Abstract

A 3D scanner, based on incoherent illumination techniques, and associated data-processing algorithms are presented that can be used to scan objects at lateral resolutions ranging from 5 to 100  μm (or more) and depth resolutions of approximately 2   μm. The scanner was designed with the specific intent to scan cuneiform tablets but can be utilized for other applications. Photometric stereo techniques are used to obtain both a surface normal map and a parameterized model of the object's bidirectional reflectance distribution function. The normal map is combined with height information, gathered by structured light techniques, to form a consistent 3D surface. Data from Lambertian and specularly diffuse spherical objects are presented and used to quantify the accuracy of the techniques. Scans of a cuneiform tablet are also presented. All presented data are at a lateral resolution of 26.8  μm as this is approximately the minimum resolution deemed necessary to accurately represent cuneiform.

© 2007 Optical Society of America

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  1. S. Kumar, D. Snyder, D. Duncan, J. Cohen, and J. Cooper, "Digital preservation of ancient cuneiform tablets using 3D-scanning," in Proceedings of IEEE Fourth International Conference on 3D Digital Imaging and Modeling (IEEE, 2003), pp. 326-333.
  2. S. E. Anderson and M. Levoy, "Unwrapping and visualizing cuneiform tablets," IEEE Comput. Graphics Appl. 22, 82-88 (2002).
    [CrossRef]
  3. S. I. Woolley, N. J. Flowers, T. N. Arvanitis, A. Livingstone, T. R. Davis, and J. Ellison, "3D capture, representation, and manipulation of cuneiform tablets," in Three-Dimensional Image Capture and Applications IV, Proc. SPIE 4298, 103-110 (2001).
    [CrossRef]
  4. D. V. Hahn, D. D. Duncan, K. C. Baldwin, J. D. Cohen, and B. Purnomo, "Digital Hammurabi: design and development of a 3D scanner for cuneiform tablets," in Three-Dimensional Image Capture and Applications VII, Proc. SPIE 6056, 60560E-1-12 (2006).
  5. "Cuneiform Digital Library Initiative," http://cdli.ucla.edu.
  6. J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.
  7. N. Demoli, H. Gruber, U. Dahms, and G. Wernicke, "Characterization of the cuneiform signs by the use of a multifunctional optoelectronic device," Appl. Opt. 35, 5811-5820 (1996).
    [CrossRef] [PubMed]
  8. F. Dreesen, H. Delere, and G. von Bally, "High-resolution color holography for archaeological and medical applications," in Optics and Lasers in Biomedicine and Culture, Optics within Life Sciences V, C. Fotakis, T. Papazoglou, and C. Kalpouzos, eds. (Springer, 2000), pp. 349-352.
    [CrossRef]
  9. Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, "Deformation measurement by phase-shifting digital holography," Exp. Mech. 45, 65-70 (2005).
    [CrossRef]
  10. R. J. Woodham, "Photometric method for determining surface orientation from multiple images," Opt. Eng. 19, 139-144 (1980).
  11. J. Pan, P. S. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44, 23606-1-9 (2005).
    [CrossRef]
  12. G. Sansoni, M. Carocci, and R. Rodella, "Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors," Appl. Opt. 38, 6565-6573 (1999).
    [CrossRef]
  13. D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, "Shape and spatially-varying BRDF's from photometric stereo," in Proceedings of the Tenth IEEE International Conference on Computer Vision (IEEE, 2000), pp. 341-348.
  14. C. Buil, CCD Astronomy (Willmann-Bell, Inc., 1991).
  15. G. J. Ward, "Measuring and modeling anisotropic reflection," Comput. Graph. 26, 265-272 (1992).
    [CrossRef]
  16. R. Klette and K. Schlüns, "Height data from gradient fields," in Machine Vision Applications, Architectures, and Systems Integration V, Proc. SPIE 2908, pp. 204-215 (1996).
    [CrossRef]
  17. W. Tan, Y. Wang, Y. Chen, and B. Xu, "Shape and reflectance recovery based on a photometric stereo approach," in Proceeding 426 Computer Graphics and Imaging, M.H.Hamza, ed. (2004), pp. 350-354.
  18. S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601-1-8 (2006).
    [CrossRef]
  19. K. J. Gåsvik, Optical Metrology, 2nd ed. (Wiley, 1995), pp. 254-260.
  20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, 1996).
  21. Q. Kemao, S. Fangjun, and W. Xiaoping, "Determination of the best phase step of the Carré algorithm in phase shifting interferometry," Meas. Sci. Technol. 11, 1220-1223 (2000).
    [CrossRef]
  22. D. J. Smith and A. G. Bors, "Height estimation from vector fields of surface normals," in Proceedings of IEEE 14th International Conference on Digital Signal Processing (IEEE, 2002), pp. 1031-1034.
  23. J. D. Barchers, D. J. Fried, and J. D. Link, "Evaluation of the performance of Hartman sensors in strong scintillation," Appl. Opt. 41, 1012-1021 (2002).
    [CrossRef] [PubMed]
  24. J. Cooper, Professor, Department of Near Eastern Studies, Johns Hopkins University, 3400 N. Charles St., Baltimore, Md. 21218 (personal communication, 2005).
  25. D. Snyder, Manager, Digital Hammurabi Project, Computer Science Department, Johns Hopkins University, 3400 N. Charles St., Baltimore, Md. 21218 (personal communication, 2005).

