Abstract

We address the problem of simultaneous estimation of scene structure and restoration of images from blurred photometric measurements. In photometric stereo, the structure of an object is determined by using a particular reflectance model (the image irradiance equation) without considering the blurring effect. What we show is that, given arbitrarily blurred observations of a static scene captured with a stationary camera under different illuminant directions, we still can obtain the structure represented by the surface gradients and the albedo and also perform a blind image restoration. The surface gradients and the albedo are modeled as separate Markov random fields, and a suitable regularization scheme is used to estimate the different fields as well as the blur parameter. The results of the experimentations are illustrated with real as well as synthetic images.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. K. P. Horn, “Shape from shading: a method for obtaining the shape of a smooth opaque object from one view,” Ph.D. thesis (Massachussetts Institute of Technology, Cambridge, Mass., 1970).
  2. K. Ikeuchi, B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artif. Intell. 17, 141–184 (1981).
    [CrossRef]
  3. A. P. Pentland, “Local shading analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 170–187 (1984).
    [CrossRef] [PubMed]
  4. A. P. Pentland, “Shape information from shading: a theory about human perception,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1988), pp. 404–413.
  5. P. S. Tsai, M. Shah, “Shape from shading using linear approximation,” Image Vis. Comput. 12, 487–498 (1994).
    [CrossRef]
  6. R. J. Woodham, “Reflectance map techniques for analyzing surface defects in metal castings,” Tech. Rep. 457 (MIT Artificial Intelligence Laboratory, Cambridge, Mass., 1978).
  7. R. J. Woodham, “Photometric method for determining surface orientation from multiple images,” Opt. Eng. (Bellingham) 19, 139–144 (1980).
    [CrossRef]
  8. K. Ikeuchi, “Determining surface orientations of specular surfaces by using the photometric stereo method,” IEEE Trans. Pattern Anal. Mach. Intell. 3, 661–669 (1981).
    [CrossRef] [PubMed]
  9. W. M. Silver, “Determining shape and reflectance using multiple images,” M.S. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1980).
  10. K. M. Lee, C. C. Jay Kuo, “Shape reconstruction from photometric stereo,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1992), pp. 479–484.
  11. C. Y. Chen, R. Klette, R. Kakarala, “Albedo recovery using a photometric stereo approach,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 700–703.
  12. Y. Iwahori, R. J. Woodham, M. Ozaki, H. Tanaka, N. Ishi, “Neural network based photometric stereo with a nearby rotational moving light source,” IEICE Trans. Inf. Syst. E-80-D, 948–957 (1997).
  13. Y. Iwahori, R. J. Woodhan, A. Bagheri, “Principal component analysis and neural network implementation of Photometric Stereo,” in Proceedings of the Workshop on Physics based Modeling in Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 117–125.
  14. R. J. Woodham, “Gradient and curvature from the photometric stereo method including local confidence estimation,” J. Opt. Soc. Am. A 11, 3050–3068 (1994).
    [CrossRef]
  15. Y. Iwahori, R. J. Woodham, Y. Watanabe, A. Iwata, “Self calibration and neural network implementation of photometric stereo,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 359–362.
  16. O. Drbohlav, R. Sara, “Unambiguous determination of shape from photometric stereo with unknown light sources,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 2001), pp. 581–586.
  17. R. Basri, D. Jacobs, “Photometric stereo with general unknown lighting,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2001), pp. 374–381.
  18. U. Sakarya, I. Erkmen, “An improved method of photometric stereo using local shape from shading,” Image Vis. Comput. 21, 941–954 (2003).
    [CrossRef]
  19. J. J. Clark, “Active photometric stereo,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1992), pp. 29–34.
  20. J. R. A. Torreao, “A new approach to photometric stereo,” Pattern Recogn. Lett. 20, 535–540 (1999).
    [CrossRef]
  21. G. McGunnigle, M. J. Chantler, “Rotation invariant classification of rough surfaces,” IEE Proc. Vision Image Signal Process. 146, 345–352 (1999).
    [CrossRef]
  22. G. McGunnigle, M. J. Chantler, “Rough surface classification using point statistics from photometric stereo,” Protein Eng. 21, 593–604 (2000).
  23. G. McGunnigle, M. J. Chantler, “Modelling deposition of surface texture,” Electron. Lett. 37, 749–750 (2001).
    [CrossRef]
  24. M. L. Smith, T. Hill, G. Smith, “Gradient space analysis of surface defects using a photometric stereo derived bump map,” Image Vis. Comput. 17, 321–332 (1999).
    [CrossRef]
  25. P. Hansson, P. Johansson, “Topography and reflectance analysis of paper surfaces using photometric stereo method,” Opt. Eng. (Bellingham) 39, 2555–2561 (2000).
    [CrossRef]
  26. G. McGunnigle, M. J. Chantler, “Segmentation of machined surfaces,” presented at the Irish Machine Vision and Image Processing Conference, Maynooth, Ireland, September, 2001.
  27. M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag. Vol. 14 (2) 1997, pp. 24–41.
    [CrossRef]
  28. D. Rajan, S. Chaudhuri, “Simultaneous estimation of super-resolved scene and depth map from low resolution defocused observations,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1102–1117 (2003).
    [CrossRef]
  29. A. N. Rajagopalan, S. Chaudhuri, “An MRF model based approach to simultaneous recovery of depth and restoration from defocused images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 577–589 (1999).
    [CrossRef]
  30. D. Kundur, D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. March 1996, pp. 43–64.
  31. Y. You, M. Kaveh, “A regularization approach to joint blind identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
    [CrossRef]
  32. R. L. Lagendijk, J. Biemond, Iterative Identification and Restoration of Images, (Kluwer Academic, Boston, Mass., 2001).
  33. R. L. Lagendijk, J. Biemond, D. E. Boekee, “Identification and restoration of noisy blurred images using the expectation maximization algorithm,” IEEE Trans. Acoust., Speech, Signal Process. 38, 1180–1191 (1990).
    [CrossRef]
  34. K. T. Lay, A. K. Katsaggelos, “Image identification and restoration based on the expectation maximization algorithm,” Opt. Eng. (Bellingham) 29, 436–445 (1990).
    [CrossRef]
  35. M. K. Ozkan, A. M. Tekalp, M. I. Sezan, “POCS based restoration of space varying blurred images,” IEEE Trans. Image Process. 3, 450–454 (1995).
    [CrossRef]
  36. M. I. Sezan, A. M. Tekalp, “Iterative image restoration with ringing suppression using POCS,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE Press, Piscataway, N.J., 1988), pp. 1300–1303.
  37. M. I. Sezan, H. J. Trussell, “Prototype image constraints for set theoretic image restoration,” IEEE Trans. Signal Process. 39, 2275–2285 (1991).
    [CrossRef]
  38. H. J. Trussell, M. R. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust., Speech, Signal Process. 32, 201–212 (1984).
    [CrossRef]
  39. Y. Yang, N. P. Galatsanos, A. K. Katsaggelos, “Projection-based spatially adaptive reconstruction of block-transform compressed images,” IEEE Trans. Image Process. 4, 896–908 (1995).
    [CrossRef] [PubMed]
  40. V. F. Candela, A. Marquina, S. Serna, “A local spectral inversion of a linearized TV model for denoising and deblurring,” IEEE Trans. Image Process. 12, 808–816 (2003).
    [CrossRef]
  41. B. Besserer, L. Joyeux, S. Boukir, O. Buisson, “Reconstruction of degraded image sequences. Application to film restoration,” Image Vis. Comput. 19, 503–516 (2001).
    [CrossRef]
  42. L. Bedini, A. Tonazzini, S. Minutoli, “Unsupervised edge-preserving image restoration via a saddle point approximation,” Image Vis. Comput. 17, 779–793 (1999).
    [CrossRef]
  43. B. K. P. Horn, Robot Vision (MIT Press, Cambridge, Mass., 1986).
  44. S. Chaudhuri, A. N. Rajagopalan, Depth From Defocus: A Real Aperture Imaging Approach (Springer-Verlag, New York, 1999).
  45. R. C. Dubes, A. K. Jain, “Random field models in image analysis,” J. Appl. Statistics 16, 131–164 (1989).
    [CrossRef]
  46. J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. Ser. B. Methodol. 36, 192–236 (1974).
  47. M. Subbarao, “Parallel depth recovery by changing camera parameters,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1998), pp. 149–155.
  48. T. F. Chan, C. K. Wong, “Convergence of the alternating minimization algorithm for blind deconvolution,” Tech. Rep. 19, UCLA Computational and Applied Mathematics Series (University of California, Los Angeles, Calif., 1999).

