Abstract

In classical photometric stereo (PS), a Lambertian surface is illuminated from three distant light sources to recover one normal direction per pixel of the input image. In continuous noiseless cases, PS allows us to reconstruct the textured surfaces in three-dimensions with a high degree of accuracy and a high resolution. In the real world, an image is a digital quantization, a limited and noisy representation of a surface. In this paper, we present an accurate 3D recovery approach for real textured surfaces based on an acquisition PS method. The proposed method uses a sequence of images for each light source to recover an accurate and unlimited representation of a surface. To evaluate the performances of the proposed method, we compare it to other traditional PS methods on real textured surfaces.

© 2013 Optical Society of America

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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 the Permanent International Association of Road Congresses (PIARC) (World Road Association-PARC, 2000), pp. 195–205.
  2. O. Faugeras, Three-Dimensional Computer Vision: A Geometric View-Point (Cambridge University, 1995).
  3. B. Shahraray and M. Brown, “Robust depth estimation from optical flow,” in Second International Conference on Computer Vision (IEEE, 1988), pp. 641–650.
  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).
    [CrossRef]
  7. J. E. N. Coleman and R. C. Jain, “Obtaining three-dimensional shape of textured and specular surface using four-source photometry,” Comput. Graph. 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. PAMI-3, 661–669 (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, 66–73 (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).
    [CrossRef]
  12. S. Barsky and M. Petrou, “The four-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 Vis. Comput. 25, 1050–1057 (2007).
    [CrossRef]
  14. V. Argyriou, S. Barsky, and M. Petrou, “Photometric stereo with an arbitrary number of illuminants,” Comput. Vis. Image Underst. 114, 887–900 (2010).
    [CrossRef]
  15. B. Bringier, A. Bony, and M. Khoudeir, “Specularity and shadow detection for the multisource photometric reconstruction of a textured surface,” J. Opt. Soc. Am. A 29, 11–21 (2012).
    [CrossRef]
  16. N. Alldrin, T. Zickler, and D. Kriegman, “Photometric stereo with non-parametric and spatially-varying reflectance,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.
  17. D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, “Shape and spatially-varying BRDFs from photometric stereo,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 2005), pp. 341–348.
  18. A. Agrawal, R. Raskar, S. K. Nayar, and Y. Li, “Removing photography artifacts using gradient projection and flash-exposure sampling,” ACM Trans. Graph. 24, 828–835 (2005).
    [CrossRef]
  19. J. Lambert, Photometria (Augsburg, 1760).
  20. B. K. P. Horn, Robot Vision (Massachusetts Institute of Technology, 1986).
  21. S. Mann and R. W. Picard, “Being ‘undigital’ with digital cameras: extending dynamic range by combining differently exposed pictures,” in Proceedings of IS&T 48th Annual Conference (IS&T, 1995), pp. 422–428.
  22. P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1997), pp. 369–378.
  23. T. Mitsunaga and S. K. Nayar, “Radiometric self calibration,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), p. 374.
  24. M. D. Grossberg and S. K. Nayar, “High dynamic range from multiple images: which exposures to combine?,” in Proceeding of IEEE Workshop on Color and Photometric Methods in Computer Vision (IEEE, 2003).
  25. ISO 25178-2:2012, “Geometrical product specifications (GPS)—surface texture: areal—part 2: terms, definitions and surface texture parameters,” http://www.iso.org/iso/home/store/catalogue_tc/catalogue_detail.htm?csnumber=42785 (2012).
  26. B. Muralikrishnan and J. Raja, Computational Surface and Roundness Metrology (Springer, 2008).

2012 (1)

2010 (1)

V. Argyriou, S. Barsky, and M. Petrou, “Photometric stereo with an arbitrary number of illuminants,” Comput. Vis. 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 Vis. Comput. 25, 1050–1057 (2007).
[CrossRef]

2005 (1)

A. Agrawal, R. Raskar, S. K. Nayar, and Y. Li, “Removing photography artifacts using gradient projection and flash-exposure sampling,” ACM Trans. Graph. 24, 828–835 (2005).
[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).
[CrossRef]

2003 (3)

S. Barsky and M. Petrou, “The four-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, 66–73 (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]

1982 (1)

J. E. N. Coleman and R. C. Jain, “Obtaining three-dimensional shape of textured and specular surface using four-source photometry,” Comput. Graph. 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. PAMI-3, 661–669 (1981).
[CrossRef]

1980 (1)

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

Agrawal, A.

