Abstract

The depth-from-focus–defocus approach to 3D reconstruction is based on the fact that objects closer to or farther from the object in focus appear blurred, and the amount of blur increases with the distance from the object in focus. An important characteristic of any depth-from-defocus system is the depth reconstruction accuracy. Several 3D reconstruction algorithms have been proposed, and the influence of image noise and image spectrum on the system accuracy has been studied. However, so far the effect of optics on the accuracy has not been fully explored. Here, we derive an expression estimating the system accuracy as a function of its optical parameters. It turns out that optics plays a major role in the accuracy, and tenfold increase of the lens focal length, and the aperture can increase the overall accuracy by a factor of more than 1000. The derived expression allows one to review several results, revealing that the accuracy is defined primarily by the optics. We also provide guidelines for the design of new depth-from-defocus systems in compliance with predefined specifications by choosing the appropriate optics.

© 2007 Optical Society of America

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  1. P. Favaro, A. Menucci, and S. Soatto, "Observing shape from defocused images," Int. J. Comput. Vis. 52, 25-43 (2003).
    [CrossRef]
  2. P. Favaro and S. Soatto, "A geometric approach to shape from defocus," IEEE Trans. Pattern Anal. Mach. Intell. 27, 406-415 (2005).
    [CrossRef] [PubMed]
  3. M. Gokstorp, "Computing depth from out-of-focus blur using a local frequency representation," in Proceedings of International Conference on Pattern Recognition (IEEE, 1994), pp. 153-158.
    [CrossRef]
  4. H. Jin and P. Favarao, "A variational approach to shape from defocus," in Proceedings of European Conference on Computer Vision (2002), pp. 18-30.
  5. S. K. Nayar and Y. Nakagawa, "Shape from focus: an effective approach for rough surfaces," IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
    [CrossRef]
  6. M. Noguchi and S. K. Nayar, "Microscopic shape from focus using active illumination," in Proceedings of International Conference on Pattern Recognition (IEEE, 1994), pp. 147-152.
    [CrossRef]
  7. A. P. Pentland, "A new sense for depth of field," IEEE Trans. Pattern Anal. Mach. Intell. 9, 523-531 (1987).
    [CrossRef] [PubMed]
  8. A. P. Pentland, T. Darrel, M. Turk, and W. Huang, "A simple, real time range camera," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256-261.
  9. A. N. Rajagopalan and S. Chaudhuri, "A block shift-variant blur model for recovering depth from defocused images," in Proceedings of International Conference on Image Processing (IEEE, 1995), pp. 636-639.
    [CrossRef]
  10. S. Soatto and P. Favaro, "A geometric approach to blind deconvolution with application to shape from defocus," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 2000), pp. 10-17.
    [CrossRef]
  11. D. Ziou, "Passive depth from defocus using spatial domain approach," in Proceedings of International Conference on Computer Vision (IEEE, 1998), pp. 799-804.
  12. Y. Schechner and N. Kiryati, "Depth from defocus vs. stereo: how different really are they," in Proceedings of International Conference on Pattern Recognition (IEEE, 1998), pp. 1784-1786.
  13. A. N. Rajagopalan and S. Chaudhuri, "Performance analysis of maximum likelihood estimator for recovery of depth from defocused images and optimal selection of camera parameters," Int. J. Comput. Vis. 30, 175-190 (1998).
    [CrossRef]
  14. A. N. Rajagopalan, S. Chaudhuri, and R. Chellappa, "Quantitative analysis of error bounds in the recovery of depth from defocused images," J. Opt. Soc. Am. A 17, 1722-1731 (2000).
    [CrossRef]
  15. M. Subbarao and J. K. Tyan, "Noise sensitivity analysis of depth-from-defocus by a spatial-domain approach," Proc. SPIE 3174, 174-187 (1994).
  16. Y. Schechner and N. Kiryati, "The optimal axial interval in estimating depth from defocus," in Proceedings of International Conference on Computer Vision (IEEE, 1993), pp. 843-848.
  17. M. Subbarao and T. Choi, "Accurate recovery of three-dimensional shape from image focus," IEEE Trans. Pattern Anal. Mach. Intell. 17, 266-274 (1995).
    [CrossRef]
  18. M. Subbarao and G. Surya, "Depth from defocus: a spatial domain approach," Int. J. Comput. Vis. 13, 271-294 (1994).
    [CrossRef]
  19. J. Ens and P. Lawrence, "An investigation of methods for determining depth from focus," IEEE Trans. Pattern Anal. Mach. Intell. 15, 97-108 (1993).
    [CrossRef]
  20. M. Watanabe and S. K. Nayar, "Rational filters for passive depth from defocus," Int. J. Comput. Vis. 27, 203-225 (1998).
    [CrossRef]
  21. Y. Xiong and S. A. Shafer, "Depth from focusing and defocusing," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1993), pp. 68-73.
    [CrossRef]
  22. M. Baba, N. Asada, A. Oda, and T. Migita, "A thin lens based camera model for depth estimation from defocus and translation by zooming," in Proceedings of ICVI (2002), pp. 274-281.
  23. O. Ghita and P. Whelan, "A video-rate sensor based on depth from defocus," Opt. Laser Technol. 33, 167-176 (2001).
    [CrossRef]
  24. S. K. Nayar, M. Watanabe, and M. Noguchi, "Real-time focus range sensor," IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186-1198 (1996).
    [CrossRef]
  25. A. E. Savakis and H. J. Trussel, "On the accuracy of PSF representation in image restoration," IEEE Trans. Image Process. 2, 252-259 (1993).
    [CrossRef] [PubMed]
  26. W. J. Smith, Modern Lens Design (McGraw-Hill, 1992), pp. 43-49.
  27. M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), pp. 395-397.
  28. G. Arfken, Mathematical Methods for Physicists (Academic, 1985), pp. 573-636.
  29. E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974).
  30. B. K. P. Horn, Robot Vision (MIT Press, 1986).
  31. F. Deschenes, D. Ziou, and P. Fuchs, "Simultaneous computation of defocus blur and apparent shifts in spatial domain," in Actes de 15th International Conference on Vision Interface (1992), pp. 236-243.
  32. A. P. Pentland, S. Scherock, T. Darrel, and B. Girod, "Simple range cameras based on focal error," J. Opt. Soc. Am. A 11, 2925-2934 (1994).
    [CrossRef]