2006

D. V. Hahn, D. D. Duncan, K. C. Baldwin, J. D. Cohen, and B. Purnomo, "Digital Hammurabi: design and development of a 3D scanner for cuneiform tablets," in Three-Dimensional Image Capture and Applications VII, Proc. SPIE 6056, 60560E-1-12 (2006).

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601-1-8 (2006).
[CrossRef]

2005

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, "Deformation measurement by phase-shifting digital holography," Exp. Mech. 45, 65-70 (2005).
[CrossRef]

J. Pan, P. S. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44, 23606-1-9 (2005).
[CrossRef]

2002

J. D. Barchers, D. J. Fried, and J. D. Link, "Evaluation of the performance of Hartman sensors in strong scintillation," Appl. Opt. 41, 1012-1021 (2002).
[CrossRef] [PubMed]

S. E. Anderson and M. Levoy, "Unwrapping and visualizing cuneiform tablets," IEEE Comput. Graphics Appl. 22, 82-88 (2002).
[CrossRef]

2001

S. I. Woolley, N. J. Flowers, T. N. Arvanitis, A. Livingstone, T. R. Davis, and J. Ellison, "3D capture, representation, and manipulation of cuneiform tablets," in Three-Dimensional Image Capture and Applications IV, Proc. SPIE 4298, 103-110 (2001).
[CrossRef]

2000

Q. Kemao, S. Fangjun, and W. Xiaoping, "Determination of the best phase step of the Carré algorithm in phase shifting interferometry," Meas. Sci. Technol. 11, 1220-1223 (2000).
[CrossRef]

1999

1996

N. Demoli, H. Gruber, U. Dahms, and G. Wernicke, "Characterization of the cuneiform signs by the use of a multifunctional optoelectronic device," Appl. Opt. 35, 5811-5820 (1996).
[CrossRef] [PubMed]

R. Klette and K. Schlüns, "Height data from gradient fields," in Machine Vision Applications, Architectures, and Systems Integration V, Proc. SPIE 2908, pp. 204-215 (1996).
[CrossRef]

1992

G. J. Ward, "Measuring and modeling anisotropic reflection," Comput. Graph. 26, 265-272 (1992).
[CrossRef]

1980

R. J. Woodham, "Photometric method for determining surface orientation from multiple images," Opt. Eng. 19, 139-144 (1980).

Anderson, S. E.