2003 (3)

U. Sakarya, I. Erkmen, “An improved method of photometric stereo using local shape from shading,” Image Vis. Comput. 21, 941–954 (2003).
[CrossRef]

D. Rajan, S. Chaudhuri, “Simultaneous estimation of super-resolved scene and depth map from low resolution defocused observations,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1102–1117 (2003).
[CrossRef]

V. F. Candela, A. Marquina, S. Serna, “A local spectral inversion of a linearized TV model for denoising and deblurring,” IEEE Trans. Image Process. 12, 808–816 (2003).
[CrossRef]

2001 (2)

B. Besserer, L. Joyeux, S. Boukir, O. Buisson, “Reconstruction of degraded image sequences. Application to film restoration,” Image Vis. Comput. 19, 503–516 (2001).
[CrossRef]

G. McGunnigle, M. J. Chantler, “Modelling deposition of surface texture,” Electron. Lett. 37, 749–750 (2001).
[CrossRef]

2000 (2)

P. Hansson, P. Johansson, “Topography and reflectance analysis of paper surfaces using photometric stereo method,” Opt. Eng. (Bellingham) 39, 2555–2561 (2000).
[CrossRef]

G. McGunnigle, M. J. Chantler, “Rough surface classification using point statistics from photometric stereo,” Protein Eng. 21, 593–604 (2000).

1999 (5)

L. Bedini, A. Tonazzini, S. Minutoli, “Unsupervised edge-preserving image restoration via a saddle point approximation,” Image Vis. Comput. 17, 779–793 (1999).
[CrossRef]

M. L. Smith, T. Hill, G. Smith, “Gradient space analysis of surface defects using a photometric stereo derived bump map,” Image Vis. Comput. 17, 321–332 (1999).
[CrossRef]

J. R. A. Torreao, “A new approach to photometric stereo,” Pattern Recogn. Lett. 20, 535–540 (1999).
[CrossRef]

G. McGunnigle, M. J. Chantler, “Rotation invariant classification of rough surfaces,” IEE Proc. Vision Image Signal Process. 146, 345–352 (1999).
[CrossRef]

A. N. Rajagopalan, S. Chaudhuri, “An MRF model based approach to simultaneous recovery of depth and restoration from defocused images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 577–589 (1999).
[CrossRef]

1997 (2)

M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag. Vol. 14 (2) 1997, pp. 24–41.
[CrossRef]

Y. Iwahori, R. J. Woodham, M. Ozaki, H. Tanaka, N. Ishi, “Neural network based photometric stereo with a nearby rotational moving light source,” IEICE Trans. Inf. Syst. E-80-D, 948–957 (1997).

