Abstract

Textured surface analysis is essential for many applications. In this paper, we present a three-dimensional (3D) recovery approach for real textured surfaces based on photometric stereo. The aim is to be able to reconstruct the textured surfaces in 3D with a high degree of accuracy. For this, the proposed method uses a sequence of six images and a Lambertian bidirectional reflectance distribution function (BRDF) to recover the surface height map. A hierarchical selection of these images is employed to eliminate the effects of shadows and highlights for all surface facets. To evaluate the performances of our method, we compare it to other traditional photometric stereo methods on real textured surfaces using six or more images.

© 2012 Optical Society of America

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References

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  1. H. Zahouani, R. Vargiolu, and M.-T. Do, “Characterization of micro texture related to wet road/tire friction,” in Proceedings of AIPCR/PIARC (World Road Association-PARC, 2000), pp. 195–205.
  2. O. Faugeras, Three-Dimensional Computer Vision: a Geometric Viewpoint (The MIT Press, 1995).
  3. B. Shahraray and M. Brown, “Robust depth estimation from optical flow,” in Proceedings of the Second International Conference on Computer Vision ( IEEE Computer Society, 1988), pp. 641–650.
    [CrossRef]
  4. B. Horn, “Shape from shading : A method for obtaining the shape of a smooth opaque object from one view,” Ph.D. thesis (Massachusetts Institute of Technology, 1970).
  5. R. Zhang, P. Tsai, J. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690–706(1999).
    [CrossRef]
  6. R. Woodham, “Photometric method for determining surface orientation from multiple images,” Opt. Eng. 19, 139–144 (1980).
  7. J. E. N. Coleman and R. C. Jain, “Obtaining 3-dimensional shape of textured and specular surface using four-source photometry,” Comput. Graphics Image Process. 18, 309–328 (1982).
    [CrossRef]
  8. K. Ikeuchi, “Determining surface orientations of specular surfaces by using the photometric stereo method,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 141–184 (1981).
    [CrossRef]
  9. G. McGunnigle and M. Chantler, “Rough surface description using photometric stereo,” Meas. Sci. Technol. 14, 699–709 (2003).
    [CrossRef]
  10. A. Ben Slimane, M. Khoudeir, J. Brochard, V. Legeay, and M.-T. Do, “Relief reconstruction of rough textured surface through image analysis,” Proc. SPIE 5011, 66 (2003).
    [CrossRef]
  11. M. Khoudeir, J. Brochard, A. Benslimane, and M.-T. Do, “Estimation of the luminance map for a lambertian photometric model: application to the study of road surface roughness,” J. Electron. Imaging 3, 512–522 (2004).
  12. S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239–1252 (2003).
    [CrossRef]
  13. J. Sun, M. Smith, L. Smith, S. Midha, and J. Bamber, “Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities,” Image Vision Comput. 25, 1050–1057 (2007).
    [CrossRef]
  14. V. Argyriou, S. Barsky, and M. Petrou, “Photometric stereo with an arbitrary number of illuminants,” Comput. Vision Image Underst. 114, 887–900 (2010).
    [CrossRef]
  15. S. K. Nayar, “Shape and reflectance from image intensities,” in Proceedings of the Third Annual Conference on Intelligent Robotic Systems for Space Exploration (IEEE, 1991), pp. 81–98.
    [CrossRef]
  16. A. S. Georghiades, “Incorporating the torrance and sparrow model of reflectance in uncalibrated photometric stereo,” in Proceedings of the Ninth IEEE International Conference on Computer Vision 2 (IEEE, 2003), pp. 816–823.
    [CrossRef]
  17. F. Salomon and K. Ikeuchi, “Extracting the shape and roughness of specular lobe objects using four light photometric stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 449–454(1996).
    [CrossRef]
  18. T. Higo, Y. Matsushita, and K. Ikeuchi, “Consensus photometric stereo,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1157–1164.
    [CrossRef]
  19. J. Lambert, Photometria (Augsburg, 1760).
  20. B. Horn, “Height and gradient from shading,” Int. J. Comput. Vision 5, 37–75 (1990).
    [CrossRef]
  21. T. Wei and R. Klette, “Height from gradient using surface curvature and area constraints,” in Proceedings of the Third Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP, 2002), pp. 204–210.
  22. A. Woodward and P. Delmas, “Synthetic ground truth for comparison of gradient field integration methods for human faces,” presented at the Conference on Image and Vision Computing New Zealand, Dunedin, New Zealand, 2005.
  23. A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field?” in Proceedings of the European Conference on Computer Vision (ECCV) (2006), pp. 578–591.
  24. R. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. 10, 439–451 (1988).
    [CrossRef]
  25. K. Schlüns and R. Klette, “Local and global integration of discrete vector fields”, presented at the conference on Advances in Computer Vision, Wien, Austria, 1997.
  26. C. Hernández, G. Vogiatzis, and R. Cipolla, “Shadows in three-source photometric stereo,” in Proceedings of the 10th European Conference on Computer Vision: Part I (ECCV, 2008), pp. 290–303.
  27. A. El Gendy, A. Shalaby, M. Saleh, and G. W. Flintsch, “Stereo-vision applications to reconstruct the 3D texture of pavement surface,” Intern. J. Pavement Eng. 12, 263–273 (2011).
    [CrossRef]
  28. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
    [CrossRef]

