Abstract

A simulated annealing algorithm is introduced to encode binary phase-only filters optimally for image recognition. Similar patterns that cannot be distinguished with conventional filter encoding methods are clearly distinguished with the optimized filter. The computational requirements for optimizing the filter are not excessive.

© 1989 Optical Society of America

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References

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  1. J. L. Horner, P. D. Gianino, Appl. Opt. 23, 812 (1984).
    [CrossRef] [PubMed]
  2. M. W. Farn, J. W. Goodman, Appl. Opt. 27, 4431 (1988).
    [CrossRef] [PubMed]
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    [CrossRef]
  4. J. L. Horner, H. O. Bartelt, Appl. Opt. 24, 2889 (1985).
    [CrossRef] [PubMed]
  5. D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).
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    [CrossRef] [PubMed]
  7. H. Szu, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312 (1986).
  8. M. R. Feldman, C. C. Guest, Opt. Lett. 14, 479 (1989).
    [CrossRef] [PubMed]

1989 (1)

1988 (1)

1987 (1)

1986 (1)

H. Szu, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312 (1986).

1985 (1)

1984 (2)

J. L. Horner, P. D. Gianino, Appl. Opt. 23, 812 (1984).
[CrossRef] [PubMed]

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

1983 (1)

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Allebach, J. P.

Bartelt, H. O.

Farn, M. W.

Feldman, M. R.

Gelatt, C. D.

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Gianino, P. D.

Goodman, J. W.

Guest, C. C.

Horner, J. L.

Kirpatrick, S.

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Seldowitz, M. S.

Sweeney, D. W.

Szu, H.

H. Szu, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312 (1986).

Vecchi, M. P.

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Appl. Opt. (4)

Opt. Eng. (1)

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

H. Szu, Proc. Soc. Photo-Opt. Instrum. Eng. 634, 312 (1986).

Science (1)

S. Kirpatrick, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Input characters to be distinguished. (b) The characters reconstructed from the BPOF.

Fig. 2
Fig. 2

Correlation of the BPOF with P as the input.

Fig. 3
Fig. 3

Correlation of the OBPOF with P as the input.

Fig. 4
Fig. 4

(a) Characters reconstructed from the OBPOF. (b) The phase ϕ versus the temperature parameter.

Tables (1)

Tables Icon

Table 1 Performance Comparison of Three Types of Correlation Filters

Equations (20)

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F ̂ ( u , υ ) = 1 for Re [ F ( u , υ ) ] > 0 , F ̂ ( u , υ ) = 1 otherwise
F ̂ ( u , υ ) = 1 for Im [ F ( u , υ ) ] 0 , F ̂ ( u , υ ) = 1 otherwise ,
F ̂ ( u , υ ) = [ 1 exp ( j ϕ ) ] B ( u , υ ) + exp ( j ϕ ) ,
F ̂ ( u , υ ) = 1 for B ( u , υ ) = 1 = exp ( j ϕ ) for B ( u , υ ) = 0 .
G ( u , υ ) = [ 1 exp ( j ϕ ) ] B ( u , υ ) A ( u , υ ) + exp ( j ϕ ) A ( u , υ ) ,
G ( u , υ ) = [ 1 exp ( j ϕ ) ] k = K / 2 K / 2 l = L / 2 L / 2 B k l A k l × rect ( u k Δ u Δ u , υ l Δ υ Δ υ ) + exp ( j ϕ ) k = K / 2 K / 2 l = L / 2 L / 2 A k l × rect ( u k Δ u Δ u , υ l Δ υ Δ υ ) ,
g ( x , y ) = [ 1 exp ( j ϕ ) ] C g ˜ ( x , y ) + exp ( j ϕ ) C a ˜ ( x , y ) ,
C = Δ u Δ υ sinc ( x Δ u , y Δ υ ) ,
g ˜ ( x , y ) = k l B k l A k l exp [ 2 π j ( k x Δ u + l y Δ υ ) ] ,
a ˜ ( x , y ) = k l A k l exp [ 2 π j ( k x Δ u + l y Δ υ ) ] ,
g ( m Δ x , n Δ y ) = [ 1 exp ( j ϕ ) ] C g ˜ m n + exp ( j ϕ ) C a ˜ m n ,
g ˜ m n = k l B k l A k l exp [ 2 π j ( k m / K + l n / L ) ] ,
a ˜ m n = k l A k l exp [ 2 π j ( k m / K + l n / L ) ] .
g m n = [ 1 exp ( j ϕ ) ] g ˜ m n + exp ( j ϕ ) a ˜ m n ,
Δ E = E new E old ,
P ( Δ E ) = 1 1 + exp ( Δ E / T ) ,
E = ( H A A C [ P , P ] ) 2 + ( H A A C [ R , R ] ) 2 + ( H C C C [ P , R ] ) 2 + ( H C C C [ R , P ] ) 2 ,
g ˜ m n new = g ˜ m n old A k l exp [ 2 π j ( m k / K + n l / L ) ] .
g ˜ m n new = g ˜ m n old + A k l exp [ 2 π j ( m k / K + n l / L ) ] .
T = ( D T ) r T initial and D T = ( T final / T initial ) 1 / q ,

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