1996 (1)

Y. You, M. Kaveh, “A regularization approach to joint blind identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef]

1995 (2)

M. K. Ozkan, A. M. Tekalp, M. I. Sezan, “POCS based restoration of space varying blurred images,” IEEE Trans. Image Process. 3, 450–454 (1995).
[CrossRef]

Y. Yang, N. P. Galatsanos, A. K. Katsaggelos, “Projection-based spatially adaptive reconstruction of block-transform compressed images,” IEEE Trans. Image Process. 4, 896–908 (1995).
[CrossRef] [PubMed]

1994 (2)

1991 (1)

M. I. Sezan, H. J. Trussell, “Prototype image constraints for set theoretic image restoration,” IEEE Trans. Signal Process. 39, 2275–2285 (1991).
[CrossRef]

1990 (2)

R. L. Lagendijk, J. Biemond, D. E. Boekee, “Identification and restoration of noisy blurred images using the expectation maximization algorithm,” IEEE Trans. Acoust., Speech, Signal Process. 38, 1180–1191 (1990).
[CrossRef]

K. T. Lay, A. K. Katsaggelos, “Image identification and restoration based on the expectation maximization algorithm,” Opt. Eng. (Bellingham) 29, 436–445 (1990).
[CrossRef]

1989 (1)

R. C. Dubes, A. K. Jain, “Random field models in image analysis,” J. Appl. Statistics 16, 131–164 (1989).
[CrossRef]

1984 (2)

H. J. Trussell, M. R. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust., Speech, Signal Process. 32, 201–212 (1984).
[CrossRef]

A. P. Pentland, “Local shading analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 170–187 (1984).
[CrossRef] [PubMed]

1981 (2)

K. Ikeuchi, B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artif. Intell. 17, 141–184 (1981).
[CrossRef]

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

1980 (1)

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

1974 (1)

J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. Ser. B. Methodol. 36, 192–236 (1974).

Bagheri, A.

Y. Iwahori, R. J. Woodhan, A. Bagheri, “Principal component analysis and neural network implementation of Photometric Stereo,” in Proceedings of the Workshop on Physics based Modeling in Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 117–125.

Banham, M. R.

M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag. Vol. 14 (2) 1997, pp. 24–41.
[CrossRef]

Basri, R.

R. Basri, D. Jacobs, “Photometric stereo with general unknown lighting,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2001), pp. 374–381.

Bedini, L.

L. Bedini, A. Tonazzini, S. Minutoli, “Unsupervised edge-preserving image restoration via a saddle point approximation,” Image Vis. Comput. 17, 779–793 (1999).
[CrossRef]

Besag, J.

J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. Ser. B. Methodol. 36, 192–236 (1974).

Besserer, B.

B. Besserer, L. Joyeux, S. Boukir, O. Buisson, “Reconstruction of degraded image sequences. Application to film restoration,” Image Vis. Comput. 19, 503–516 (2001).
[CrossRef]

Biemond, J.

R. L. Lagendijk, J. Biemond, D. E. Boekee, “Identification and restoration of noisy blurred images using the expectation maximization algorithm,” IEEE Trans. Acoust., Speech, Signal Process. 38, 1180–1191 (1990).
[CrossRef]

R. L. Lagendijk, J. Biemond, Iterative Identification and Restoration of Images, (Kluwer Academic, Boston, Mass., 2001).

Boekee, D. E.

R. L. Lagendijk, J. Biemond, D. E. Boekee, “Identification and restoration of noisy blurred images using the expectation maximization algorithm,” IEEE Trans. Acoust., Speech, Signal Process. 38, 1180–1191 (1990).
[CrossRef]

Boukir, S.

B. Besserer, L. Joyeux, S. Boukir, O. Buisson, “Reconstruction of degraded image sequences. Application to film restoration,” Image Vis. Comput. 19, 503–516 (2001).
[CrossRef]

Buisson, O.

B. Besserer, L. Joyeux, S. Boukir, O. Buisson, “Reconstruction of degraded image sequences. Application to film restoration,” Image Vis. Comput. 19, 503–516 (2001).
[CrossRef]

Candela, V. F.

V. F. Candela, A. Marquina, S. Serna, “A local spectral inversion of a linearized TV model for denoising and deblurring,” IEEE Trans. Image Process. 12, 808–816 (2003).
[CrossRef]

Chan, T. F.

T. F. Chan, C. K. Wong, “Convergence of the alternating minimization algorithm for blind deconvolution,” Tech. Rep. 19, UCLA Computational and Applied Mathematics Series (University of California, Los Angeles, Calif., 1999).

Chantler, M. J.

G. McGunnigle, M. J. Chantler, “Modelling deposition of surface texture,” Electron. Lett. 37, 749–750 (2001).
[CrossRef]

G. McGunnigle, M. J. Chantler, “Rough surface classification using point statistics from photometric stereo,” Protein Eng. 21, 593–604 (2000).

G. McGunnigle, M. J. Chantler, “Rotation invariant classification of rough surfaces,” IEE Proc. Vision Image Signal Process. 146, 345–352 (1999).
[CrossRef]

G. McGunnigle, M. J. Chantler, “Segmentation of machined surfaces,” presented at the Irish Machine Vision and Image Processing Conference, Maynooth, Ireland, September, 2001.

Chaudhuri, S.