2011 (1)

A. El Gendy, A. Shalaby, M. Saleh, and G. W. Flintsch, “Stereo-vision applications to reconstruct the 3D texture of pavement surface,” Intern. J. Pavement Eng. 12, 263–273 (2011).
[CrossRef]

2010 (1)

V. Argyriou, S. Barsky, and M. Petrou, “Photometric stereo with an arbitrary number of illuminants,” Comput. Vision Image Underst. 114, 887–900 (2010).
[CrossRef]

2007 (1)

J. Sun, M. Smith, L. Smith, S. Midha, and J. Bamber, “Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities,” Image Vision Comput. 25, 1050–1057 (2007).
[CrossRef]

2004 (1)

M. Khoudeir, J. Brochard, A. Benslimane, and M.-T. Do, “Estimation of the luminance map for a lambertian photometric model: application to the study of road surface roughness,” J. Electron. Imaging 3, 512–522 (2004).

2003 (3)

S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239–1252 (2003).
[CrossRef]

G. McGunnigle and M. Chantler, “Rough surface description using photometric stereo,” Meas. Sci. Technol. 14, 699–709 (2003).
[CrossRef]

A. Ben Slimane, M. Khoudeir, J. Brochard, V. Legeay, and M.-T. Do, “Relief reconstruction of rough textured surface through image analysis,” Proc. SPIE 5011, 66 (2003).
[CrossRef]

1999 (1)

R. Zhang, P. Tsai, J. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690–706(1999).
[CrossRef]

1996 (1)

F. Salomon and K. Ikeuchi, “Extracting the shape and roughness of specular lobe objects using four light photometric stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 449–454(1996).
[CrossRef]

1990 (1)

B. Horn, “Height and gradient from shading,” Int. J. Comput. Vision 5, 37–75 (1990).
[CrossRef]

1988 (1)

R. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. 10, 439–451 (1988).
[CrossRef]

1982 (1)

J. E. N. Coleman and R. C. Jain, “Obtaining 3-dimensional shape of textured and specular surface using four-source photometry,” Comput. Graphics Image Process. 18, 309–328 (1982).
[CrossRef]

1981 (1)

K. Ikeuchi, “Determining surface orientations of specular surfaces by using the photometric stereo method,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 141–184 (1981).
[CrossRef]

1980 (1)

R. Woodham, “Photometric method for determining surface orientation from multiple images,” Opt. Eng. 19, 139–144 (1980).

1975 (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

Agrawal, A.

A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field?” in Proceedings of the European Conference on Computer Vision (ECCV) (2006), pp. 578–591.

Argyriou, V.

V. Argyriou, S. Barsky, and M. Petrou, “Photometric stereo with an arbitrary number of illuminants,” Comput. Vision Image Underst. 114, 887–900 (2010).
[CrossRef]

Bamber, J.

J. Sun, M. Smith, L. Smith, S. Midha, and J. Bamber, “Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities,” Image Vision Comput. 25, 1050–1057 (2007).
[CrossRef]

Barsky, S.