2005 (1)

P. Favaro and S. Soatto, "A geometric approach to shape from defocus," IEEE Trans. Pattern Anal. Mach. Intell. 27, 406-415 (2005).
[CrossRef] [PubMed]

2003 (1)

P. Favaro, A. Menucci, and S. Soatto, "Observing shape from defocused images," Int. J. Comput. Vis. 52, 25-43 (2003).
[CrossRef]

2002 (2)

H. Jin and P. Favarao, "A variational approach to shape from defocus," in Proceedings of European Conference on Computer Vision (2002), pp. 18-30.

M. Baba, N. Asada, A. Oda, and T. Migita, "A thin lens based camera model for depth estimation from defocus and translation by zooming," in Proceedings of ICVI (2002), pp. 274-281.

2001 (1)

O. Ghita and P. Whelan, "A video-rate sensor based on depth from defocus," Opt. Laser Technol. 33, 167-176 (2001).
[CrossRef]

2000 (2)

S. Soatto and P. Favaro, "A geometric approach to blind deconvolution with application to shape from defocus," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 2000), pp. 10-17.
[CrossRef]

A. N. Rajagopalan, S. Chaudhuri, and R. Chellappa, "Quantitative analysis of error bounds in the recovery of depth from defocused images," J. Opt. Soc. Am. A 17, 1722-1731 (2000).
[CrossRef]

1998 (4)

D. Ziou, "Passive depth from defocus using spatial domain approach," in Proceedings of International Conference on Computer Vision (IEEE, 1998), pp. 799-804.