D. Rajan, S. Chaudhuri, “Simultaneous estimation of super-resolved scene and depth map from low resolution defocused observations,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1102–1117 (2003).
[CrossRef]

A. N. Rajagopalan, S. Chaudhuri, “An MRF model based approach to simultaneous recovery of depth and restoration from defocused images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 577–589 (1999).
[CrossRef]

S. Chaudhuri, A. N. Rajagopalan, Depth From Defocus: A Real Aperture Imaging Approach (Springer-Verlag, New York, 1999).

Chen, C. Y.

C. Y. Chen, R. Klette, R. Kakarala, “Albedo recovery using a photometric stereo approach,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 700–703.

Civanlar, M. R.

H. J. Trussell, M. R. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust., Speech, Signal Process. 32, 201–212 (1984).
[CrossRef]

Clark, J. J.

J. J. Clark, “Active photometric stereo,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1992), pp. 29–34.

Drbohlav, O.

O. Drbohlav, R. Sara, “Unambiguous determination of shape from photometric stereo with unknown light sources,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 2001), pp. 581–586.

Dubes, R. C.

R. C. Dubes, A. K. Jain, “Random field models in image analysis,” J. Appl. Statistics 16, 131–164 (1989).
[CrossRef]

Erkmen, I.

U. Sakarya, I. Erkmen, “An improved method of photometric stereo using local shape from shading,” Image Vis. Comput. 21, 941–954 (2003).
[CrossRef]

Galatsanos, N. P.

Y. Yang, N. P. Galatsanos, A. K. Katsaggelos, “Projection-based spatially adaptive reconstruction of block-transform compressed images,” IEEE Trans. Image Process. 4, 896–908 (1995).
[CrossRef] [PubMed]

Hansson, P.

P. Hansson, P. Johansson, “Topography and reflectance analysis of paper surfaces using photometric stereo method,” Opt. Eng. (Bellingham) 39, 2555–2561 (2000).
[CrossRef]

Hatzinakos, D.

D. Kundur, D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. March 1996, pp. 43–64.

Hill, T.

M. L. Smith, T. Hill, G. Smith, “Gradient space analysis of surface defects using a photometric stereo derived bump map,” Image Vis. Comput. 17, 321–332 (1999).
[CrossRef]

Horn, B. K. P.

K. Ikeuchi, B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artif. Intell. 17, 141–184 (1981).
[CrossRef]

B. K. P. Horn, Robot Vision (MIT Press, Cambridge, Mass., 1986).

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

Ikeuchi, K.

K. Ikeuchi, B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artif. Intell. 17, 141–184 (1981).
[CrossRef]

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

Ishi, N.

Y. Iwahori, R. J. Woodham, M. Ozaki, H. Tanaka, N. Ishi, “Neural network based photometric stereo with a nearby rotational moving light source,” IEICE Trans. Inf. Syst. E-80-D, 948–957 (1997).

Iwahori, Y.

Y. Iwahori, R. J. Woodham, M. Ozaki, H. Tanaka, N. Ishi, “Neural network based photometric stereo with a nearby rotational moving light source,” IEICE Trans. Inf. Syst. E-80-D, 948–957 (1997).

Y. Iwahori, R. J. Woodhan, A. Bagheri, “Principal component analysis and neural network implementation of Photometric Stereo,” in Proceedings of the Workshop on Physics based Modeling in Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 117–125.

Y. Iwahori, R. J. Woodham, Y. Watanabe, A. Iwata, “Self calibration and neural network implementation of photometric stereo,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 359–362.

Iwata, A.

Y. Iwahori, R. J. Woodham, Y. Watanabe, A. Iwata, “Self calibration and neural network implementation of photometric stereo,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 359–362.

Jacobs, D.

R. Basri, D. Jacobs, “Photometric stereo with general unknown lighting,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2001), pp. 374–381.

Jain, A. K.

R. C. Dubes, A. K. Jain, “Random field models in image analysis,” J. Appl. Statistics 16, 131–164 (1989).
[CrossRef]

Jay Kuo, C. C.

K. M. Lee, C. C. Jay Kuo, “Shape reconstruction from photometric stereo,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1992), pp. 479–484.

Johansson, P.

P. Hansson, P. Johansson, “Topography and reflectance analysis of paper surfaces using photometric stereo method,” Opt. Eng. (Bellingham) 39, 2555–2561 (2000).
[CrossRef]

Joyeux, L.

B. Besserer, L. Joyeux, S. Boukir, O. Buisson, “Reconstruction of degraded image sequences. Application to film restoration,” Image Vis. Comput. 19, 503–516 (2001).
[CrossRef]

Kakarala, R.

C. Y. Chen, R. Klette, R. Kakarala, “Albedo recovery using a photometric stereo approach,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 700–703.

Katsaggelos, A. K.

M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag. Vol. 14 (2) 1997, pp. 24–41.
[CrossRef]

Y. Yang, N. P. Galatsanos, A. K. Katsaggelos, “Projection-based spatially adaptive reconstruction of block-transform compressed images,” IEEE Trans. Image Process. 4, 896–908 (1995).
[CrossRef] [PubMed]

K. T. Lay, A. K. Katsaggelos, “Image identification and restoration based on the expectation maximization algorithm,” Opt. Eng. (Bellingham) 29, 436–445 (1990).
[CrossRef]

Kaveh, M.

Y. You, M. Kaveh, “A regularization approach to joint blind identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef]

Klette, R.

C. Y. Chen, R. Klette, R. Kakarala, “Albedo recovery using a photometric stereo approach,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 700–703.

Kundur, D.

D. Kundur, D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. March 1996, pp. 43–64.

Lagendijk, R. L.