S. E. Anderson and M. Levoy, "Unwrapping and visualizing cuneiform tablets," IEEE Comput. Graphics Appl. 22, 82-88 (2002).
[CrossRef]

Arvanitis, T. N.

S. I. Woolley, N. J. Flowers, T. N. Arvanitis, A. Livingstone, T. R. Davis, and J. Ellison, "3D capture, representation, and manipulation of cuneiform tablets," in Three-Dimensional Image Capture and Applications IV, Proc. SPIE 4298, 103-110 (2001).
[CrossRef]

Baldwin, K. C.

D. V. Hahn, D. D. Duncan, K. C. Baldwin, J. D. Cohen, and B. Purnomo, "Digital Hammurabi: design and development of a 3D scanner for cuneiform tablets," in Three-Dimensional Image Capture and Applications VII, Proc. SPIE 6056, 60560E-1-12 (2006).

Barchers, J. D.

Bors, A. G.

D. J. Smith and A. G. Bors, "Height estimation from vector fields of surface normals," in Proceedings of IEEE 14th International Conference on Digital Signal Processing (IEEE, 2002), pp. 1031-1034.

Buil, C.

C. Buil, CCD Astronomy (Willmann-Bell, Inc., 1991).

Carocci, M.

Chen, Y.

W. Tan, Y. Wang, Y. Chen, and B. Xu, "Shape and reflectance recovery based on a photometric stereo approach," in Proceeding 426 Computer Graphics and Imaging, M.H.Hamza, ed. (2004), pp. 350-354.

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

Chiang, F.

J. Pan, P. S. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44, 23606-1-9 (2005).
[CrossRef]

Cohen, J.

S. Kumar, D. Snyder, D. Duncan, J. Cohen, and J. Cooper, "Digital preservation of ancient cuneiform tablets using 3D-scanning," in Proceedings of IEEE Fourth International Conference on 3D Digital Imaging and Modeling (IEEE, 2003), pp. 326-333.

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

Cohen, J. D.

D. V. Hahn, D. D. Duncan, K. C. Baldwin, J. D. Cohen, and B. Purnomo, "Digital Hammurabi: design and development of a 3D scanner for cuneiform tablets," in Three-Dimensional Image Capture and Applications VII, Proc. SPIE 6056, 60560E-1-12 (2006).

Cooper, J.

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

S. Kumar, D. Snyder, D. Duncan, J. Cohen, and J. Cooper, "Digital preservation of ancient cuneiform tablets using 3D-scanning," in Proceedings of IEEE Fourth International Conference on 3D Digital Imaging and Modeling (IEEE, 2003), pp. 326-333.

J. Cooper, Professor, Department of Near Eastern Studies, Johns Hopkins University, 3400 N. Charles St., Baltimore, Md. 21218 (personal communication, 2005).

Curless, B.

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, "Shape and spatially-varying BRDF's from photometric stereo," in Proceedings of the Tenth IEEE International Conference on Computer Vision (IEEE, 2000), pp. 341-348.

Dahms, U.

Davis, T. R.

S. I. Woolley, N. J. Flowers, T. N. Arvanitis, A. Livingstone, T. R. Davis, and J. Ellison, "3D capture, representation, and manipulation of cuneiform tablets," in Three-Dimensional Image Capture and Applications IV, Proc. SPIE 4298, 103-110 (2001).
[CrossRef]

Delere, H.

F. Dreesen, H. Delere, and G. von Bally, "High-resolution color holography for archaeological and medical applications," in Optics and Lasers in Biomedicine and Culture, Optics within Life Sciences V, C. Fotakis, T. Papazoglou, and C. Kalpouzos, eds. (Springer, 2000), pp. 349-352.
[CrossRef]

Demoli, N.

Dreesen, F.

F. Dreesen, H. Delere, and G. von Bally, "High-resolution color holography for archaeological and medical applications," in Optics and Lasers in Biomedicine and Culture, Optics within Life Sciences V, C. Fotakis, T. Papazoglou, and C. Kalpouzos, eds. (Springer, 2000), pp. 349-352.
[CrossRef]

Duncan, D.