A. Agrawal, R. Raskar, S. K. Nayar, and Y. Li, “Removing photography artifacts using gradient projection and flash-exposure sampling,” ACM Trans. Graph. 24, 828–835 (2005).
[CrossRef]

Alldrin, N.

N. Alldrin, T. Zickler, and D. Kriegman, “Photometric stereo with non-parametric and spatially-varying reflectance,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Argyriou, V.

V. Argyriou, S. Barsky, and M. Petrou, “Photometric stereo with an arbitrary number of illuminants,” Comput. Vis. 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 Vis. Comput. 25, 1050–1057 (2007).
[CrossRef]

Barsky, S.

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

S. Barsky and M. Petrou, “The four-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]

Ben Slimane, A.

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, 66–73 (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).
[CrossRef]

Bony, A.

Bringier, B.

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).
[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, 66–73 (2003).
[CrossRef]

Brown, M.

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

Chantler, M.

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

Coleman, J. E. N.

J. E. N. Coleman and R. C. Jain, “Obtaining three-dimensional shape of textured and specular surface using four-source photometry,” Comput. Graph. 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]

Curless, B.

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, “Shape and spatially-varying BRDFs from photometric stereo,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 2005), pp. 341–348.

Debevec, P. E.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1997), pp. 369–378.

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).
[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, 66–73 (2003).
[CrossRef]

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

Faugeras, O.

O. Faugeras, Three-Dimensional Computer Vision: A Geometric View-Point (Cambridge University, 1995).

Goldman, D. B.

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, “Shape and spatially-varying BRDFs from photometric stereo,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 2005), pp. 341–348.

Grossberg, M. D.

M. D. Grossberg and S. K. Nayar, “High dynamic range from multiple images: which exposures to combine?,” in Proceeding of IEEE Workshop on Color and Photometric Methods in Computer Vision (IEEE, 2003).

Hertzmann, A.

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, “Shape and spatially-varying BRDFs from photometric stereo,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 2005), pp. 341–348.

Horn, B.

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).

Horn, B. K. P.

B. K. P. Horn, Robot Vision (Massachusetts Institute of Technology, 1986).

Ikeuchi, K.

K. Ikeuchi, “Determining surface orientations of specular surfaces by using the photometric stereo method,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3, 661–669 (1981).
[CrossRef]

Jain, R. C.

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

Khoudeir, M.

B. Bringier, A. Bony, and M. Khoudeir, “Specularity and shadow detection for the multisource photometric reconstruction of a textured surface,” J. Opt. Soc. Am. A 29, 11–21 (2012).
[CrossRef]

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).
[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, 66–73 (2003).
[CrossRef]

Kriegman, D.

N. Alldrin, T. Zickler, and D. Kriegman, “Photometric stereo with non-parametric and spatially-varying reflectance,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

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, 66–73 (2003).
[CrossRef]

Li, Y.

A. Agrawal, R. Raskar, S. K. Nayar, and Y. Li, “Removing photography artifacts using gradient projection and flash-exposure sampling,” ACM Trans. Graph. 24, 828–835 (2005).
[CrossRef]

Malik, J.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1997), pp. 369–378.

Mann, S.

S. Mann and R. W. Picard, “Being ‘undigital’ with digital cameras: extending dynamic range by combining differently exposed pictures,” in Proceedings of IS&T 48th Annual Conference (IS&T, 1995), pp. 422–428.

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 Vis. Comput. 25, 1050–1057 (2007).
[CrossRef]

Mitsunaga, T.

T. Mitsunaga and S. K. Nayar, “Radiometric self calibration,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), p. 374.

Muralikrishnan, B.

B. Muralikrishnan and J. Raja, Computational Surface and Roundness Metrology (Springer, 2008).

Nayar, S. K.