R. L. Lagendijk, J. Biemond, D. E. Boekee, “Identification and restoration of noisy blurred images using the expectation maximization algorithm,” IEEE Trans. Acoust., Speech, Signal Process. 38, 1180–1191 (1990).
[CrossRef]

R. L. Lagendijk, J. Biemond, Iterative Identification and Restoration of Images, (Kluwer Academic, Boston, Mass., 2001).

Lay, K. T.

K. T. Lay, A. K. Katsaggelos, “Image identification and restoration based on the expectation maximization algorithm,” Opt. Eng. (Bellingham) 29, 436–445 (1990).
[CrossRef]

Lee, K. M.

K. M. Lee, C. C. Jay Kuo, “Shape reconstruction from photometric stereo,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1992), pp. 479–484.

Marquina, A.

V. F. Candela, A. Marquina, S. Serna, “A local spectral inversion of a linearized TV model for denoising and deblurring,” IEEE Trans. Image Process. 12, 808–816 (2003).
[CrossRef]

McGunnigle, G.

G. McGunnigle, M. J. Chantler, “Modelling deposition of surface texture,” Electron. Lett. 37, 749–750 (2001).
[CrossRef]

G. McGunnigle, M. J. Chantler, “Rough surface classification using point statistics from photometric stereo,” Protein Eng. 21, 593–604 (2000).

G. McGunnigle, M. J. Chantler, “Rotation invariant classification of rough surfaces,” IEE Proc. Vision Image Signal Process. 146, 345–352 (1999).
[CrossRef]

G. McGunnigle, M. J. Chantler, “Segmentation of machined surfaces,” presented at the Irish Machine Vision and Image Processing Conference, Maynooth, Ireland, September, 2001.

Minutoli, S.

L. Bedini, A. Tonazzini, S. Minutoli, “Unsupervised edge-preserving image restoration via a saddle point approximation,” Image Vis. Comput. 17, 779–793 (1999).
[CrossRef]

Ozaki, M.

Y. Iwahori, R. J. Woodham, M. Ozaki, H. Tanaka, N. Ishi, “Neural network based photometric stereo with a nearby rotational moving light source,” IEICE Trans. Inf. Syst. E-80-D, 948–957 (1997).

Ozkan, M. K.

M. K. Ozkan, A. M. Tekalp, M. I. Sezan, “POCS based restoration of space varying blurred images,” IEEE Trans. Image Process. 3, 450–454 (1995).
[CrossRef]

Pentland, A. P.

A. P. Pentland, “Local shading analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 170–187 (1984).
[CrossRef] [PubMed]

A. P. Pentland, “Shape information from shading: a theory about human perception,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1988), pp. 404–413.

Rajagopalan, A. N.

A. N. Rajagopalan, S. Chaudhuri, “An MRF model based approach to simultaneous recovery of depth and restoration from defocused images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 577–589 (1999).
[CrossRef]

S. Chaudhuri, A. N. Rajagopalan, Depth From Defocus: A Real Aperture Imaging Approach (Springer-Verlag, New York, 1999).

Rajan, D.

D. Rajan, S. Chaudhuri, “Simultaneous estimation of super-resolved scene and depth map from low resolution defocused observations,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1102–1117 (2003).
[CrossRef]

Sakarya, U.

U. Sakarya, I. Erkmen, “An improved method of photometric stereo using local shape from shading,” Image Vis. Comput. 21, 941–954 (2003).
[CrossRef]

Sara, R.

O. Drbohlav, R. Sara, “Unambiguous determination of shape from photometric stereo with unknown light sources,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 2001), pp. 581–586.

Serna, S.

V. F. Candela, A. Marquina, S. Serna, “A local spectral inversion of a linearized TV model for denoising and deblurring,” IEEE Trans. Image Process. 12, 808–816 (2003).
[CrossRef]

Sezan, M. I.

M. K. Ozkan, A. M. Tekalp, M. I. Sezan, “POCS based restoration of space varying blurred images,” IEEE Trans. Image Process. 3, 450–454 (1995).
[CrossRef]

M. I. Sezan, H. J. Trussell, “Prototype image constraints for set theoretic image restoration,” IEEE Trans. Signal Process. 39, 2275–2285 (1991).
[CrossRef]

M. I. Sezan, A. M. Tekalp, “Iterative image restoration with ringing suppression using POCS,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE Press, Piscataway, N.J., 1988), pp. 1300–1303.

Shah, M.

P. S. Tsai, M. Shah, “Shape from shading using linear approximation,” Image Vis. Comput. 12, 487–498 (1994).
[CrossRef]

Silver, W. M.

W. M. Silver, “Determining shape and reflectance using multiple images,” M.S. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1980).

Smith, G.

M. L. Smith, T. Hill, G. Smith, “Gradient space analysis of surface defects using a photometric stereo derived bump map,” Image Vis. Comput. 17, 321–332 (1999).
[CrossRef]

Smith, M. L.

M. L. Smith, T. Hill, G. Smith, “Gradient space analysis of surface defects using a photometric stereo derived bump map,” Image Vis. Comput. 17, 321–332 (1999).
[CrossRef]

Subbarao, M.

M. Subbarao, “Parallel depth recovery by changing camera parameters,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1998), pp. 149–155.

Tanaka, H.

Y. Iwahori, R. J. Woodham, M. Ozaki, H. Tanaka, N. Ishi, “Neural network based photometric stereo with a nearby rotational moving light source,” IEICE Trans. Inf. Syst. E-80-D, 948–957 (1997).

Tekalp, A. M.

M. K. Ozkan, A. M. Tekalp, M. I. Sezan, “POCS based restoration of space varying blurred images,” IEEE Trans. Image Process. 3, 450–454 (1995).
[CrossRef]

M. I. Sezan, A. M. Tekalp, “Iterative image restoration with ringing suppression using POCS,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE Press, Piscataway, N.J., 1988), pp. 1300–1303.

