Abstract

We show that the Hough transform filter can be obtained easily by use of rotational multiplexing. To demonstrate our method experimentally, we recorded the Hough transform filter for 18 discrete projection angles and compared experimental transform results with simulated ones for a few input patterns.

© 1998 Optical Society of America

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References

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  1. R. D. Duda, P. E. Hart, “Use of the Hough transform to detect lines and curves of space-variant holographic filters,” Commun. ACM 15, 11–15 (1972).
    [CrossRef]
  2. L. Feng, Y. Fainman, “Detection of a general ellipse by an optical Hough transform,” Appl. Opt. 31, 3259–3262 (1992).
    [CrossRef] [PubMed]
  3. W. H. Steier, R. K. Shori, “Optical Hough transform,” Appl. Opt. 25, 2734–2738 (1986).
    [CrossRef] [PubMed]
  4. G. Eichmann, B. Z. Dong, “Coherent optical production of the Hough transform,” Appl. Opt. 22, 3641–3648 (1987).
  5. P. Ambs, S. H. Lee, Q. Tian, Y. Fainman, “Optical implementation of the Hough transform by a matrix of holograms,” Appl. Opt. 25, 4039–4045 (1986).
    [CrossRef] [PubMed]
  6. K. Mori, R. Ohba, “Optical Hough-transform processor with a two-dimensional array of computer-generated holograms,” Appl. Opt. 33, 3111–3117 (1994).
    [CrossRef] [PubMed]
  7. J. Richards, P. Vermeulen, E. Barnard, D. P. Casasent, “Parallel holographic generation of multiple Hough transform slices,” Appl. Opt. 27, 4540–4545 (1988).
    [CrossRef] [PubMed]
  8. K. Curtis, A. Pu, D. Psaltis, “Method for holographic storage using peristrophic multiplexing,” Opt. Lett. 19, 993–994 (1994).
    [CrossRef] [PubMed]
  9. J.-S. Jang, D.-H. Shin, “Parallel optical-feature extraction by use of rotationally multiplexed holograms,” Opt. Lett. 21, 1612–1614 (1996).
    [CrossRef] [PubMed]
  10. J.-S. Jang, D.-H. Shin, “Shift- and deformation-robust optical character recognition based on parallel extraction of simple features,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 265–276 (1997).
    [CrossRef]
  11. A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
    [CrossRef]

1996

J.-S. Jang, D.-H. Shin, “Parallel optical-feature extraction by use of rotationally multiplexed holograms,” Opt. Lett. 21, 1612–1614 (1996).
[CrossRef] [PubMed]

A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
[CrossRef]

1994

1992

1988

1987

G. Eichmann, B. Z. Dong, “Coherent optical production of the Hough transform,” Appl. Opt. 22, 3641–3648 (1987).

1986

1972

R. D. Duda, P. E. Hart, “Use of the Hough transform to detect lines and curves of space-variant holographic filters,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Ambs, P.

Barnard, E.

Casasent, D. P.

Curtis, K.

A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
[CrossRef]

K. Curtis, A. Pu, D. Psaltis, “Method for holographic storage using peristrophic multiplexing,” Opt. Lett. 19, 993–994 (1994).
[CrossRef] [PubMed]

Dong, B. Z.

G. Eichmann, B. Z. Dong, “Coherent optical production of the Hough transform,” Appl. Opt. 22, 3641–3648 (1987).

Duda, R. D.

R. D. Duda, P. E. Hart, “Use of the Hough transform to detect lines and curves of space-variant holographic filters,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Eichmann, G.

G. Eichmann, B. Z. Dong, “Coherent optical production of the Hough transform,” Appl. Opt. 22, 3641–3648 (1987).

Fainman, Y.

Feng, L.

Hart, P. E.

R. D. Duda, P. E. Hart, “Use of the Hough transform to detect lines and curves of space-variant holographic filters,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Jang, J.-S.

J.-S. Jang, D.-H. Shin, “Parallel optical-feature extraction by use of rotationally multiplexed holograms,” Opt. Lett. 21, 1612–1614 (1996).
[CrossRef] [PubMed]

J.-S. Jang, D.-H. Shin, “Shift- and deformation-robust optical character recognition based on parallel extraction of simple features,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 265–276 (1997).
[CrossRef]

Lee, S. H.

Mori, K.

Ohba, R.

Psaltis, D.

A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
[CrossRef]

K. Curtis, A. Pu, D. Psaltis, “Method for holographic storage using peristrophic multiplexing,” Opt. Lett. 19, 993–994 (1994).
[CrossRef] [PubMed]

Pu, A.

A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
[CrossRef]

K. Curtis, A. Pu, D. Psaltis, “Method for holographic storage using peristrophic multiplexing,” Opt. Lett. 19, 993–994 (1994).
[CrossRef] [PubMed]

Richards, J.

Shin, D.-H.

J.-S. Jang, D.-H. Shin, “Parallel optical-feature extraction by use of rotationally multiplexed holograms,” Opt. Lett. 21, 1612–1614 (1996).
[CrossRef] [PubMed]

J.-S. Jang, D.-H. Shin, “Shift- and deformation-robust optical character recognition based on parallel extraction of simple features,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 265–276 (1997).
[CrossRef]

Shori, R. K.

Steier, W. H.

Tian, Q.

Vermeulen, P.

Appl. Opt.

Commun. ACM

R. D. Duda, P. E. Hart, “Use of the Hough transform to detect lines and curves of space-variant holographic filters,” Commun. ACM 15, 11–15 (1972).
[CrossRef]

Opt. Eng.

A. Pu, K. Curtis, D. Psaltis, “Exposure schedule for multiplexing holograms in photopolymer films,” Opt. Eng. 35, 2824–2829 (1996).
[CrossRef]

Opt. Lett.

Other

J.-S. Jang, D.-H. Shin, “Shift- and deformation-robust optical character recognition based on parallel extraction of simple features,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 265–276 (1997).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Optical setup for recording the HT filter by use of rotational multiplexing. (b) Method for obtaining the result of the HT with the recorded filter. PF, photopolymer film; R, reference.

Fig. 2
Fig. 2

(a) Experimental results for the case of plane-wave input. The zeroth-order beam was blocked. (b) Enlargement of the results of 18 holograms |c i (ρ, θ i )|2 detected one by one by a CCD camera. (c) Diffraction efficiencies of the holograms for each projection angle.

Fig. 3
Fig. 3

Experimental results for some patterns. (a), (d) Input patterns. (b), (e) Experimental results. (c), (f) Simulation results.

Fig. 4
Fig. 4

Compensation process for the nonuniformity of the diffracted beam for obtaining more precise results. (a) The intensity distribution of Fig. 3(e) when θ i = 0°. (b) The intensity distribution |β i (ρ)|2 of Fig. 2(b) when θ i = 0°. (c) The compensated result with Eq. (4) for all θ i .

Equations (5)

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c i x ,   y =   h i * u - x ,   v - y f u ,   v d u d v ,
c i x ,   y =   δ x   cos   θ i + y   sin   θ i - u   cos   θ i - v   sin   θ i f u ,   v d u d v ,
c i ρ ,   θ i =   δ ρ - u   cos   θ i - v   sin   θ i f u ,   v d u d v .
| c i ρ ,   θ i | 2 = α i | β i ρ | 2 - 1 | c i ρ ,   θ i | 2 .
F i a ,   b ,   r i =   δ x - a 2 + y - b 2 - r i 2 × f x ,   y d x d y ,

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