V. Argyriou, S. Barsky, and M. Petrou, “Photometric stereo with an arbitrary number of illuminants,” Comput. Vision Image Underst. 114, 887–900 (2010).
[CrossRef]

S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239–1252 (2003).
[CrossRef]

Benslimane, A.

M. Khoudeir, J. Brochard, A. Benslimane, and M.-T. Do, “Estimation of the luminance map for a lambertian photometric model: application to the study of road surface roughness,” J. Electron. Imaging 3, 512–522 (2004).

Brochard, J.

M. Khoudeir, J. Brochard, A. Benslimane, and M.-T. Do, “Estimation of the luminance map for a lambertian photometric model: application to the study of road surface roughness,” J. Electron. Imaging 3, 512–522 (2004).

A. Ben Slimane, M. Khoudeir, J. Brochard, V. Legeay, and M.-T. Do, “Relief reconstruction of rough textured surface through image analysis,” Proc. SPIE 5011, 66 (2003).
[CrossRef]

Brown, M.

B. Shahraray and M. Brown, “Robust depth estimation from optical flow,” in Proceedings of the Second International Conference on Computer Vision ( IEEE Computer Society, 1988), pp. 641–650.
[CrossRef]

Chantler, M.

G. McGunnigle and M. Chantler, “Rough surface description using photometric stereo,” Meas. Sci. Technol. 14, 699–709 (2003).
[CrossRef]

Chellappa, R.

R. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. 10, 439–451 (1988).
[CrossRef]

A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field?” in Proceedings of the European Conference on Computer Vision (ECCV) (2006), pp. 578–591.

Cipolla, R.

C. Hernández, G. Vogiatzis, and R. Cipolla, “Shadows in three-source photometric stereo,” in Proceedings of the 10th European Conference on Computer Vision: Part I (ECCV, 2008), pp. 290–303.

Coleman, J. E. N.

J. E. N. Coleman and R. C. Jain, “Obtaining 3-dimensional shape of textured and specular surface using four-source photometry,” Comput. Graphics Image Process. 18, 309–328 (1982).
[CrossRef]

Cryer, J.

R. Zhang, P. Tsai, J. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690–706(1999).
[CrossRef]

Delmas, P.

A. Woodward and P. Delmas, “Synthetic ground truth for comparison of gradient field integration methods for human faces,” presented at the Conference on Image and Vision Computing New Zealand, Dunedin, New Zealand, 2005.

Do, M.-T.

M. Khoudeir, J. Brochard, A. Benslimane, and M.-T. Do, “Estimation of the luminance map for a lambertian photometric model: application to the study of road surface roughness,” J. Electron. Imaging 3, 512–522 (2004).

A. Ben Slimane, M. Khoudeir, J. Brochard, V. Legeay, and M.-T. Do, “Relief reconstruction of rough textured surface through image analysis,” Proc. SPIE 5011, 66 (2003).
[CrossRef]

H. Zahouani, R. Vargiolu, and M.-T. Do, “Characterization of micro texture related to wet road/tire friction,” in Proceedings of AIPCR/PIARC (World Road Association-PARC, 2000), pp. 195–205.

Faugeras, O.

O. Faugeras, Three-Dimensional Computer Vision: a Geometric Viewpoint (The MIT Press, 1995).

Flintsch, G. W.

A. El Gendy, A. Shalaby, M. Saleh, and G. W. Flintsch, “Stereo-vision applications to reconstruct the 3D texture of pavement surface,” Intern. J. Pavement Eng. 12, 263–273 (2011).
[CrossRef]

Frankot, R.

R. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. 10, 439–451 (1988).
[CrossRef]

Gendy, A. El

A. El Gendy, A. Shalaby, M. Saleh, and G. W. Flintsch, “Stereo-vision applications to reconstruct the 3D texture of pavement surface,” Intern. J. Pavement Eng. 12, 263–273 (2011).
[CrossRef]

Georghiades, A. S.

A. S. Georghiades, “Incorporating the torrance and sparrow model of reflectance in uncalibrated photometric stereo,” in Proceedings of the Ninth IEEE International Conference on Computer Vision 2 (IEEE, 2003), pp. 816–823.
[CrossRef]

Hernández, C.