S. Kumar, D. Snyder, D. Duncan, J. Cohen, and J. Cooper, "Digital preservation of ancient cuneiform tablets using 3D-scanning," in Proceedings of IEEE Fourth International Conference on 3D Digital Imaging and Modeling (IEEE, 2003), pp. 326-333.

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

Duncan, D. D.

D. V. Hahn, D. D. Duncan, K. C. Baldwin, J. D. Cohen, and B. Purnomo, "Digital Hammurabi: design and development of a 3D scanner for cuneiform tablets," in Three-Dimensional Image Capture and Applications VII, Proc. SPIE 6056, 60560E-1-12 (2006).

Ellison, J.

S. I. Woolley, N. J. Flowers, T. N. Arvanitis, A. Livingstone, T. R. Davis, and J. Ellison, "3D capture, representation, and manipulation of cuneiform tablets," in Three-Dimensional Image Capture and Applications IV, Proc. SPIE 4298, 103-110 (2001).
[CrossRef]

Fangjun, S.

Q. Kemao, S. Fangjun, and W. Xiaoping, "Determination of the best phase step of the Carré algorithm in phase shifting interferometry," Meas. Sci. Technol. 11, 1220-1223 (2000).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, 1996).

Flowers, N. J.

S. I. Woolley, N. J. Flowers, T. N. Arvanitis, A. Livingstone, T. R. Davis, and J. Ellison, "3D capture, representation, and manipulation of cuneiform tablets," in Three-Dimensional Image Capture and Applications IV, Proc. SPIE 4298, 103-110 (2001).
[CrossRef]

Fried, D. J.

Fujigaki, M.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, "Deformation measurement by phase-shifting digital holography," Exp. Mech. 45, 65-70 (2005).
[CrossRef]

Gåsvik, K. J.

K. J. Gåsvik, Optical Metrology, 2nd ed. (Wiley, 1995), pp. 254-260.

Goldman, D. B.

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, "Shape and spatially-varying BRDF's from photometric stereo," in Proceedings of the Tenth IEEE International Conference on Computer Vision (IEEE, 2000), pp. 341-348.

Graettinger, J.

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

Gruber, H.

Hahn, D.

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

Hahn, D. V.

D. V. Hahn, D. D. Duncan, K. C. Baldwin, J. D. Cohen, and B. Purnomo, "Digital Hammurabi: design and development of a 3D scanner for cuneiform tablets," in Three-Dimensional Image Capture and Applications VII, Proc. SPIE 6056, 60560E-1-12 (2006).

Hertzmann, A.

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, "Shape and spatially-varying BRDF's from photometric stereo," in Proceedings of the Tenth IEEE International Conference on Computer Vision (IEEE, 2000), pp. 341-348.

Huang, P. S.

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601-1-8 (2006).
[CrossRef]

J. Pan, P. S. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44, 23606-1-9 (2005).
[CrossRef]

Kemao, Q.

Q. Kemao, S. Fangjun, and W. Xiaoping, "Determination of the best phase step of the Carré algorithm in phase shifting interferometry," Meas. Sci. Technol. 11, 1220-1223 (2000).
[CrossRef]

Klette, R.

R. Klette and K. Schlüns, "Height data from gradient fields," in Machine Vision Applications, Architectures, and Systems Integration V, Proc. SPIE 2908, pp. 204-215 (1996).
[CrossRef]

Kumar, S.

S. Kumar, D. Snyder, D. Duncan, J. Cohen, and J. Cooper, "Digital preservation of ancient cuneiform tablets using 3D-scanning," in Proceedings of IEEE Fourth International Conference on 3D Digital Imaging and Modeling (IEEE, 2003), pp. 326-333.

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

Levoy, M.

S. E. Anderson and M. Levoy, "Unwrapping and visualizing cuneiform tablets," IEEE Comput. Graphics Appl. 22, 82-88 (2002).
[CrossRef]

Link, J. D.