A. Agrawal, R. Raskar, S. K. Nayar, and Y. Li, “Removing photography artifacts using gradient projection and flash-exposure sampling,” ACM Trans. Graph. 24, 828–835 (2005).
[CrossRef]

M. D. Grossberg and S. K. Nayar, “High dynamic range from multiple images: which exposures to combine?,” in Proceeding of IEEE Workshop on Color and Photometric Methods in Computer Vision (IEEE, 2003).

T. Mitsunaga and S. K. Nayar, “Radiometric self calibration,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), p. 374.

Petrou, M.

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

S. Barsky and M. Petrou, “The four-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]

Picard, R. W.

S. Mann and R. W. Picard, “Being ‘undigital’ with digital cameras: extending dynamic range by combining differently exposed pictures,” in Proceedings of IS&T 48th Annual Conference (IS&T, 1995), pp. 422–428.

Raja, J.

B. Muralikrishnan and J. Raja, Computational Surface and Roundness Metrology (Springer, 2008).

Raskar, R.

A. Agrawal, R. Raskar, S. K. Nayar, and Y. Li, “Removing photography artifacts using gradient projection and flash-exposure sampling,” ACM Trans. Graph. 24, 828–835 (2005).
[CrossRef]

Seitz, S. M.

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, “Shape and spatially-varying BRDFs from photometric stereo,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 2005), pp. 341–348.

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 Second International Conference on Computer Vision (IEEE, 1988), pp. 641–650.

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 Vis. 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 Vis. 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 Vis. 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 the Permanent International Association of Road Congresses (PIARC) (World Road Association-PARC, 2000), pp. 195–205.

Woodham, R.

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

Zahouani, H.

H. Zahouani, R. Vargiolu, and M.-T. Do, “Characterization of micro texture related to wet road/tire friction,” in Proceedings of the Permanent International Association of Road Congresses (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]

Zickler, T.

N. Alldrin, T. Zickler, and D. Kriegman, “Photometric stereo with non-parametric and spatially-varying reflectance,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

ACM Trans. Graph. (1)

A. Agrawal, R. Raskar, S. K. Nayar, and Y. Li, “Removing photography artifacts using gradient projection and flash-exposure sampling,” ACM Trans. Graph. 24, 828–835 (2005).
[CrossRef]

Comput. Graph. Image Process. (1)

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

Comput. Vis. Image Underst. (1)

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

IEEE Trans. Pattern Anal. Mach. Intell. (3)

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 four-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. PAMI-3, 661–669 (1981).
[CrossRef]

Image Vis. 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 Vis. Comput. 25, 1050–1057 (2007).
[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).
[CrossRef]

J. Opt. Soc. Am. A (1)

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).
[CrossRef]

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, 66–73 (2003).
[CrossRef]

Other (14)

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

O. Faugeras, Three-Dimensional Computer Vision: A Geometric View-Point (Cambridge University, 1995).

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

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).

J. Lambert, Photometria (Augsburg, 1760).

B. K. P. Horn, Robot Vision (Massachusetts Institute of Technology, 1986).

S. Mann and R. W. Picard, “Being ‘undigital’ with digital cameras: extending dynamic range by combining differently exposed pictures,” in Proceedings of IS&T 48th Annual Conference (IS&T, 1995), pp. 422–428.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1997), pp. 369–378.

T. Mitsunaga and S. K. Nayar, “Radiometric self calibration,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), p. 374.

M. D. Grossberg and S. K. Nayar, “High dynamic range from multiple images: which exposures to combine?,” in Proceeding of IEEE Workshop on Color and Photometric Methods in Computer Vision (IEEE, 2003).

ISO 25178-2:2012, “Geometrical product specifications (GPS)—surface texture: areal—part 2: terms, definitions and surface texture parameters,” http://www.iso.org/iso/home/store/catalogue_tc/catalogue_detail.htm?csnumber=42785 (2012).

B. Muralikrishnan and J. Raja, Computational Surface and Roundness Metrology (Springer, 2008).

N. Alldrin, T. Zickler, and D. Kriegman, “Photometric stereo with non-parametric and spatially-varying reflectance,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, “Shape and spatially-varying BRDFs from photometric stereo,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 2005), pp. 341–348.

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