C. Hernández, G. Vogiatzis, and R. Cipolla, “Shadows in three-source photometric stereo,” in Proceedings of the 10th European Conference on Computer Vision: Part I (ECCV, 2008), pp. 290–303.

Higo, T.

T. Higo, Y. Matsushita, and K. Ikeuchi, “Consensus photometric stereo,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1157–1164.
[CrossRef]

Horn, B.

B. Horn, “Height and gradient from shading,” Int. J. Comput. Vision 5, 37–75 (1990).
[CrossRef]

B. Horn, “Shape from shading : A method for obtaining the shape of a smooth opaque object from one view,” Ph.D. thesis (Massachusetts Institute of Technology, 1970).

Ikeuchi, K.

F. Salomon and K. Ikeuchi, “Extracting the shape and roughness of specular lobe objects using four light photometric stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 449–454(1996).
[CrossRef]

K. Ikeuchi, “Determining surface orientations of specular surfaces by using the photometric stereo method,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 141–184 (1981).
[CrossRef]

T. Higo, Y. Matsushita, and K. Ikeuchi, “Consensus photometric stereo,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1157–1164.
[CrossRef]

Jain, R. C.

J. E. N. Coleman and R. C. Jain, “Obtaining 3-dimensional shape of textured and specular surface using four-source photometry,” Comput. Graphics Image Process. 18, 309–328 (1982).
[CrossRef]

Khoudeir, M.

M. Khoudeir, J. Brochard, A. Benslimane, and M.-T. Do, “Estimation of the luminance map for a lambertian photometric model: application to the study of road surface roughness,” J. Electron. Imaging 3, 512–522 (2004).

A. Ben Slimane, M. Khoudeir, J. Brochard, V. Legeay, and M.-T. Do, “Relief reconstruction of rough textured surface through image analysis,” Proc. SPIE 5011, 66 (2003).
[CrossRef]

Klette, R.

T. Wei and R. Klette, “Height from gradient using surface curvature and area constraints,” in Proceedings of the Third Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP, 2002), pp. 204–210.

K. Schlüns and R. Klette, “Local and global integration of discrete vector fields”, presented at the conference on Advances in Computer Vision, Wien, Austria, 1997.

Lambert, J.

J. Lambert, Photometria (Augsburg, 1760).

Legeay, V.

A. Ben Slimane, M. Khoudeir, J. Brochard, V. Legeay, and M.-T. Do, “Relief reconstruction of rough textured surface through image analysis,” Proc. SPIE 5011, 66 (2003).
[CrossRef]

Matsushita, Y.

T. Higo, Y. Matsushita, and K. Ikeuchi, “Consensus photometric stereo,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1157–1164.
[CrossRef]

McGunnigle, G.

G. McGunnigle and M. Chantler, “Rough surface description using photometric stereo,” Meas. Sci. Technol. 14, 699–709 (2003).
[CrossRef]

Midha, S.

J. Sun, M. Smith, L. Smith, S. Midha, and J. Bamber, “Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities,” Image Vision Comput. 25, 1050–1057 (2007).
[CrossRef]

Nayar, S. K.

S. K. Nayar, “Shape and reflectance from image intensities,” in Proceedings of the Third Annual Conference on Intelligent Robotic Systems for Space Exploration (IEEE, 1991), pp. 81–98.
[CrossRef]

Petrou, M.

V. Argyriou, S. Barsky, and M. Petrou, “Photometric stereo with an arbitrary number of illuminants,” Comput. Vision Image Underst. 114, 887–900 (2010).
[CrossRef]

S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239–1252 (2003).
[CrossRef]

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

Raskar, R.

A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field?” in Proceedings of the European Conference on Computer Vision (ECCV) (2006), pp. 578–591.

Saleh, M.

A. El Gendy, A. Shalaby, M. Saleh, and G. W. Flintsch, “Stereo-vision applications to reconstruct the 3D texture of pavement surface,” Intern. J. Pavement Eng. 12, 263–273 (2011).
[CrossRef]

Salomon, F.

F. Salomon and K. Ikeuchi, “Extracting the shape and roughness of specular lobe objects using four light photometric stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 449–454(1996).
[CrossRef]

Schlüns, K.