Y. Schechner and N. Kiryati, "Depth from defocus vs. stereo: how different really are they," in Proceedings of International Conference on Pattern Recognition (IEEE, 1998), pp. 1784-1786.

A. N. Rajagopalan and S. Chaudhuri, "Performance analysis of maximum likelihood estimator for recovery of depth from defocused images and optimal selection of camera parameters," Int. J. Comput. Vis. 30, 175-190 (1998).
[CrossRef]

M. Watanabe and S. K. Nayar, "Rational filters for passive depth from defocus," Int. J. Comput. Vis. 27, 203-225 (1998).
[CrossRef]

1996 (1)

S. K. Nayar, M. Watanabe, and M. Noguchi, "Real-time focus range sensor," IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186-1198 (1996).
[CrossRef]

1995 (2)

A. N. Rajagopalan and S. Chaudhuri, "A block shift-variant blur model for recovering depth from defocused images," in Proceedings of International Conference on Image Processing (IEEE, 1995), pp. 636-639.
[CrossRef]

M. Subbarao and T. Choi, "Accurate recovery of three-dimensional shape from image focus," IEEE Trans. Pattern Anal. Mach. Intell. 17, 266-274 (1995).
[CrossRef]

1994 (6)

M. Subbarao and G. Surya, "Depth from defocus: a spatial domain approach," Int. J. Comput. Vis. 13, 271-294 (1994).
[CrossRef]

M. Subbarao and J. K. Tyan, "Noise sensitivity analysis of depth-from-defocus by a spatial-domain approach," Proc. SPIE 3174, 174-187 (1994).

S. K. Nayar and Y. Nakagawa, "Shape from focus: an effective approach for rough surfaces," IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
[CrossRef]

M. Noguchi and S. K. Nayar, "Microscopic shape from focus using active illumination," in Proceedings of International Conference on Pattern Recognition (IEEE, 1994), pp. 147-152.
[CrossRef]

M. Gokstorp, "Computing depth from out-of-focus blur using a local frequency representation," in Proceedings of International Conference on Pattern Recognition (IEEE, 1994), pp. 153-158.
[CrossRef]

A. P. Pentland, S. Scherock, T. Darrel, and B. Girod, "Simple range cameras based on focal error," J. Opt. Soc. Am. A 11, 2925-2934 (1994).
[CrossRef]

1993 (4)

A. E. Savakis and H. J. Trussel, "On the accuracy of PSF representation in image restoration," IEEE Trans. Image Process. 2, 252-259 (1993).
[CrossRef] [PubMed]

Y. Xiong and S. A. Shafer, "Depth from focusing and defocusing," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1993), pp. 68-73.
[CrossRef]

Y. Schechner and N. Kiryati, "The optimal axial interval in estimating depth from defocus," in Proceedings of International Conference on Computer Vision (IEEE, 1993), pp. 843-848.

J. Ens and P. Lawrence, "An investigation of methods for determining depth from focus," IEEE Trans. Pattern Anal. Mach. Intell. 15, 97-108 (1993).
[CrossRef]

1992 (2)

W. J. Smith, Modern Lens Design (McGraw-Hill, 1992), pp. 43-49.

F. Deschenes, D. Ziou, and P. Fuchs, "Simultaneous computation of defocus blur and apparent shifts in spatial domain," in Actes de 15th International Conference on Vision Interface (1992), pp. 236-243.

1989 (1)

A. P. Pentland, T. Darrel, M. Turk, and W. Huang, "A simple, real time range camera," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256-261.

1987 (1)

A. P. Pentland, "A new sense for depth of field," IEEE Trans. Pattern Anal. Mach. Intell. 9, 523-531 (1987).
[CrossRef] [PubMed]

1986 (1)

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

1985 (1)

G. Arfken, Mathematical Methods for Physicists (Academic, 1985), pp. 573-636.

1975 (1)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), pp. 395-397.

