Abstract

This paper explains the use of a sharpening filter to calculate the depth of an object from a blurred image of it. It presents a technique which is independent of edge orientation. The technique is based on the assumption that a defocused image of an object is the convolution of a sharp image of the same object with a two-dimensional Gaussian function whose spread parameter (SP) is related to the object depth. A sharp image of an object is obtained from a defocused image of the same object by applying sharpening filters. The defocused and sharp images of the object are used to calculate the SP which is then related to the object depth. The paper gives experimental results which show the feasibility of employing sharpening filters for depth computation.

© 2007 Optical Society of America

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References

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  1. M. Hebert, "Active and passive range sensing for robotics," in Proceedings of IEEE Conference on Robotics and Automation, (Institute of Electrical and Electronics Engineers, San Francisco, CA, 2000), pp. 102-110.
  2. P. Grossmann, "Depth from focus," Pattern Recogn. Lett. 5, 63-69 (1987).
    [CrossRef]
  3. A. P. Pentland, "A new sense for depth of field," IEEE Trans. Pattern Anal. Mach. Intell. 9, 523-531 (1987).
    [CrossRef] [PubMed]
  4. M. Subbarao and N. Gurumoorthy, "Depth recovery from blurred edges," in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, (Institute of Electrical and Electronics Engineers, Ann Arbor, MI, 1988), pp. 498-503.
  5. M. Subbarao, "Efficient depth recovery through inverse optics," Machine Vision Inspection and Measurement, H. Freeman, ed., (Academic, Boston, 1989).
  6. C. Cardillo and M. A. Sid-Ahmed, "3-D position sensing using passive monocular vision system," IEEE Trans. Pattern Anal. Mach. Intell. 13, 809-813 (1991).
    [CrossRef]
  7. R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth perception using blurring and its application in VLSI wafer probing," Mach. Vision Appl. 5, 35-45 (1992).
    [CrossRef]
  8. S. H. Lai, C. W. Fu, and S. Chang, "A generalised depth estimation algorithm with a single image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
    [CrossRef]
  9. D. T. Pham and V. Aslantas, "Depth from defocusing using a neural network," J. Pattern Recogn. 32, 715-727 (1999).
    [CrossRef]
  10. V. Aslantas, "Estimation of depth from defocusing using a neural network," in International Conference on Signal Processing, (Canakkale, Turkey, 2003), pp. 305-309.
  11. B. K. P. Horn, Robot vision (McGraw-Hill, New York, 1986).
  12. V. Aslantas and D. T. Pham, "Depth from automatic defocusing" Opt. Express 15, 1011-1023 (2007).
    [CrossRef] [PubMed]
  13. R. C. Gonzalez, and R. E. Woods, Digital image processing (Addison-Wesley, Reading, MA 1992).
  14. A. Rosenfeld and C. Kak, Digital picture processing, Second Edition, (Academic Press, New York 1982).

2007

1999

D. T. Pham and V. Aslantas, "Depth from defocusing using a neural network," J. Pattern Recogn. 32, 715-727 (1999).
[CrossRef]

1992

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth perception using blurring and its application in VLSI wafer probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

S. H. Lai, C. W. Fu, and S. Chang, "A generalised depth estimation algorithm with a single image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
[CrossRef]

1991

C. Cardillo and M. A. Sid-Ahmed, "3-D position sensing using passive monocular vision system," IEEE Trans. Pattern Anal. Mach. Intell. 13, 809-813 (1991).
[CrossRef]

1987

P. Grossmann, "Depth from focus," Pattern Recogn. Lett. 5, 63-69 (1987).
[CrossRef]

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

Al-Khalili, A. J.

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth perception using blurring and its application in VLSI wafer probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

Aslantas, V.

V. Aslantas and D. T. Pham, "Depth from automatic defocusing" Opt. Express 15, 1011-1023 (2007).
[CrossRef] [PubMed]

D. T. Pham and V. Aslantas, "Depth from defocusing using a neural network," J. Pattern Recogn. 32, 715-727 (1999).
[CrossRef]

Cardillo, C.

C. Cardillo and M. A. Sid-Ahmed, "3-D position sensing using passive monocular vision system," IEEE Trans. Pattern Anal. Mach. Intell. 13, 809-813 (1991).
[CrossRef]

Chang, S.

S. H. Lai, C. W. Fu, and S. Chang, "A generalised depth estimation algorithm with a single image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
[CrossRef]

Dantu, R. V.

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth perception using blurring and its application in VLSI wafer probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

Dimopoulos, N. J.

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth perception using blurring and its application in VLSI wafer probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

Fu, C. W.

