Abstract

Various metrics used to measure correlation filter performance are discussed. Their similarities and deficiencies are noted, and modifications are suggested. A computer simulation is included to highlight these differences.

© 1992 Optical Society of America

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References

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  1. B. V. K. Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef] [PubMed]
  2. F. M. Dickey, L. A. Romero, “Dual optimality of the phase-only filter,” Opt. Lett. 14, 4–5 (1989).
    [CrossRef] [PubMed]
  3. H. J. Caulfield, “Role of the Horner efficiency in the optimization of spatial filters for optical pattern recognition,” Appl. Opt. 21, 4391–4392 (1982).
    [CrossRef] [PubMed]
  4. J. L. Horner, H. O. Bartelt, “Two-bit correlation,” Appl. Opt. 24, 2889–2893 (1985).
    [CrossRef] [PubMed]
  5. When a mathematical delta function (unit area and peak approaching infinity) is used, the PCE can vary from zero to infinity. When a signal of a finite area and height is used, the PCE varies from zero to one. The latter is the more practical since it is representative of real, sampled data.
  6. K. H. Fielding, J. L. Horner, “Clutter effects in optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 130–137 (1990).
  7. This is sometimes referred to as a signal-to-clutter ratio (SCR). I would propose calling it peak-to-secondary ratio because the word clutter is used in many different ways and begs definition. Peak-to-secondary is immediately obvious and requires no further definition.

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When a mathematical delta function (unit area and peak approaching infinity) is used, the PCE can vary from zero to infinity. When a signal of a finite area and height is used, the PCE varies from zero to one. The latter is the more practical since it is representative of real, sampled data.

K. H. Fielding, J. L. Horner, “Clutter effects in optical correlators,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1151, 130–137 (1990).

This is sometimes referred to as a signal-to-clutter ratio (SCR). I would propose calling it peak-to-secondary ratio because the word clutter is used in many different ways and begs definition. Peak-to-secondary is immediately obvious and requires no further definition.

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Tables (2)

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Table I Phase-Only Filter

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Table II Matched Filter

Equations (11)

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PCE = C ( ϕ ) 2 / i C ( x i ) 2 ,
η H = C ( ϕ ) 2 / i s ( x i ) 2 ,
SNR 1 = C ( ϕ ) / [ 1 N i C ( x i > FWHM ) 2 ] 1 / 2 ,
PCE = SNR 1 / ( SNR 1 + N ) .
PCE = η H .
SNR i = E 2 [ C ( ϕ ) ] / VAR [ C ( ϕ ) ] ,
SNR in = E [ s ( x ) ] / σ [ n ( x ) ] ,
PC E = C ( ϕ ) / [ 1 N i C ( x i 0 ) 2 ] 1 / 2 ,
C ( x ) = C ( x ) E [ C ( x ) ] .
PC E = C ( ϕ ) / [ 1 N i C ( x i 0 ) 2 ] 1 / 2 ,
PC E = PCE / ( 1 PCE ) .

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