1974 (1)

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974).

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, 1985), pp. 573-636.

Asada, N.

M. Baba, N. Asada, A. Oda, and T. Migita, "A thin lens based camera model for depth estimation from defocus and translation by zooming," in Proceedings of ICVI (2002), pp. 274-281.

Baba, M.

M. Baba, N. Asada, A. Oda, and T. Migita, "A thin lens based camera model for depth estimation from defocus and translation by zooming," in Proceedings of ICVI (2002), pp. 274-281.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), pp. 395-397.

Chaudhuri, S.

A. N. Rajagopalan, S. Chaudhuri, and R. Chellappa, "Quantitative analysis of error bounds in the recovery of depth from defocused images," J. Opt. Soc. Am. A 17, 1722-1731 (2000).
[CrossRef]

A. N. Rajagopalan and S. Chaudhuri, "Performance analysis of maximum likelihood estimator for recovery of depth from defocused images and optimal selection of camera parameters," Int. J. Comput. Vis. 30, 175-190 (1998).
[CrossRef]

A. N. Rajagopalan and S. Chaudhuri, "A block shift-variant blur model for recovering depth from defocused images," in Proceedings of International Conference on Image Processing (IEEE, 1995), pp. 636-639.
[CrossRef]

Chellappa, R.

Choi, T.

M. Subbarao and T. Choi, "Accurate recovery of three-dimensional shape from image focus," IEEE Trans. Pattern Anal. Mach. Intell. 17, 266-274 (1995).
[CrossRef]

Darrel, T.

A. P. Pentland, S. Scherock, T. Darrel, and B. Girod, "Simple range cameras based on focal error," J. Opt. Soc. Am. A 11, 2925-2934 (1994).
[CrossRef]

A. P. Pentland, T. Darrel, M. Turk, and W. Huang, "A simple, real time range camera," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256-261.

Deschenes, F.

F. Deschenes, D. Ziou, and P. Fuchs, "Simultaneous computation of defocus blur and apparent shifts in spatial domain," in Actes de 15th International Conference on Vision Interface (1992), pp. 236-243.

Ens, J.

J. Ens and P. Lawrence, "An investigation of methods for determining depth from focus," IEEE Trans. Pattern Anal. Mach. Intell. 15, 97-108 (1993).
[CrossRef]

Favarao, P.

H. Jin and P. Favarao, "A variational approach to shape from defocus," in Proceedings of European Conference on Computer Vision (2002), pp. 18-30.

Favaro, P.

P. Favaro and S. Soatto, "A geometric approach to shape from defocus," IEEE Trans. Pattern Anal. Mach. Intell. 27, 406-415 (2005).
[CrossRef] [PubMed]

P. Favaro, A. Menucci, and S. Soatto, "Observing shape from defocused images," Int. J. Comput. Vis. 52, 25-43 (2003).
[CrossRef]

S. Soatto and P. Favaro, "A geometric approach to blind deconvolution with application to shape from defocus," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 2000), pp. 10-17.
[CrossRef]

Fuchs, P.

F. Deschenes, D. Ziou, and P. Fuchs, "Simultaneous computation of defocus blur and apparent shifts in spatial domain," in Actes de 15th International Conference on Vision Interface (1992), pp. 236-243.

Ghita, O.

O. Ghita and P. Whelan, "A video-rate sensor based on depth from defocus," Opt. Laser Technol. 33, 167-176 (2001).
[CrossRef]

Girod, B.

Gokstorp, M.

M. Gokstorp, "Computing depth from out-of-focus blur using a local frequency representation," in Proceedings of International Conference on Pattern Recognition (IEEE, 1994), pp. 153-158.
[CrossRef]

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974).

Horn, B. K. P.

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

Huang, W.