K. Schlüns and R. Klette, “Local and global integration of discrete vector fields”, presented at the conference on Advances in Computer Vision, Wien, Austria, 1997.

Shah, M.

R. Zhang, P. Tsai, J. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690–706(1999).
[CrossRef]

Shahraray, B.

B. Shahraray and M. Brown, “Robust depth estimation from optical flow,” in Proceedings of the Second International Conference on Computer Vision ( IEEE Computer Society, 1988), pp. 641–650.
[CrossRef]

Shalaby, A.

A. El Gendy, A. Shalaby, M. Saleh, and G. W. Flintsch, “Stereo-vision applications to reconstruct the 3D texture of pavement surface,” Intern. J. Pavement Eng. 12, 263–273 (2011).
[CrossRef]

Slimane, A. Ben

A. Ben Slimane, M. Khoudeir, J. Brochard, V. Legeay, and M.-T. Do, “Relief reconstruction of rough textured surface through image analysis,” Proc. SPIE 5011, 66 (2003).
[CrossRef]

Smith, L.

J. Sun, M. Smith, L. Smith, S. Midha, and J. Bamber, “Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities,” Image Vision Comput. 25, 1050–1057 (2007).
[CrossRef]

Smith, M.

J. Sun, M. Smith, L. Smith, S. Midha, and J. Bamber, “Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities,” Image Vision Comput. 25, 1050–1057 (2007).
[CrossRef]

Sun, J.

J. Sun, M. Smith, L. Smith, S. Midha, and J. Bamber, “Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities,” Image Vision Comput. 25, 1050–1057 (2007).
[CrossRef]

Tsai, P.

R. Zhang, P. Tsai, J. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690–706(1999).
[CrossRef]

Vargiolu, R.

H. Zahouani, R. Vargiolu, and M.-T. Do, “Characterization of micro texture related to wet road/tire friction,” in Proceedings of AIPCR/PIARC (World Road Association-PARC, 2000), pp. 195–205.

Vogiatzis, G.

C. Hernández, G. Vogiatzis, and R. Cipolla, “Shadows in three-source photometric stereo,” in Proceedings of the 10th European Conference on Computer Vision: Part I (ECCV, 2008), pp. 290–303.

Wei, T.

T. Wei and R. Klette, “Height from gradient using surface curvature and area constraints,” in Proceedings of the Third Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP, 2002), pp. 204–210.

Woodham, R.

R. Woodham, “Photometric method for determining surface orientation from multiple images,” Opt. Eng. 19, 139–144 (1980).

Woodward, A.

A. Woodward and P. Delmas, “Synthetic ground truth for comparison of gradient field integration methods for human faces,” presented at the Conference on Image and Vision Computing New Zealand, Dunedin, New Zealand, 2005.

Zahouani, H.

H. Zahouani, R. Vargiolu, and M.-T. Do, “Characterization of micro texture related to wet road/tire friction,” in Proceedings of AIPCR/PIARC (World Road Association-PARC, 2000), pp. 195–205.

Zhang, R.

R. Zhang, P. Tsai, J. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690–706(1999).
[CrossRef]

Commun. ACM (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

Comput. Graphics Image Process. (1)

J. E. N. Coleman and R. C. Jain, “Obtaining 3-dimensional shape of textured and specular surface using four-source photometry,” Comput. Graphics Image Process. 18, 309–328 (1982).
[CrossRef]

Comput. Vision Image Underst. (1)

V. Argyriou, S. Barsky, and M. Petrou, “Photometric stereo with an arbitrary number of illuminants,” Comput. Vision Image Underst. 114, 887–900 (2010).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (5)

F. Salomon and K. Ikeuchi, “Extracting the shape and roughness of specular lobe objects using four light photometric stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 449–454(1996).
[CrossRef]

R. Zhang, P. Tsai, J. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690–706(1999).
[CrossRef]

S. Barsky and M. Petrou, “The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1239–1252 (2003).
[CrossRef]

K. Ikeuchi, “Determining surface orientations of specular surfaces by using the photometric stereo method,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 141–184 (1981).
[CrossRef]

R. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. 10, 439–451 (1988).
[CrossRef]