Livingstone, A.

S. I. Woolley, N. J. Flowers, T. N. Arvanitis, A. Livingstone, T. R. Davis, and J. Ellison, "3D capture, representation, and manipulation of cuneiform tablets," in Three-Dimensional Image Capture and Applications IV, Proc. SPIE 4298, 103-110 (2001).
[CrossRef]

Morimoto, Y.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, "Deformation measurement by phase-shifting digital holography," Exp. Mech. 45, 65-70 (2005).
[CrossRef]

Nomura, T.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, "Deformation measurement by phase-shifting digital holography," Exp. Mech. 45, 65-70 (2005).
[CrossRef]

Pan, J.

J. Pan, P. S. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44, 23606-1-9 (2005).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, 1996).

Purnomo, B.

D. V. Hahn, D. D. Duncan, K. C. Baldwin, J. D. Cohen, and B. Purnomo, "Digital Hammurabi: design and development of a 3D scanner for cuneiform tablets," in Three-Dimensional Image Capture and Applications VII, Proc. SPIE 6056, 60560E-1-12 (2006).

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

Rodella, R.

Sansoni, G.

Schlüns, K.

R. Klette and K. Schlüns, "Height data from gradient fields," in Machine Vision Applications, Architectures, and Systems Integration V, Proc. SPIE 2908, pp. 204-215 (1996).
[CrossRef]

Seitz, S. M.

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, "Shape and spatially-varying BRDF's from photometric stereo," in Proceedings of the Tenth IEEE International Conference on Computer Vision (IEEE, 2000), pp. 341-348.

Smith, D. J.

D. J. Smith and A. G. Bors, "Height estimation from vector fields of surface normals," in Proceedings of IEEE 14th International Conference on Digital Signal Processing (IEEE, 2002), pp. 1031-1034.

Snyder, D.

S. Kumar, D. Snyder, D. Duncan, J. Cohen, and J. Cooper, "Digital preservation of ancient cuneiform tablets using 3D-scanning," in Proceedings of IEEE Fourth International Conference on 3D Digital Imaging and Modeling (IEEE, 2003), pp. 326-333.

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

D. Snyder, Manager, Digital Hammurabi Project, Computer Science Department, Johns Hopkins University, 3400 N. Charles St., Baltimore, Md. 21218 (personal communication, 2005).

Takahashi, I.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, "Deformation measurement by phase-shifting digital holography," Exp. Mech. 45, 65-70 (2005).
[CrossRef]

Tan, W.

W. Tan, Y. Wang, Y. Chen, and B. Xu, "Shape and reflectance recovery based on a photometric stereo approach," in Proceeding 426 Computer Graphics and Imaging, M.H.Hamza, ed. (2004), pp. 350-354.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, 1996).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, 1996).

von Bally, G.

F. Dreesen, H. Delere, and G. von Bally, "High-resolution color holography for archaeological and medical applications," in Optics and Lasers in Biomedicine and Culture, Optics within Life Sciences V, C. Fotakis, T. Papazoglou, and C. Kalpouzos, eds. (Springer, 2000), pp. 349-352.
[CrossRef]

Wang, Y.

W. Tan, Y. Wang, Y. Chen, and B. Xu, "Shape and reflectance recovery based on a photometric stereo approach," in Proceeding 426 Computer Graphics and Imaging, M.H.Hamza, ed. (2004), pp. 350-354.

Ward, G. J.

G. J. Ward, "Measuring and modeling anisotropic reflection," Comput. Graph. 26, 265-272 (1992).
[CrossRef]

Wernicke, G.

Woodham, R. J.

R. J. Woodham, "Photometric method for determining surface orientation from multiple images," Opt. Eng. 19, 139-144 (1980).

Woolley, S. I.