A. P. Pentland, T. Darrel, M. Turk, and W. Huang, "A simple, real time range camera," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256-261.

Jin, H.

H. Jin and P. Favarao, "A variational approach to shape from defocus," in Proceedings of European Conference on Computer Vision (2002), pp. 18-30.

Kiryati, N.

Y. Schechner and N. Kiryati, "Depth from defocus vs. stereo: how different really are they," in Proceedings of International Conference on Pattern Recognition (IEEE, 1998), pp. 1784-1786.

Y. Schechner and N. Kiryati, "The optimal axial interval in estimating depth from defocus," in Proceedings of International Conference on Computer Vision (IEEE, 1993), pp. 843-848.

Lawrence, P.

J. Ens and P. Lawrence, "An investigation of methods for determining depth from focus," IEEE Trans. Pattern Anal. Mach. Intell. 15, 97-108 (1993).
[CrossRef]

Menucci, A.

P. Favaro, A. Menucci, and S. Soatto, "Observing shape from defocused images," Int. J. Comput. Vis. 52, 25-43 (2003).
[CrossRef]

Migita, T.

M. Baba, N. Asada, A. Oda, and T. Migita, "A thin lens based camera model for depth estimation from defocus and translation by zooming," in Proceedings of ICVI (2002), pp. 274-281.

Nakagawa, Y.

S. K. Nayar and Y. Nakagawa, "Shape from focus: an effective approach for rough surfaces," IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
[CrossRef]

Nayar, S. K.

M. Watanabe and S. K. Nayar, "Rational filters for passive depth from defocus," Int. J. Comput. Vis. 27, 203-225 (1998).
[CrossRef]

S. K. Nayar, M. Watanabe, and M. Noguchi, "Real-time focus range sensor," IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186-1198 (1996).
[CrossRef]

M. Noguchi and S. K. Nayar, "Microscopic shape from focus using active illumination," in Proceedings of International Conference on Pattern Recognition (IEEE, 1994), pp. 147-152.
[CrossRef]

S. K. Nayar and Y. Nakagawa, "Shape from focus: an effective approach for rough surfaces," IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
[CrossRef]

Noguchi, M.

S. K. Nayar, M. Watanabe, and M. Noguchi, "Real-time focus range sensor," IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186-1198 (1996).
[CrossRef]

M. Noguchi and S. K. Nayar, "Microscopic shape from focus using active illumination," in Proceedings of International Conference on Pattern Recognition (IEEE, 1994), pp. 147-152.
[CrossRef]

Oda, A.

M. Baba, N. Asada, A. Oda, and T. Migita, "A thin lens based camera model for depth estimation from defocus and translation by zooming," in Proceedings of ICVI (2002), pp. 274-281.

Pentland, A. P.

A. P. Pentland, S. Scherock, T. Darrel, and B. Girod, "Simple range cameras based on focal error," J. Opt. Soc. Am. A 11, 2925-2934 (1994).
[CrossRef]

A. P. Pentland, T. Darrel, M. Turk, and W. Huang, "A simple, real time range camera," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256-261.

A. P. Pentland, "A new sense for depth of field," IEEE Trans. Pattern Anal. Mach. Intell. 9, 523-531 (1987).
[CrossRef] [PubMed]

Rajagopalan, A. N.

A. N. Rajagopalan, S. Chaudhuri, and R. Chellappa, "Quantitative analysis of error bounds in the recovery of depth from defocused images," J. Opt. Soc. Am. A 17, 1722-1731 (2000).
[CrossRef]

A. N. Rajagopalan and S. Chaudhuri, "Performance analysis of maximum likelihood estimator for recovery of depth from defocused images and optimal selection of camera parameters," Int. J. Comput. Vis. 30, 175-190 (1998).
[CrossRef]

A. N. Rajagopalan and S. Chaudhuri, "A block shift-variant blur model for recovering depth from defocused images," in Proceedings of International Conference on Image Processing (IEEE, 1995), pp. 636-639.
[CrossRef]

Savakis, A. E.