Image Vision Comput. (1)

J. Sun, M. Smith, L. Smith, S. Midha, and J. Bamber, “Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities,” Image Vision Comput. 25, 1050–1057 (2007).
[CrossRef]

Int. J. Comput. Vision (1)

B. Horn, “Height and gradient from shading,” Int. J. Comput. Vision 5, 37–75 (1990).
[CrossRef]

Intern. J. Pavement Eng. (1)

A. El Gendy, A. Shalaby, M. Saleh, and G. W. Flintsch, “Stereo-vision applications to reconstruct the 3D texture of pavement surface,” Intern. J. Pavement Eng. 12, 263–273 (2011).
[CrossRef]

J. Electron. Imaging (1)

M. Khoudeir, J. Brochard, A. Benslimane, and M.-T. Do, “Estimation of the luminance map for a lambertian photometric model: application to the study of road surface roughness,” J. Electron. Imaging 3, 512–522 (2004).

Meas. Sci. Technol. (1)

G. McGunnigle and M. Chantler, “Rough surface description using photometric stereo,” Meas. Sci. Technol. 14, 699–709 (2003).
[CrossRef]

Opt. Eng. (1)

R. Woodham, “Photometric method for determining surface orientation from multiple images,” Opt. Eng. 19, 139–144 (1980).

Proc. SPIE (1)

A. Ben Slimane, M. Khoudeir, J. Brochard, V. Legeay, and M.-T. Do, “Relief reconstruction of rough textured surface through image analysis,” Proc. SPIE 5011, 66 (2003).
[CrossRef]

Other (13)

H. Zahouani, R. Vargiolu, and M.-T. Do, “Characterization of micro texture related to wet road/tire friction,” in Proceedings of AIPCR/PIARC (World Road Association-PARC, 2000), pp. 195–205.

O. Faugeras, Three-Dimensional Computer Vision: a Geometric Viewpoint (The MIT Press, 1995).

B. Shahraray and M. Brown, “Robust depth estimation from optical flow,” in Proceedings of the Second International Conference on Computer Vision ( IEEE Computer Society, 1988), pp. 641–650.
[CrossRef]

B. Horn, “Shape from shading : A method for obtaining the shape of a smooth opaque object from one view,” Ph.D. thesis (Massachusetts Institute of Technology, 1970).

T. Higo, Y. Matsushita, and K. Ikeuchi, “Consensus photometric stereo,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1157–1164.
[CrossRef]

J. Lambert, Photometria (Augsburg, 1760).

S. K. Nayar, “Shape and reflectance from image intensities,” in Proceedings of the Third Annual Conference on Intelligent Robotic Systems for Space Exploration (IEEE, 1991), pp. 81–98.
[CrossRef]

A. S. Georghiades, “Incorporating the torrance and sparrow model of reflectance in uncalibrated photometric stereo,” in Proceedings of the Ninth IEEE International Conference on Computer Vision 2 (IEEE, 2003), pp. 816–823.
[CrossRef]

K. Schlüns and R. Klette, “Local and global integration of discrete vector fields”, presented at the conference on Advances in Computer Vision, Wien, Austria, 1997.

C. Hernández, G. Vogiatzis, and R. Cipolla, “Shadows in three-source photometric stereo,” in Proceedings of the 10th European Conference on Computer Vision: Part I (ECCV, 2008), pp. 290–303.

T. Wei and R. Klette, “Height from gradient using surface curvature and area constraints,” in Proceedings of the Third Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP, 2002), pp. 204–210.

A. Woodward and P. Delmas, “Synthetic ground truth for comparison of gradient field integration methods for human faces,” presented at the Conference on Image and Vision Computing New Zealand, Dunedin, New Zealand, 2005.

A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field?” in Proceedings of the European Conference on Computer Vision (ECCV) (2006), pp. 578–591.

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Figures (14)

Fig. 1
Fig. 1

Geometric definition of angles σ and τ.

Fig. 2
Fig. 2

Shadow and specularity representation.

Fig. 3
Fig. 3

Six synthetic images of two semispheres with hard shadow and specularity. The zenith angle σ is equal to π 6 and a)  τ = 0 , b)  τ = π 3 , c)  τ = 2 π 3 , d)  τ = π , e)  τ = 4 π 3 , and f)  τ = 5 π 3 .