S. H. Lai, C. W. Fu, and S. Chang, "A generalised depth estimation algorithm with a single image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
[CrossRef]

Grossmann, P.

P. Grossmann, "Depth from focus," Pattern Recogn. Lett. 5, 63-69 (1987).
[CrossRef]

Lai, S. H.

S. H. Lai, C. W. Fu, and S. Chang, "A generalised depth estimation algorithm with a single image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
[CrossRef]

Patel, R. V.

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth perception using blurring and its application in VLSI wafer probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

Pentland, A. P.

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

Pham, D. T.

V. Aslantas and D. T. Pham, "Depth from automatic defocusing" Opt. Express 15, 1011-1023 (2007).
[CrossRef] [PubMed]

D. T. Pham and V. Aslantas, "Depth from defocusing using a neural network," J. Pattern Recogn. 32, 715-727 (1999).
[CrossRef]

Sid-Ahmed, M. A.

C. Cardillo and M. A. Sid-Ahmed, "3-D position sensing using passive monocular vision system," IEEE Trans. Pattern Anal. Mach. Intell. 13, 809-813 (1991).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

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

S. H. Lai, C. W. Fu, and S. Chang, "A generalised depth estimation algorithm with a single image," IEEE Trans. Pattern Anal. Mach. Intell. 14, 405-411 (1992).
[CrossRef]

C. Cardillo and M. A. Sid-Ahmed, "3-D position sensing using passive monocular vision system," IEEE Trans. Pattern Anal. Mach. Intell. 13, 809-813 (1991).
[CrossRef]

J. Pattern Recogn.

D. T. Pham and V. Aslantas, "Depth from defocusing using a neural network," J. Pattern Recogn. 32, 715-727 (1999).
[CrossRef]

Mach. Vision Appl.

R. V. Dantu, N. J. Dimopoulos, R. V. Patel, and A. J. Al-Khalili, "Depth perception using blurring and its application in VLSI wafer probing," Mach. Vision Appl. 5, 35-45 (1992).
[CrossRef]

Opt. Express

Pattern Recogn. Lett.

P. Grossmann, "Depth from focus," Pattern Recogn. Lett. 5, 63-69 (1987).
[CrossRef]

Other

M. Hebert, "Active and passive range sensing for robotics," in Proceedings of IEEE Conference on Robotics and Automation, (Institute of Electrical and Electronics Engineers, San Francisco, CA, 2000), pp. 102-110.

M. Subbarao and N. Gurumoorthy, "Depth recovery from blurred edges," in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, (Institute of Electrical and Electronics Engineers, Ann Arbor, MI, 1988), pp. 498-503.

M. Subbarao, "Efficient depth recovery through inverse optics," Machine Vision Inspection and Measurement, H. Freeman, ed., (Academic, Boston, 1989).

V. Aslantas, "Estimation of depth from defocusing using a neural network," in International Conference on Signal Processing, (Canakkale, Turkey, 2003), pp. 305-309.

B. K. P. Horn, Robot vision (McGraw-Hill, New York, 1986).

R. C. Gonzalez, and R. E. Woods, Digital image processing (Addison-Wesley, Reading, MA 1992).

A. Rosenfeld and C. Kak, Digital picture processing, Second Edition, (Academic Press, New York 1982).

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Figures (3)

Fig. 1.
Fig. 1.

Basic image formation geometry

Fig. 2.
Fig. 2.

Pictures of blurred step edge

Fig. 3.
Fig. 3.

Estimated a) σ b) depth

Equations (19)

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

i x y = h ( x ξ , y η , d ξ η ) s ξ η dξdη
i x y = h x ξ y η s ξ η dξdη
i x y = h x y s x y
I u v = H u v S u v
h x y = exp ( ( x 2 + y 2 ) ( 2 σ 2 ) ) ( 2 πσ 2 )
R =
H u v = exp ( ( u 2 + v 2 ) σ 2 2 )
σ 2 = 2 In ( I u v S u v ) ( u 2 + v 2 )
σ 2 = 2 A ∫∫ R 1 ( u 2 + v 2 ) ln ( I u v S u v ) dudv
D OL = FD LS D LS F 2 fkσ
D OL = FD LS D LS F + 2 fkσ
2 i = 2 i x 2 + 2 i y 2
i t = c∇ 2 i
i x y , 0 = i x y , τ τ i t x y , τ + τ 2 2 2 i t 2 x y , τ
s x y = i x y 2 i x y
S x y h x y = ( i x y σ 2 i x y ) h x y
i x y = ( i x y σ 2 i x y ) h x y
min P [ i x y ( 1 h x y ) + σ 2 i x y h x y ] 2
D OL = 35.1 σ 2 + 100.24 σ + 562.61

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