## 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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### Equations (11)

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(1)
$$\text{PCE}={{C}_{(\varphi )}}^{2}/{\displaystyle \sum _{i}{{C}_{\left({x}_{i}\right)}}^{2}},$$
(2)
$${\eta}_{H}={{C}_{(\varphi )}}^{2}/{\displaystyle \sum _{i}{{s}_{\left({x}_{i}\right)}}^{2}},$$
(3)
$${\text{SNR}}_{1}={C}_{(\varphi )}/{\left[\frac{1}{N}{\displaystyle \sum _{i}{{C}_{\left({x}_{i}>\text{FWHM}\right)}}^{2}}\right]}^{1/2},$$
(4)
$$\text{PCE}={\text{SNR}}_{1}/\left({\text{SNR}}_{1}+N\right).$$
(5)
$$\text{PCE}={\eta}_{H}.$$
(6)
$${\text{SNR}}_{i}={E}^{2}\left[{C}_{(\varphi )}\right]/\text{VAR}\left[{C}_{(\varphi )}\right],$$
(7)
$${\text{SNR}}_{\text{in}}=E\left[{s}_{\left(x\right)}\right]/{\sigma}_{\left[n\left(x\right)\right]},$$
(8)
$$\text{PC}{\mathrm{E}}^{\prime}={{{C}_{(\varphi )}}^{\prime}/\left[\frac{1}{N}{\displaystyle \sum _{i}{{C}_{\left({x}_{i}\ne 0\right)}}^{\prime 2}}\right]}^{1/2},$$
(9)
$${{C}_{\left(x\right)}}^{\prime}={C}_{\left(x\right)}-E\left[{C}_{\left(x\right)}\right].$$
(10)
$$\text{PC}{\mathrm{E}}^{\u2033}={{C}_{(\varphi )}/\left[\frac{1}{N}{\displaystyle \sum _{i}{{C}_{\left({x}_{i}\ne 0\right)}}^{2}}\right]}^{1/2},$$
(11)
$$\text{PC}{\mathrm{E}}^{\u2033}=\text{PCE}/\left(1-\text{PCE}\right).$$