Abstract

The normalization of the correlation filter response effects intensity invariance. We discuss the implications of a normalization based on the Cauchy–Schwarz inequality for the discrimination problem. It is shown that normalized phase-only and synthetic discriminant functions do not provide the discrimination/recognition obtained with the classical matched filter.

© 1991 Optical Society of America

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References

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  1. D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
    [Crossref]
  2. F. M. Dickey, B. V. K. V. Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
    [Crossref]
  3. B. V. K. V. Kumar, L. Hassebrook, Appl. Opt. 29, 2997 (1990).
    [Crossref] [PubMed]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, p. 179.
  5. N. Bleistein, R. A. Handelsman, Asymptotic Expansion of Integrals (Dover, New York, 1986), Chap. 3, p. 80.
  6. Z. Bahri, B. V. K. V. Kumar, J. Opt. Soc. Am. A 5, 562 (1988).
    [Crossref]

1990 (2)

F. M. Dickey, B. V. K. V. Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[Crossref]

B. V. K. V. Kumar, L. Hassebrook, Appl. Opt. 29, 2997 (1990).
[Crossref] [PubMed]

1989 (1)

D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
[Crossref]

1988 (1)

Bahri, Z.

Bleistein, N.

N. Bleistein, R. A. Handelsman, Asymptotic Expansion of Integrals (Dover, New York, 1986), Chap. 3, p. 80.

Connelly, J. M.

F. M. Dickey, B. V. K. V. Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[Crossref]

Dickey, F. M.

F. M. Dickey, B. V. K. V. Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[Crossref]

Flannery, D. L.

D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, p. 179.

Handelsman, R. A.

N. Bleistein, R. A. Handelsman, Asymptotic Expansion of Integrals (Dover, New York, 1986), Chap. 3, p. 80.

Hassebrook, L.

Horner, J. L.

D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
[Crossref]

Kumar, B. V. K. V.

Romero, L. A.

F. M. Dickey, B. V. K. V. Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[Crossref]

Appl. Opt. (1)

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

Opt. Eng. (1)

F. M. Dickey, B. V. K. V. Kumar, L. A. Romero, J. M. Connelly, Opt. Eng. 29, 994 (1990).
[Crossref]

Proc. IEEE (1)

D. L. Flannery, J. L. Horner, Proc. IEEE 77, 1511 (1989).
[Crossref]

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 7, p. 179.

N. Bleistein, R. A. Handelsman, Asymptotic Expansion of Integrals (Dover, New York, 1986), Chap. 3, p. 80.

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Equations (17)

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c ( y x 0 ) = | h * ( x ) S h ( x ) f ( x + y x 0 ) d x | 2 ,
S h ( x ) = { 1 x support of h ( x ) 0 otherwise ,
S h ( x ) h ( x ) = h ( x ) ,
S h 2 ( x ) = S h ( x ) .
c ( y x 0 ) | f ( x + y x 0 ) | 2 S h ( x ) d x | h ( x ) | 2 d x .
c ˆ ( y x 0 ) = | h * ( x ) f ( x + y x 0 ) d x | 2 | f ( x + y x 0 ) | 2 S h ( x ) d x | h ( x ) | 2 d x 1 .
h ( x ) = λ f ( x ) S h ( x ) .
c ˆ ( y x 0 ) = | H * ( ν ) F ( ν ) exp [ i 2 π ν ( y x 0 ) ] d ν | 2 [ F ( ν ) F ( ν ) ] * S ˜ h ( ν ) exp [ i 2 π ν ( y x 0 ) ] d ν | H ( ν ) | 2 d ν ,
H * ( ν ) = F * ( ν ) | F ( ν ) | , ν Ω ,
c ˆ ( 0 ) = [ Ω | F ( ν ) | d ν ] 2 B Ω [ F ( ν ) F ( ν ) ] * S ˜ h ( ν ) d ν .
B = Ω d ν
| F ( ν ) | = 0 ( 1 / ν ) as ν ± .
c ˆ ( 0 ) 0 as B .
| h * ( x ) f i ( x ) d x | 2 = 1
f i * ( x ) f j ( x ) d x = δ i j | f i ( x ) | 2 d x
h ( x ) = i α i f i ( x ) f i ( x ) 2 + ϕ ( x ) ,
c ˆ ( 0 ) = 1 [ k = 1 N 1 f k ( x ) 2 + ϕ ( x ) 2 ] f i ( x ) 2 1 N max k , j f i ( x ) 2 f k ( x ) 2 .

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