Abstract

Projection-onto-constraint sets is an efficient algorithm for constructing synthetic discriminant functions to be employed in pattern-recognition systems. The algorithm is implemented by a digital procedure based on a simulated joint-transform correlator.

© 1991 Optical Society of America

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References

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  1. J. P. Allebach, D. W. Sweeney, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 2 (1988).
  2. R. J. Marks, Appl. Opt. 26, 2005 (1987).
    [CrossRef]
  3. C. F. Hester, D. Casasent, Appl. Opt. 19, 1758 (1980).
    [CrossRef] [PubMed]
  4. R. R. Kallman, Appl. Opt. 25, 1032 (1986).
    [CrossRef] [PubMed]
  5. M. Fleisher, U. Mahlab, J. Shamir, Appl. Opt. 29, 2091 (1990).
    [CrossRef] [PubMed]
  6. D. C. Youla, H. Webb, IEEE Trans. Med. Imag. MI-1, 81 (1982).
    [CrossRef]
  7. C. S. Weaver, J. W. Goodman, Appl. Opt. 5, 1248 (1966).
    [CrossRef] [PubMed]

1990

1988

J. P. Allebach, D. W. Sweeney, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 2 (1988).

1987

1986

1982

D. C. Youla, H. Webb, IEEE Trans. Med. Imag. MI-1, 81 (1982).
[CrossRef]

1980

1966

Allebach, J. P.

J. P. Allebach, D. W. Sweeney, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 2 (1988).

Casasent, D.

Fleisher, M.

Goodman, J. W.

Hester, C. F.

Kallman, R. R.

Mahlab, U.

Marks, R. J.

Shamir, J.

Sweeney, D. W.

J. P. Allebach, D. W. Sweeney, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 2 (1988).

Weaver, C. S.

Webb, H.

D. C. Youla, H. Webb, IEEE Trans. Med. Imag. MI-1, 81 (1982).
[CrossRef]

Youla, D. C.

D. C. Youla, H. Webb, IEEE Trans. Med. Imag. MI-1, 81 (1982).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Various regions in the correlation plane to be operated on by the operator P1.

Fig. 2
Fig. 2

Block diagram of the POCS process (see the text for details). FT, Fourier transform; FT−1, inverse Fourier transform; PE, phase extractor; MF, minimum finder.

Fig. 3
Fig. 3

Input training set. (a) Patterns to be detected, (b) patterns to be rejected.

Fig. 4
Fig. 4

Output correlation planes (in arbitrary units). (a) After the first iteration, (b) after 60 iterations.

Equations (6)

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C 1 = { c ( x ) : c ( x ) T 1 if x R 1 ; c ( x ) T 2 if x R 3 } ,
P 1 [ c ( x ) ] = { T 1 if x R 1 and c ( x ) < T 1 T 2 if x R 3 and c ( x ) > T 2 c ( x ) otherwise .
c ( x ) = f ( x ) f ( x ) + h ( x ) h ( x ) + f ( x ) h ( x - 2 b ) + h ( x ) f ( x + 2 b ) ,
C 2 = { s ( x ) : s ( x ) = g ( x - b ) + h ( x + b ) ; h ( x ) R ; h ( x ) = 0 if x > ω h 2 } .
P 2 [ s ( x ) ] = { s ( x ) if ( - b - w h 2 ) < x < ( - b + w h 2 ) g ( x - b ) if x > 0 0 otherwise .
C 2 = { s ( x ) : s ( x ) = g ( x - b ) + h ( x + b ) ; h ( x ) { 0 , 1 } ; h ( x ) = 0 if x > w h 2 } .

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