Tonazzini, A.

L. Bedini, A. Tonazzini, S. Minutoli, “Unsupervised edge-preserving image restoration via a saddle point approximation,” Image Vis. Comput. 17, 779–793 (1999).
[CrossRef]

Torreao, J. R. A.

J. R. A. Torreao, “A new approach to photometric stereo,” Pattern Recogn. Lett. 20, 535–540 (1999).
[CrossRef]

Trussell, H. J.

M. I. Sezan, H. J. Trussell, “Prototype image constraints for set theoretic image restoration,” IEEE Trans. Signal Process. 39, 2275–2285 (1991).
[CrossRef]

H. J. Trussell, M. R. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust., Speech, Signal Process. 32, 201–212 (1984).
[CrossRef]

Tsai, P. S.

P. S. Tsai, M. Shah, “Shape from shading using linear approximation,” Image Vis. Comput. 12, 487–498 (1994).
[CrossRef]

Watanabe, Y.

Y. Iwahori, R. J. Woodham, Y. Watanabe, A. Iwata, “Self calibration and neural network implementation of photometric stereo,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 359–362.

Wong, C. K.

T. F. Chan, C. K. Wong, “Convergence of the alternating minimization algorithm for blind deconvolution,” Tech. Rep. 19, UCLA Computational and Applied Mathematics Series (University of California, Los Angeles, Calif., 1999).

Woodham, R. J.

Y. Iwahori, R. J. Woodham, M. Ozaki, H. Tanaka, N. Ishi, “Neural network based photometric stereo with a nearby rotational moving light source,” IEICE Trans. Inf. Syst. E-80-D, 948–957 (1997).

R. J. Woodham, “Gradient and curvature from the photometric stereo method including local confidence estimation,” J. Opt. Soc. Am. A 11, 3050–3068 (1994).
[CrossRef]

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

Y. Iwahori, R. J. Woodham, Y. Watanabe, A. Iwata, “Self calibration and neural network implementation of photometric stereo,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 359–362.

R. J. Woodham, “Reflectance map techniques for analyzing surface defects in metal castings,” Tech. Rep. 457 (MIT Artificial Intelligence Laboratory, Cambridge, Mass., 1978).

Woodhan, R. J.

Y. Iwahori, R. J. Woodhan, A. Bagheri, “Principal component analysis and neural network implementation of Photometric Stereo,” in Proceedings of the Workshop on Physics based Modeling in Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 117–125.

Yang, Y.

Y. Yang, N. P. Galatsanos, A. K. Katsaggelos, “Projection-based spatially adaptive reconstruction of block-transform compressed images,” IEEE Trans. Image Process. 4, 896–908 (1995).
[CrossRef] [PubMed]

You, Y.

Y. You, M. Kaveh, “A regularization approach to joint blind identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef]

Artif. Intell. (1)

K. Ikeuchi, B. K. P. Horn, “Numerical shape from shading and occluding boundaries,” Artif. Intell. 17, 141–184 (1981).
[CrossRef]

Electron. Lett. (1)

G. McGunnigle, M. J. Chantler, “Modelling deposition of surface texture,” Electron. Lett. 37, 749–750 (2001).
[CrossRef]

IEE Proc. Vision Image Signal Process. (1)

G. McGunnigle, M. J. Chantler, “Rotation invariant classification of rough surfaces,” IEE Proc. Vision Image Signal Process. 146, 345–352 (1999).
[CrossRef]

IEEE Signal Process. Mag. (1)

M. R. Banham, A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag. Vol. 14 (2) 1997, pp. 24–41.
[CrossRef]

IEEE Trans. Acoust., Speech, Signal Process. (2)

R. L. Lagendijk, J. Biemond, D. E. Boekee, “Identification and restoration of noisy blurred images using the expectation maximization algorithm,” IEEE Trans. Acoust., Speech, Signal Process. 38, 1180–1191 (1990).
[CrossRef]

H. J. Trussell, M. R. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust., Speech, Signal Process. 32, 201–212 (1984).
[CrossRef]

IEEE Trans. Image Process. (4)

Y. Yang, N. P. Galatsanos, A. K. Katsaggelos, “Projection-based spatially adaptive reconstruction of block-transform compressed images,” IEEE Trans. Image Process. 4, 896–908 (1995).
[CrossRef] [PubMed]

V. F. Candela, A. Marquina, S. Serna, “A local spectral inversion of a linearized TV model for denoising and deblurring,” IEEE Trans. Image Process. 12, 808–816 (2003).
[CrossRef]

M. K. Ozkan, A. M. Tekalp, M. I. Sezan, “POCS based restoration of space varying blurred images,” IEEE Trans. Image Process. 3, 450–454 (1995).
[CrossRef]

Y. You, M. Kaveh, “A regularization approach to joint blind identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (4)

D. Rajan, S. Chaudhuri, “Simultaneous estimation of super-resolved scene and depth map from low resolution defocused observations,” IEEE Trans. Pattern Anal. Mach. Intell. 25, 1102–1117 (2003).
[CrossRef]

A. N. Rajagopalan, S. Chaudhuri, “An MRF model based approach to simultaneous recovery of depth and restoration from defocused images,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 577–589 (1999).
[CrossRef]

A. P. Pentland, “Local shading analysis,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 170–187 (1984).
[CrossRef] [PubMed]

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

IEEE Trans. Signal Process. (1)

M. I. Sezan, H. J. Trussell, “Prototype image constraints for set theoretic image restoration,” IEEE Trans. Signal Process. 39, 2275–2285 (1991).
[CrossRef]

IEICE Trans. Inf. Syst. (1)

Y. Iwahori, R. J. Woodham, M. Ozaki, H. Tanaka, N. Ishi, “Neural network based photometric stereo with a nearby rotational moving light source,” IEICE Trans. Inf. Syst. E-80-D, 948–957 (1997).