S. I. Woolley, N. J. Flowers, T. N. Arvanitis, A. Livingstone, T. R. Davis, and J. Ellison, "3D capture, representation, and manipulation of cuneiform tablets," in Three-Dimensional Image Capture and Applications IV, Proc. SPIE 4298, 103-110 (2001).
[CrossRef]

Xiaoping, W.

Q. Kemao, S. Fangjun, and W. Xiaoping, "Determination of the best phase step of the Carré algorithm in phase shifting interferometry," Meas. Sci. Technol. 11, 1220-1223 (2000).
[CrossRef]

Xu, B.

W. Tan, Y. Wang, Y. Chen, and B. Xu, "Shape and reflectance recovery based on a photometric stereo approach," in Proceeding 426 Computer Graphics and Imaging, M.H.Hamza, ed. (2004), pp. 350-354.

Yoneyama, S.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, "Deformation measurement by phase-shifting digital holography," Exp. Mech. 45, 65-70 (2005).
[CrossRef]

Zhang, S.

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601-1-8 (2006).
[CrossRef]

Appl. Opt.

Comput. Graph.

G. J. Ward, "Measuring and modeling anisotropic reflection," Comput. Graph. 26, 265-272 (1992).
[CrossRef]

Exp. Mech.

Y. Morimoto, T. Nomura, M. Fujigaki, S. Yoneyama, and I. Takahashi, "Deformation measurement by phase-shifting digital holography," Exp. Mech. 45, 65-70 (2005).
[CrossRef]

IEEE Comput. Graphics Appl.

S. E. Anderson and M. Levoy, "Unwrapping and visualizing cuneiform tablets," IEEE Comput. Graphics Appl. 22, 82-88 (2002).
[CrossRef]

Meas. Sci. Technol.

Q. Kemao, S. Fangjun, and W. Xiaoping, "Determination of the best phase step of the Carré algorithm in phase shifting interferometry," Meas. Sci. Technol. 11, 1220-1223 (2000).
[CrossRef]

Opt. Eng.

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601-1-8 (2006).
[CrossRef]

R. J. Woodham, "Photometric method for determining surface orientation from multiple images," Opt. Eng. 19, 139-144 (1980).

J. Pan, P. S. Huang, and F. Chiang, "Color-coded binary fringe projection technique for 3-D shape measurement," Opt. Eng. 44, 23606-1-9 (2005).
[CrossRef]

Proc. SPIE

S. I. Woolley, N. J. Flowers, T. N. Arvanitis, A. Livingstone, T. R. Davis, and J. Ellison, "3D capture, representation, and manipulation of cuneiform tablets," in Three-Dimensional Image Capture and Applications IV, Proc. SPIE 4298, 103-110 (2001).
[CrossRef]

D. V. Hahn, D. D. Duncan, K. C. Baldwin, J. D. Cohen, and B. Purnomo, "Digital Hammurabi: design and development of a 3D scanner for cuneiform tablets," in Three-Dimensional Image Capture and Applications VII, Proc. SPIE 6056, 60560E-1-12 (2006).

R. Klette and K. Schlüns, "Height data from gradient fields," in Machine Vision Applications, Architectures, and Systems Integration V, Proc. SPIE 2908, pp. 204-215 (1996).
[CrossRef]

Other

W. Tan, Y. Wang, Y. Chen, and B. Xu, "Shape and reflectance recovery based on a photometric stereo approach," in Proceeding 426 Computer Graphics and Imaging, M.H.Hamza, ed. (2004), pp. 350-354.

K. J. Gåsvik, Optical Metrology, 2nd ed. (Wiley, 1995), pp. 254-260.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, 1996).

D. J. Smith and A. G. Bors, "Height estimation from vector fields of surface normals," in Proceedings of IEEE 14th International Conference on Digital Signal Processing (IEEE, 2002), pp. 1031-1034.

J. Cooper, Professor, Department of Near Eastern Studies, Johns Hopkins University, 3400 N. Charles St., Baltimore, Md. 21218 (personal communication, 2005).

