Abstract

Recently, new approaches for location of a target in nonoverlapping noise, which are optimal in the maximum-likelihood sense, have been proposed. In particular, different methods for deterministic or fluctuating targets have been developed. We propose a unified and optimal processor for a target with either known or unknown gray levels. We demonstrate the efficiency and robustness of this method in comparison with previously developed processors.

© 1998 Optical Society of America

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References

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1996 (2)

1995 (1)

1993 (1)

1992 (1)

1989 (1)

1986 (1)

1964 (1)

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).

Arsenault, H.

Campos, J.

Casasent, D. P.

Duda, R. O.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), pp. 10–35.

Ferreira, H. C.

Goudail, F.

Hart, P. E.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), pp. 10–35.

Javidi, B.

Kober, V.

Laude, V.

Levesque, M. P.

Mahalanobis, A.

Réfrégier, Ph.

Szpolik, T.

VanderLugt, A.

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).

Vijaya Kumar, B. V. K.

Wang, J.

Willet, P.

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Figures (3)

Fig. 1
Fig. 1

(a) Target reference used in the tests. (b) Binary support of the target reference.

Fig. 2
Fig. 2

(a1) Scene image with a deterministic target. (a2) Scene image with a fluctuating target. (b1), (b2) Results of the processing of (a1) and (a2), respectively, with the new optimal processor for a deterministic or a fluctuating target. (c1), (c2) Results of the processing of (a1) and (a2), respectively, with the optimal processor for a deterministic target. (d1), (d2) Results of the processing of (a1) and (a2), respectively, with the optimal processor for a fluctuating target. NB: (b1), (c1), (d1), (b2), (c2), and (d2) are plots of the maximum of each line of the output plane of the method being considered.

Fig. 3
Fig. 3

Probabilities of correct location obtained with the optimal processors for (curve  a) a deterministic target, (curve b), a fluctuating target, and (curve c) a deterministic or a fluctuating target. The pdf parameters of the background are mb=151 and σb=30.7. The pdf parameters of the target are β=d, ma=1-d×151 and σa=1-d×12.8+26.9. d0, 1.

Equations (7)

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si=βri-δ0+aiwi-δ0+bi1-wi-δ0.
d=βmrma+βmr,
P[s|δ, β, ν]={i|wi-δ=1}Pasi-βri-δ{i|wi-δ=0}Pbsi.
L[s|δ, β, ν]=-w log σa-12σa2×{i|wi-δ=1}si-βri-δ-ma2-N-w log σb-12σb2{i|wi-δ=0}si-mb2.
β˜={i|wi-δ=1}siri-δ-mr/{i|wi=1}ri-mr2, m˜a=1w{i|wi-δ=1}si-β˜ri-δ, m˜b=1N-w{i|wi-δ-0}si, σ˜a2=1w{i|wi-δ=1}si-β˜ri-δ-m˜a2, σ˜b2=1N-w{i|wi-δ-0}si-m˜b2.
Fδ=-w log σ˜a2-N-w log σ˜b2.
σ˜a2=1ws2wδ-1w2swδ2-1wmrswδ-srδ2{i|wi=1}ri-mr2, σ˜b2=1N-wi=1Nsi2-s2wδ-1N-w2i=1Nsi-swδ2.

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