A. E. Savakis and H. J. Trussel, "On the accuracy of PSF representation in image restoration," IEEE Trans. Image Process. 2, 252-259 (1993).
[CrossRef] [PubMed]

Schechner, Y.

Y. Schechner and N. Kiryati, "Depth from defocus vs. stereo: how different really are they," in Proceedings of International Conference on Pattern Recognition (IEEE, 1998), pp. 1784-1786.

Y. Schechner and N. Kiryati, "The optimal axial interval in estimating depth from defocus," in Proceedings of International Conference on Computer Vision (IEEE, 1993), pp. 843-848.

Scherock, S.

Shafer, S. A.

Y. Xiong and S. A. Shafer, "Depth from focusing and defocusing," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1993), pp. 68-73.
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Lens Design (McGraw-Hill, 1992), pp. 43-49.

Soatto, S.

P. Favaro and S. Soatto, "A geometric approach to shape from defocus," IEEE Trans. Pattern Anal. Mach. Intell. 27, 406-415 (2005).
[CrossRef] [PubMed]

P. Favaro, A. Menucci, and S. Soatto, "Observing shape from defocused images," Int. J. Comput. Vis. 52, 25-43 (2003).
[CrossRef]

S. Soatto and P. Favaro, "A geometric approach to blind deconvolution with application to shape from defocus," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 2000), pp. 10-17.
[CrossRef]

Subbarao, M.

M. Subbarao and T. Choi, "Accurate recovery of three-dimensional shape from image focus," IEEE Trans. Pattern Anal. Mach. Intell. 17, 266-274 (1995).
[CrossRef]

M. Subbarao and J. K. Tyan, "Noise sensitivity analysis of depth-from-defocus by a spatial-domain approach," Proc. SPIE 3174, 174-187 (1994).

M. Subbarao and G. Surya, "Depth from defocus: a spatial domain approach," Int. J. Comput. Vis. 13, 271-294 (1994).
[CrossRef]

Surya, G.

M. Subbarao and G. Surya, "Depth from defocus: a spatial domain approach," Int. J. Comput. Vis. 13, 271-294 (1994).
[CrossRef]

Trussel, H. J.

A. E. Savakis and H. J. Trussel, "On the accuracy of PSF representation in image restoration," IEEE Trans. Image Process. 2, 252-259 (1993).
[CrossRef] [PubMed]

Turk, M.

A. P. Pentland, T. Darrel, M. Turk, and W. Huang, "A simple, real time range camera," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256-261.

Tyan, J. K.

M. Subbarao and J. K. Tyan, "Noise sensitivity analysis of depth-from-defocus by a spatial-domain approach," Proc. SPIE 3174, 174-187 (1994).

Watanabe, M.

M. Watanabe and S. K. Nayar, "Rational filters for passive depth from defocus," Int. J. Comput. Vis. 27, 203-225 (1998).
[CrossRef]

S. K. Nayar, M. Watanabe, and M. Noguchi, "Real-time focus range sensor," IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186-1198 (1996).
[CrossRef]

Whelan, P.

O. Ghita and P. Whelan, "A video-rate sensor based on depth from defocus," Opt. Laser Technol. 33, 167-176 (2001).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), pp. 395-397.

Xiong, Y.

Y. Xiong and S. A. Shafer, "Depth from focusing and defocusing," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1993), pp. 68-73.
[CrossRef]

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974).

Ziou, D.

D. Ziou, "Passive depth from defocus using spatial domain approach," in Proceedings of International Conference on Computer Vision (IEEE, 1998), pp. 799-804.

F. Deschenes, D. Ziou, and P. Fuchs, "Simultaneous computation of defocus blur and apparent shifts in spatial domain," in Actes de 15th International Conference on Vision Interface (1992), pp. 236-243.