D. Snyder, Manager, Digital Hammurabi Project, Computer Science Department, Johns Hopkins University, 3400 N. Charles St., Baltimore, Md. 21218 (personal communication, 2005).

"Cuneiform Digital Library Initiative," http://cdli.ucla.edu.

J. Cohen, D. Duncan, D. Snyder, J. Cooper, S. Kumar, D. Hahn, Y. Chen, B. Purnomo, and J. Graettinger, "iClay: digitizing cuneiform," in Proceedings of the Fifth International Symposium on Virtual Reality, Archaeology, and Cultural Heritage (2004), pp. 135-143.

F. Dreesen, H. Delere, and G. von Bally, "High-resolution color holography for archaeological and medical applications," in Optics and Lasers in Biomedicine and Culture, Optics within Life Sciences V, C. Fotakis, T. Papazoglou, and C. Kalpouzos, eds. (Springer, 2000), pp. 349-352.
[CrossRef]

D. B. Goldman, B. Curless, A. Hertzmann, and S. M. Seitz, "Shape and spatially-varying BRDF's from photometric stereo," in Proceedings of the Tenth IEEE International Conference on Computer Vision (IEEE, 2000), pp. 341-348.

C. Buil, CCD Astronomy (Willmann-Bell, Inc., 1991).

S. Kumar, D. Snyder, D. Duncan, J. Cohen, and J. Cooper, "Digital preservation of ancient cuneiform tablets using 3D-scanning," in Proceedings of IEEE Fourth International Conference on 3D Digital Imaging and Modeling (IEEE, 2003), pp. 326-333.

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Figures (12)

Fig. 1
Fig. 1

Scanner design (Ref. [4]).

Fig. 2
Fig. 2

Scanner operation.

Fig. 3
Fig. 3

Z components of the surface normals of (a) a mouseball and (b) painted ball bearing resulting from photometric stereo analysis. The solid curve represents the initial guess assuming a Lambertian BRDF, the dotted curve the final normal map after BRDF parameter optimization, and the dashed curve the theoretical normal map assuming perfect spheres of the appropriate radii.

Fig. 4
Fig. 4

Reflectance profiles of a cut through the center of a sphere plotted against the zenith angle of the sphere's surface. The view direction is directly overhead the sphere and the incident illumination at a zenith angle of 35.8°. The diamonds represent the reflectance profile given the BRDF of the mouseball, the squares the BRDF of the painted ball bearing, and the solid and dashed curves Lambertian BRDFs of 0.85 and 0.22 reflectance, respectively. The latter Lambertian BRDF is in fact the Lambertian component of the BRDF of the ball bearing.

Fig. 5
Fig. 5

Height profile of a cut through the center of the mouseball compared to that of a perfect sphere of like radius. The solid curve and diamonds are the final surface height and structured light height of the mouseball (not all points plotted to reduce clutter), respectively, while the dashed curve represents the surface of a perfect sphere.

Fig. 6
Fig. 6

Histogram of the angular difference between the surface normals of the mouseball and those of a perfect sphere of like radius.

Fig. 7
Fig. 7

(Color online) A small cuneiform tablet (test specimen T24) compared to the size of a U.S. quarter.

Fig. 8
Fig. 8

Meshed surface maps of a 2 .68   mm × 2 .68   mm cross section of the T24 tablet showing (left) the structured light height and (right) the final surface.

Fig. 9
Fig. 9

x (top) and y components (bottom) of the normal vectors over a 2 .68   mm × 2 .68   mm cross section of the T24 tablet (left) as measured by the photometric stereo method and (right) computed from the final surface.

Fig. 10
Fig. 10

Height profiles of the T24 tablet. Circles represent the structured light height map. A local integration of the normal data is shown with squares. The stars are the final surface (10 iterations).

Fig. 11
Fig. 11

(a) Photograph and (b) rendering of the T24 tablet (Ref. [4]) from approximately the same view direction.