Fig. 4
Fig. 4

Shadow detection: a)  Var ( I ) , b) adaptive threshold function T, c) ground truth, and d) estimated.

Fig. 5
Fig. 5

Specular detection: a) error E and b) final detection of shadows and highlights.

Fig. 6
Fig. 6

3D surfaces acquired by a laser system.

Fig. 7
Fig. 7

Six synthetic images from a surface database with hard shadow and specularity. The zenith angle σ is equal to π 6 and a)  τ = 0 , b)  τ = π 3 , c)  τ = 2 π 3 , d)  τ = π , e)  τ = 4 π 3 , and f)  τ = 5 π 3 .

Fig. 8
Fig. 8

Comparison between all 3D reconstruction methods: a) M1, b) with shadow and high ground truth, c) M2, d) M3, and e) Our.

Fig. 9
Fig. 9

ROC curve of the three methods: a) shadow problematic values, b) highlight problematic values and c) shadow and highlight problematic values.

Fig. 10
Fig. 10

Six real images of two semispheres with hard shadow and specularity. The zenith angle σ is equal to π 6 and a)  τ = 5 π 6 , b)  τ = π 2 , c)  τ = 3 π 2 , d)  τ = 7 π 6 , e)  τ = π 6 , and f)  τ = 11 π 6 .

Fig. 11
Fig. 11

Comparison between all 3D reconstruction methods: a) M1, b) with shadow and high ground truth, c) M2, d) M3, and e) Our.

Fig. 12
Fig. 12

Examples of real acquisition surfaces.

Fig. 13
Fig. 13

Comparison of shadow (red) and highlight (green) detection, from left to right, part of image, M2, M3, and our method.

Fig. 14
Fig. 14

Comparison of 3D reconstruction, from left to right, M2, M3, and our method.

Tables (4)

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Table 1 Results of Shadow and Highlight Detection for Fig. 6a and the SNR between Ground Truth Correction and Other 3D Reconstructions

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Table 2 Results of Shadow and Highlight Detection for Fig. 6b and the SNR between Ground Truth Correction and Other 3D Reconstructions

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Table 3 Results of Shadow and Highlight Detection for the Database and the SNR between Ground Truth Correction and Other 3D Reconstructions

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Table 4 Results of Shadow and Highlight Detection for the Real Images and the SNR between Ground Truth Correction and Other 3D Reconstructions

Equations (15)

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I = ρ cos ( θ ) = ρ ( n · l ) ,
ρ = | ( L T L ) 1 · L T · I | N = ( ( L T L ) 1 · L T · I ) / ρ .
W = ( s ( x , y ) x p ) 2 + ( s ( x , y ) y q ) 2 d x d y ,
S ( u , v ) = j u P ( u , v ) j v Q ( u , v ) u 2 + v 2 ,
I = ϵ I A + ρ ( l · n ) + β ( r · v ) α with     r = 2 ( l · n ) n l ,
I = { ϵ I A + ρ ( n · l ) if light source   l   is visible to facet ϵ I A otherwise .
1 2 ( I 2 + I 3 ) I j 1 2 ( I 2 + I 3 ) + I j T ,
T = f ( Var ( I ) ) .
T = 1 Var ( I 2 I m ) .
a 1 l 1 + a 2 l 2 + a 3 l 3 + a 4 l 4 = 0.
a 1 ρ ( l 1 · n ) + a 2 ρ ( l 2 · n ) + a 3 ρ ( l 3 · n ) + a 4 ρ ( l 4 · n ) = 0 , a 1 I 1 + a 2 I 2 + a 3 I 3 + a 4 I 4 = 0 ,
E = i = 0 C m s 4 k = 1 m s | a i k I S k | ,
C m s 4 = m S ! 4 ! ( m S 4 ) ! .
SNR = 10 log ( 1 m n i = 0 m 1 i = 0 m 1 s ( i , j ) 2 MSE ) ,
MSE = 1 m n i = 0 m 1 i = 0 m 1 s ( i , j ) s ^ ( i , j ) 2 .

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