IEEE Trans. Image Process. (1)

A. E. Savakis and H. J. Trussel, "On the accuracy of PSF representation in image restoration," IEEE Trans. Image Process. 2, 252-259 (1993).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (6)

M. Subbarao and T. Choi, "Accurate recovery of three-dimensional shape from image focus," IEEE Trans. Pattern Anal. Mach. Intell. 17, 266-274 (1995).
[CrossRef]

S. K. Nayar, M. Watanabe, and M. Noguchi, "Real-time focus range sensor," IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186-1198 (1996).
[CrossRef]

P. Favaro and S. Soatto, "A geometric approach to shape from defocus," IEEE Trans. Pattern Anal. Mach. Intell. 27, 406-415 (2005).
[CrossRef] [PubMed]

S. K. Nayar and Y. Nakagawa, "Shape from focus: an effective approach for rough surfaces," IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
[CrossRef]

A. P. Pentland, "A new sense for depth of field," IEEE Trans. Pattern Anal. Mach. Intell. 9, 523-531 (1987).
[CrossRef] [PubMed]

J. Ens and P. Lawrence, "An investigation of methods for determining depth from focus," IEEE Trans. Pattern Anal. Mach. Intell. 15, 97-108 (1993).
[CrossRef]

Int. J. Comput. Vis. (4)

M. Watanabe and S. K. Nayar, "Rational filters for passive depth from defocus," Int. J. Comput. Vis. 27, 203-225 (1998).
[CrossRef]

A. N. Rajagopalan and S. Chaudhuri, "Performance analysis of maximum likelihood estimator for recovery of depth from defocused images and optimal selection of camera parameters," Int. J. Comput. Vis. 30, 175-190 (1998).
[CrossRef]

M. Subbarao and G. Surya, "Depth from defocus: a spatial domain approach," Int. J. Comput. Vis. 13, 271-294 (1994).
[CrossRef]

P. Favaro, A. Menucci, and S. Soatto, "Observing shape from defocused images," Int. J. Comput. Vis. 52, 25-43 (2003).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Laser Technol. (1)

O. Ghita and P. Whelan, "A video-rate sensor based on depth from defocus," Opt. Laser Technol. 33, 167-176 (2001).
[CrossRef]

Other (18)

W. J. Smith, Modern Lens Design (McGraw-Hill, 1992), pp. 43-49.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), pp. 395-397.

G. Arfken, Mathematical Methods for Physicists (Academic, 1985), pp. 573-636.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974).

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

F. Deschenes, D. Ziou, and P. Fuchs, "Simultaneous computation of defocus blur and apparent shifts in spatial domain," in Actes de 15th International Conference on Vision Interface (1992), pp. 236-243.

M. Subbarao and J. K. Tyan, "Noise sensitivity analysis of depth-from-defocus by a spatial-domain approach," Proc. SPIE 3174, 174-187 (1994).

Y. Schechner and N. Kiryati, "The optimal axial interval in estimating depth from defocus," in Proceedings of International Conference on Computer Vision (IEEE, 1993), pp. 843-848.

Y. Xiong and S. A. Shafer, "Depth from focusing and defocusing," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1993), pp. 68-73.
[CrossRef]

M. Baba, N. Asada, A. Oda, and T. Migita, "A thin lens based camera model for depth estimation from defocus and translation by zooming," in Proceedings of ICVI (2002), pp. 274-281.

A. P. Pentland, T. Darrel, M. Turk, and W. Huang, "A simple, real time range camera," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256-261.

A. N. Rajagopalan and S. Chaudhuri, "A block shift-variant blur model for recovering depth from defocused images," in Proceedings of International Conference on Image Processing (IEEE, 1995), pp. 636-639.
[CrossRef]

S. Soatto and P. Favaro, "A geometric approach to blind deconvolution with application to shape from defocus," in Proceedings of International Conference on Computer Vision and Pattern Recognition (IEEE, 2000), pp. 10-17.
[CrossRef]

D. Ziou, "Passive depth from defocus using spatial domain approach," in Proceedings of International Conference on Computer Vision (IEEE, 1998), pp. 799-804.