Fig. 12
Fig. 12

Rendering of the T24 tablet (Ref. [4]) from approximately the same view direction as the photograph in Fig. 7. The distance from the top to the bottom of this rendering is approximately the diameter of a U.S. quarter.

Equations (85)

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100   μm
2   μm
26.8   μm
50   μm
50   μm
25   μm
3   μm
5   μm
2   μm
5   μm
( x , y )
I ¯ = Q N̿ n ¯ ,
N̿
n ¯
( x , y )
[ I 1 I K ] = Q [ sin ( θ ) sin ( ϕ 1 ) sin ( θ ) cos ( ϕ 1 ) cos ( θ ) sin ( θ ) sin ( ϕ K ) sin ( θ ) cos ( ϕ K ) cos ( θ ) ] × [ n x n y n z ] ,
Q n ¯ = [ ( N̿ T N̿ ) 1 N̿ T ] I ¯ .
ρ ( θ i , θ r ) = ρ L π + ρ s cos ( θ i ) cos ( θ r ) exp ( tan 2 ( δ ) / β 2 ) 4 π β 2 ,
ρ L
ρ s
θ i
θ r
L ¯
V ¯
h ¯ = ( L ¯ + V ¯ ) / L ¯ + V ¯
ψ = k , p [ I k , p f ( n p ¯ , L k ¯ , ρ L , ρ s , β ) ] 2 ,
I k , p
f ( n p ¯ , L k ¯ , ρ L , ρ s , β )
( x , y )
φ = tan 1 [ ( I 1 I 4 + I 2 I 3 ) [ 3 ( I 2 I 3 ) ( I 1 I 4 ) ] I 2 + I 3 I 1 I 4 ] ,
I x
sin ( φ )
cos ( φ )
I 2 I 3 sin ( φ ) ,
I 2 + I 3 I 1 I 4 cos ( φ ) .
( ± n 2 π )
± n 2 π
h n + 1 ( x , y ) = h n ( x , y ) + { [ 1 λ ( x , y ) ] δ h P ( x , y ) + λ ( x , y ) δ h S L ( x , y ) } .
δ h S L
h S L
δ h S L ( x , y ) = h S L ( x , y ) h n ( x , y ) ,
[ 0 , 0.5 ]
λ ( x , y ) = { ( δ h S L ( x , y ) / χ ) 2 / 2 ; δ h S L ( x , y ) < χ 1 / 2 ; otherwise ;
δ h P
δ h P ( x , y ) = χ 4 [ δ S x ( x 1 , y ) δ S x ( x + 1 , y ) + δ S y ( x , y 1 ) δ S y ( x , y + 1 ) ] ,
δ S ¯
δ S ¯ ( x , y ) = S ¯ ( x , y ) S ¯ P ( x , y ) .
S ¯
S x ( x , y ) = h n ( x 1 , y ) h n ( x + 1 , y ) 2 χ ;
S y ( x , y ) = h n ( x , y 1 ) h n ( x , y + 1 ) 2 χ ,
S ¯ P
S ¯ P ( x , y ) = n x ( x , y ) n z ( x , y ) x ^ n y ( x , y ) n z ( x , y ) y ^ .
h 0
4 × 4
χ / 100
C ¯
  C ¯ = Q × [ C R C G C B ] | [ C R C G C B ] | ,   where
C X = ϕ ( background   corrected   r , g ,   or   b   color   images ) .
6.7   μm
4 ×
26.8   μm
0.6   mm
5   μm
5   μm
( 1 × )
22.7   mm
12 .7   mm
11   mm
22   mm
0 .2   mm
67   μm
85   μm
0 .2   mm
59   μm
76   μm
50   μm
2 .68   mm × 2 .68   mm
( 100 × 100   pixels )
2   mm × 2   mm
2   μm
50   μm
100   μm
2   μm
2 .68   mm × 2 .68   mm
2 .68   mm × 2 .68   mm

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