Image Vis. Comput. (5)

P. S. Tsai, M. Shah, “Shape from shading using linear approximation,” Image Vis. Comput. 12, 487–498 (1994).
[CrossRef]

B. Besserer, L. Joyeux, S. Boukir, O. Buisson, “Reconstruction of degraded image sequences. Application to film restoration,” Image Vis. Comput. 19, 503–516 (2001).
[CrossRef]

L. Bedini, A. Tonazzini, S. Minutoli, “Unsupervised edge-preserving image restoration via a saddle point approximation,” Image Vis. Comput. 17, 779–793 (1999).
[CrossRef]

M. L. Smith, T. Hill, G. Smith, “Gradient space analysis of surface defects using a photometric stereo derived bump map,” Image Vis. Comput. 17, 321–332 (1999).
[CrossRef]

U. Sakarya, I. Erkmen, “An improved method of photometric stereo using local shape from shading,” Image Vis. Comput. 21, 941–954 (2003).
[CrossRef]

J. Appl. Statistics (1)

R. C. Dubes, A. K. Jain, “Random field models in image analysis,” J. Appl. Statistics 16, 131–164 (1989).
[CrossRef]

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

J. R. Stat. Soc. Ser. B. Methodol. (1)

J. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. R. Stat. Soc. Ser. B. Methodol. 36, 192–236 (1974).

Opt. Eng. (Bellingham) (3)

K. T. Lay, A. K. Katsaggelos, “Image identification and restoration based on the expectation maximization algorithm,” Opt. Eng. (Bellingham) 29, 436–445 (1990).
[CrossRef]

P. Hansson, P. Johansson, “Topography and reflectance analysis of paper surfaces using photometric stereo method,” Opt. Eng. (Bellingham) 39, 2555–2561 (2000).
[CrossRef]

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

Pattern Recogn. Lett. (1)

J. R. A. Torreao, “A new approach to photometric stereo,” Pattern Recogn. Lett. 20, 535–540 (1999).
[CrossRef]

Protein Eng. (1)

G. McGunnigle, M. J. Chantler, “Rough surface classification using point statistics from photometric stereo,” Protein Eng. 21, 593–604 (2000).

Other (19)

R. L. Lagendijk, J. Biemond, Iterative Identification and Restoration of Images, (Kluwer Academic, Boston, Mass., 2001).

D. Kundur, D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. March 1996, pp. 43–64.

G. McGunnigle, M. J. Chantler, “Segmentation of machined surfaces,” presented at the Irish Machine Vision and Image Processing Conference, Maynooth, Ireland, September, 2001.

J. J. Clark, “Active photometric stereo,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1992), pp. 29–34.

Y. Iwahori, R. J. Woodham, Y. Watanabe, A. Iwata, “Self calibration and neural network implementation of photometric stereo,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 359–362.

O. Drbohlav, R. Sara, “Unambiguous determination of shape from photometric stereo with unknown light sources,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 2001), pp. 581–586.

R. Basri, D. Jacobs, “Photometric stereo with general unknown lighting,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2001), pp. 374–381.

A. P. Pentland, “Shape information from shading: a theory about human perception,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1988), pp. 404–413.

M. Subbarao, “Parallel depth recovery by changing camera parameters,” in Proceedings of the International Conference on Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1998), pp. 149–155.

T. F. Chan, C. K. Wong, “Convergence of the alternating minimization algorithm for blind deconvolution,” Tech. Rep. 19, UCLA Computational and Applied Mathematics Series (University of California, Los Angeles, Calif., 1999).

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

M. I. Sezan, A. M. Tekalp, “Iterative image restoration with ringing suppression using POCS,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE Press, Piscataway, N.J., 1988), pp. 1300–1303.

B. K. P. Horn, Robot Vision (MIT Press, Cambridge, Mass., 1986).

S. Chaudhuri, A. N. Rajagopalan, Depth From Defocus: A Real Aperture Imaging Approach (Springer-Verlag, New York, 1999).

R. J. Woodham, “Reflectance map techniques for analyzing surface defects in metal castings,” Tech. Rep. 457 (MIT Artificial Intelligence Laboratory, Cambridge, Mass., 1978).

Y. Iwahori, R. J. Woodhan, A. Bagheri, “Principal component analysis and neural network implementation of Photometric Stereo,” in Proceedings of the Workshop on Physics based Modeling in Computer Vision (IEEE Computer Society Press, Los Alamitos, Calif., 1995), pp. 117–125.

W. M. Silver, “Determining shape and reflectance using multiple images,” M.S. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1980).

K. M. Lee, C. C. Jay Kuo, “Shape reconstruction from photometric stereo,” in Proceedings of the International Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1992), pp. 479–484.

C. Y. Chen, R. Klette, R. Kakarala, “Albedo recovery using a photometric stereo approach,” in Proceedings of the International Conference on Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 2002), pp. 700–703.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (20)

Fig. 1
Fig. 1

Observation system for photometric stereo.

Fig. 2
Fig. 2

Illustration of the proposed method for image and structure recovery when the blur PSF is known.