Y. Schechner and N. Kiryati, "Depth from defocus vs. stereo: how different really are they," in Proceedings of International Conference on Pattern Recognition (IEEE, 1998), pp. 1784-1786.

M. Noguchi and S. K. Nayar, "Microscopic shape from focus using active illumination," in Proceedings of International Conference on Pattern Recognition (IEEE, 1994), pp. 147-152.
[CrossRef]

M. Gokstorp, "Computing depth from out-of-focus blur using a local frequency representation," in Proceedings of International Conference on Pattern Recognition (IEEE, 1994), pp. 153-158.
[CrossRef]

H. Jin and P. Favarao, "A variational approach to shape from defocus," in Proceedings of European Conference on Computer Vision (2002), pp. 18-30.

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Figures (6)

Fig. 1
Fig. 1

Defocus spot size.

Fig. 2
Fig. 2

Overall blur kernel is formed by convolution of the optical, defocus, and sampling kernels.

Fig. 3
Fig. 3

Step on the sharp preimage, smoothed by the optics blur and further smoothed by defocus.

Fig. 4
Fig. 4

Ratio between the distinguishable defocus spot r d and the optics blur λ F as a function of the signal-to-noise ratio.

Fig. 5
Fig. 5

Steplike profile with different defocus blurs.

Fig. 6
Fig. 6

Difference between adjacent defocused images, as a function of defocus.

Tables (1)

Tables Icon

Table 1 Summary of Reviewed Depth-from-Defocus Publications (Lengths in Millimeters)

Equations (18)

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i ( x ) = h ( x ) s ( x ) + ϵ ( x ) ,
h ( x ) = ρ ( x s ) η ( s t ) μ ( t ) d s d t .
μ ( x ) = [ 2 J 1 ( γ ) γ ] 2 .
η ( x ) = { 1 π r d 2 , x r d 0 , x > r d } ,
r d = Δ l l D 2 = l L Δ L l D 2 = f 2 L 2 Δ L D l f 2 L 2 Δ L F .
1 l + 1 L = 1 f .
ρ ( x ) = { 1 Δ x 2 , max ( x 1 , x 2 ) Δ x 2 0 , otherwise } .
F ( μ ( x ) ) = { F 2 ( γ sin γ ) , u 2 + v 2 2 λ F 0 , u 2 + v 2 > 2 λ F } ,
F ( η ( x ) ) = L 2 F 2 π f 2 Δ L u 2 + v 2 J 1 ( 2 π f 2 Δ L L 2 F u 2 + v 2 )
F ( ρ ( x ) ) = 1 2 π 1 Δ x 2 sinc u Δ x 2 sinc v Δ x 2 .
F ( I ) = F ( ρ ( x ) ) F ( μ ( x ) ) F ( s ( x ) + ϵ 1 ( x ) ) ,
F ( J ) = F ( ρ ( x ) ) F ( η ( x ) ) F ( μ ( x ) ) F ( s ( x ) + ϵ 2 ( x ) ) .
ν η min { ν ρ , ν μ } ,
1 ν η max { 1 ν ρ , 1 ν μ } 1 ν η 1 ν ρ 2 + 1 ν μ 2 .
2 π f 2 Δ L min L 2 F ( Δ x 2 ) 2 + ( λ F 2 ) 2 ,
Δ L min L 2 F 2 π f 2 ( Δ x 2 ) 2 + ( λ F 2 ) 2 .
Δ L min L = L F 2 π f 2 ( Δ x 2 ) 2 + ( λ F 2 ) 2
F ( h 3 ( x , y ) ) = F ( i 2 ( x , y ) ) F ( i 1 ( x , y ) ) .

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