(1–4), 1209–1220 (2018).
[Crossref]

Int. J. Comput. Vis. (1)

A. Tankus, A. N. Sochen, and Y. Yeshurun, “Shape-from-shading under perspective projection,” Int. J. Comput. Vis. 60(1), 21–43 (2005).

J. Comput. Sci. Technol. (1)

J. Wu, P. L. Rosin, X. Sun, and R. R. Martin, “Improving shape from shading with interactive tabu search,” J. Comput. Sci. Technol. 31(3), 450–462 (2016).
[Crossref]

J. Electron. Imaging (1)

H. L. Shen and Y. Cheng, “Calibrating light sources by using a planar mirror,” J. Electron. Imaging 20(1), 013002 (2011).
[Crossref]

Key Eng. Mater. (1)

J. Wang, F. H. Wu, X. L. Li, and J. C. Wang, “Smoothing of SFS Reconstructed Surface Based on Genetic Algorithm,” Key Eng. Mater. 579, 877–884 (2014).

Multimedia Tools Appl. (1)

Y. Sun, J. Dong, M. Jian, and L. Qi, “Fast 3D face reconstruction based on uncalibrated photometric stereo,” Multimedia Tools Appl. 74(11), 3635–3650 (2015).
[Crossref]

PhChin. J. Sci. Instrum. (1)

H. Bingwei, C. Zhipeng, L. Dongyi, and Z. Xiaolong, “Research on reconstruction method for unknown objects through incorporating SFS algorithm and active vision technology,” PhChin. J. Sci. Instrum. 4, 002 (2012).

Other (16)

X. Huang, M. Walton, G. Bearman, and O. Cossairt, “Near light correction for image relighting and 3D shape recovery,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2015),pp. 215–222.
[Crossref]

Y. C. Ju, A. Bruhn, and M. Breuß, “Variational perspective shape from shading,” in International Conference on Scale Space and Variational Methods in Computer Vision, Springer, Cham, Heidelberg (2015), pp. 538–550.

J. Ackermann, S. Fuhrmann, and M. Goesele, “Geometric Point Light Source Calibration,” in VMV (2013), pp. 161–168.

T. Aoto, T. Taketomi, T. Sato, Y. Mukaigawa, and N. Yokoya, “Position estimation of near point light sources using a clear hollow sphere,” in Proceedings of IEEE Conference on Digital Heritage (IEEE, 2012), Vol. 1, pp. 3721–3724.

A. Giachetti, C. Daffara, C. Reghelin, E. Gobbetti, and R. Pintus, “Light calibration and quality assessment methods for Reflectance Transformation Imaging applied to artworks’ analysis,” in Optics for Arts, Architecture, and Archaeology V (2015), Vol. 9527, p. 95270B.

T. S. F. Haines and R. C. Wilson, “Combining shape-from-shading and stereo using Gaussian-Markov random fields,” in Proceedings of IEEE Conference on Pattern Recognition (IEEE, ICPR, 2008), pp. 1–4.
[Crossref]

M. G. H. Mostafa, S. M. Yamany, and A. A. Farag, “Integrating stereo and shape from shading,” in Proceedings of IEEE Conference on Image Processing (IEEE, 1999), Vol. 3, pp. 130–134.

J. Ma, P. Zhao, and B. Gong, “A shape-from-shading method based on surface reflectance component estimation,” in Proceedings of IEEE Conference on Fuzzy Systems and Knowledge Discovery (IEEE, 2012 9th), pp. 1690–1693.
[Crossref]

J. Hou, “A novel cloud surface shape estimation method based on SFS,” in Proceedings of IEEE Conference on Computer Science and Network Technology (IEEE, 2016 5th), pp. 80–83.
[Crossref]

Y. Zhang and J. Peng, “Surface shape estimation of textureless area using shape from shading for Landsat imagery,” in Remote Sensing of the Atmosphere, Clouds, and Precipitation V (2014), Vol. 9259, p. 92591S.

L. Min, D. Li, and S. Dong, “3D Surface Roughness Measurement Based on SFS Method,” in Proceedings of IEEE Conference on Intelligent Human-Machine Systems and Cybernetics (IEEE, 2016 8th), Vol. 2, pp. 484–488.
[Crossref]

M. T. E. Melegy, A. S. Abdelrahim, and A. A. Farag, “Better Shading for Better Shape Recovery,” In CVPR, 2307–2312 (2014)

D. Roxo, N. Gonçalves, and J. P. Barreto, “Perspective shape from shading for wide-fov near-lighting endoscopes,” in Iberian Conference on Pattern Recognition and Image Analysis, Springer, Berlin, Heidelberg (2013), pp. 21–30.
[Crossref]

H. Tang, L. Yan, and P. Gao, “A modified SFS algorithm based on stereo images for the three-dimension reconstruction of Urban buildings,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2009), pp. IV-390.
[Crossref]

G. D. Martino, A. D. Simone, A. Iodice, D. Riccio, and G. Ruello, “SAR Shape from Shading in suburban areas,” In Urban Remote Sensing Event (JURSE) (2015), pp. 1–4.

L. Yang, Y. Xue, Y. Li, C. Li, J. Guang, X. He, J. Dong, and T. Hou, “Uncertainty from Lambertian surface assumption in satellite aerosol retrieval,” in Proceedings of IEEE Conference on Geoscience and Remote Sensing Symposium (IEEE, 2012), pp. 3662–3665.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Evaluation of the point light model.
Fig. 2
Fig. 2 Evaluation of the point light model.
Fig. 3
Fig. 3 Tube used in the measurement.
Fig. 4
Fig. 4 Tube measurement result.
Fig. 5
Fig. 5 Tube measurement result.

Tables (2)

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Table 1 Formula and the range of variables (unit in mm).

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Table 2 Statistics of deviation.

Equations (12)

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I s ( ϕ )= I 0 cos μ ( ϕ )
E( M )= ρ π I s ( ϕ )cos( θ )
ε( m )=E( M ) π 4 ( d f ) 2 cos 4 ( α )
{ R org ( m )=K 1 r ( M ) 2 cos 4 ( α )cos( θ ) cos μ ( ϕ ) K=β I 0 ρ 4 ( d f ) 2
sm=BM
M=s B 1 m
Z( X,Y )=300
R( m )= ( ( M- L p ) T L a ) μ ( L a T L a ) μ 2 ( ( M- L p ) T ( M- L p ) ) 1+ μ 2 * ( M x × M y ) T ( M L p ) ( M x × M y ) T ( M x × M y ) ( M L p ) T ( M L p )
{ C L = Ω ( I( m )R( m ) ) 2 dΩ C S = Ω ( M xx T M xx + M yy T M yy ) 2 dΩ C I = Ω ( M xy - M yx ) T ( M xy - M yx )dΩ
C= λ L C L + λ S C S + λ I C I = Ω f( s, s x , s y , s xx , s yy , s xy , s yx )dΩ
s t+1 = s t δ C s
C s = f s x ( f s x ) y ( f s y )+ 2 x 2 ( f s xx ) + 2 y 2 ( f s yy )+ 2 xy ( f s xy )+ 2 yx ( f s yx )

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