Fig. 3
Fig. 3

Illustration of the proposed method for image and structure recovery when the blur PSF is unknown. A comparison with Fig. 2 shows that we have added another block, “Estimate blur,” to estimate the blurs between ( g 1 , f ̂ 1 ( n + 1 ) ) , ( g 2 , f ̂ 2 ( n + 1 ) ) , …, and ( g k , f ̂ k ( n + 1 ) ) .

Fig. 4
Fig. 4

(a) Focused image of Jodu captured with a light-source position ( p s = 0.3639 , q s = 0.5865 ) . (b) Simulated blurred observation of Jodu obtained by using a mask size of 5 × 5 for the image shown in (a).

Fig. 5
Fig. 5

(a) Restored Jodu image for the observation given in Fig. 4b obtained by using the proposed approach when the blur is known. (b) Restored Jodu obtained by the deconvolution operation.

Fig. 6
Fig. 6

(a) True depth map obtained from PS by using the observations not suffering from blurring. (b) Recovered albedo obtained by using nonblurred or focused images.

Fig. 7
Fig. 7

(a) Depth map obtained by using the standard PS method on blurred observations. (b) Albedo for the surface of Jodu with a blur of 5 × 5 mask obtained by using the standard PS on blurred observations.

Fig. 8
Fig. 8

(a) Recovered depth map obtained by using the proposed technique utilizing the knowledge of PSF. (b) Estimated albedo.

Fig. 9
Fig. 9

(a) Focused image of Jodu captured with light-source positions ( p s = 0.8389 , q s = 0.7193 ) . (b) Simulated blurred observation of Jodu obtained by using a mask size of 9 × 9 for the image shown in (a).

Fig. 10
Fig. 10

Restored Jodu image by using (a) the proposed method and (b) direct image deconvolution.

Fig. 11
Fig. 11

Reconstructed depth map obtained by using the proposed technique.

Fig. 12
Fig. 12

(a) True depth map without considering the blur. (b) Depth map obtained from direct application of PS on blurred observations.

Fig. 13
Fig. 13

(a) Surface albedo for Jodu computed from blurred data. (b) Estimated albedo obtained by using the proposed technique.

Fig. 14
Fig. 14

(a) Synthesized image of a checkerboard-textured spherical surface for a light-source position ( p s = 0.45 , q s = 0.80 ) . (b) Simulated observation obtained by using a Gaussian blur σ = 1 and additive noise corresponding to the figure in (a).

Fig. 15
Fig. 15

Restored checkerboard image obtained by using the proposed technique.

Fig. 16
Fig. 16

Recovered depth map obtained by using (a) the standard PS method and (b) the proposed method.

Fig. 17
Fig. 17

(a) Observed image of Jodu with an arbitrary camera defocus for the same light-source position used for the image shown in Fig. 4a. (b) Restored Jodu image obtained by using the proposed method.

Fig. 18
Fig. 18

(a) Restored Jodu image obtained by using a standard MATLAB blind deconvolution tool. (b) Recovered albedo obtained by using the proposed method.

Fig. 19
Fig. 19

Recovered depth map obtained by using (a) the standard PS method and (b) the proposed method.

Fig. 20
Fig. 20

Recovered depth map shown as a mesh plot obtained by using (a) the standard PS method and (b) the proposed method.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

f ( x , y ) = ρ ( x , y ) R ( p ( x , y ) , q ( x , y ) ) = ρ ( x , y ) n ̂ ( x , y ) s ̂ ,
g ( x , y ) = h ( x , y ) f ( x , y ) + η ( x , y ) ,
g m ( x , y ) = h ( x , y ) f m ( x , y ) + η m ( x , y ) , m = 1 , , k .
g m = H ( σ ) f m ( ρ , p , q ) + η m , m = 1 , , k ,
P ( η m ) = 1 ( 2 π σ η 2 ) N 2 2 exp ( 1 2 σ η 2 η m T η m ) ,
c C V c ( z ) = μ k = 1 N 2 l = 1 N 2 [ ( z k , l z k , l 1 ) 2 + ( z k , l z k 1 , l ) 2 + ( z k , l + 1 z k , l ) 2 + ( z k + 1 , l z k , l ) 2 ] = U ( z ) ,
U ( w ) = μ w k = 1 N 2 l = 1 N 2 [ ( w k , l w k , l 1 ) 2 + ( w k , l w k 1 , l ) 2 + ( w k , l + 1 w k , l ) 2 + ( w k + 1 , l w k , l ) 2 ] ,
ϵ = m = 1 k g m H ( σ ) f m ( ρ , p , q ) 2 + U ( p ) + U ( q ) + U ( ρ ) .
2 d ( x , y ) = p x ( x , y ) + q y ( x , y ) ,
g ( x , y ) = h ( x , y ; σ ) f ( x , y ) .
H ( w x , w y ) = exp [ ( w x 2 + w y 2 ) σ 2 2 ] .
σ 2 = 2 w x 2 + w y 2 log G ( w x , w y ) F ( w x , w y ) ,
σ 2 = 1 A R 2 w x 2 + w y 2 log G ( w x , w y ) F ( w x , w y ) d w x d w y ,
{ p ( n + 1 ) , q ( n + 1 ) , ρ ( n + 1 ) } arg min p , q , ρ m = 1 k g m H ( σ ) f m ( ρ , p , q ) 2 + U ( p ) + U ( q ) + U ( ρ ) .
σ i 2 = 1 A R 2 w x 2 + w y 2 log G i ( w x , w y ) F ̂ i ( w x , w y ) d w x d w y ,
2 d ( x , y ) = p x ( x , y ) + q y ( x , y ) .
h ( x , y ) = { 1 π r 2 if x 2 + y 2 r 0 otherwise } .

Metrics