Abstract

A multiple-hypothesis method is used to detect a target or a reference signal in the presence of additive noise with unknown statistics. The receiver is designed to detect the target and to be tolerant of the variations in rotation and illumination of the target. A multiple-hypothesis test with unknown-noise parameters is used to locate the target position. The proposed method does not use any specific distortion-invariant-filtering technique, but it relies on a multiple-hypothesis approach. Maximum-likelihood estimates of the illumination constant and the unknown noise parameters are obtained. Computer simulations are presented to evaluate the performance of the receiver for various distorted noisy true-class targets with varying illumination and false-class objects.

© 2002 Optical Society of America

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References

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2000 (1)

1998 (3)

1995 (2)

1993 (2)

W. Li, N. M. Nasrabadi, “Invariant object recognition based on network of cascade RCE nets,” Int. J. Pattern Recognition and Artificial Intelligence, 7, 815–829 (1993).
[CrossRef]

B. Javidi, P. Réfrégier, P. Willett, “Optimum receiver design for pattern recognition with nonoverlapping target and scene noise,” Opt. Lett. 18, 1660–1664 (1993).
[CrossRef] [PubMed]

1990 (1)

1986 (1)

1984 (1)

1982 (1)

1980 (1)

1976 (1)

1969 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory, 19, 139–145 (1964).

1960 (1)

J. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory IT-6, 311–329 (1960).
[CrossRef]

Abu-Naser, A.

Arsenault, H. H.

Casasent, D.

Caulfield, H. J.

Chatwin, C. R.

Dalsgaard, E.

Duda, R. O.

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

Fukunaga, F.

F. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, New York, 1972).

Galatsanos, N. P.

Gianino, P. D.

Hart, P. E.

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

Haykin, S.

S. Haykin, Neural Networks: a Comprehensive Foundation (Prentice Hall, Englewood Cliffs, New Jersey1998).

Hester, C. F.

Horner, J. L.

Hsu, Y.-N.

Jamal-Aldin, L. S.

Javidi, B.

Kallman, R. R.

Lefebvre, D.

Li, W.

W. Li, N. M. Nasrabadi, “Invariant object recognition based on network of cascade RCE nets,” Int. J. Pattern Recognition and Artificial Intelligence, 7, 815–829 (1993).
[CrossRef]

Mahalanobis, A.

A. Mahalanobis, “Review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing; Critical Reviews of Optical Science Technology, B. Javidi, K. M. Johnson, eds., CR65, SPIE Press, 240–260 (1996).

A. Mahalanobis, “Processing of multi-sensor data using correlation filters,” Algorithms, Devices, and Systems for Optical Information Processing II, B. Javidi, D. Psaltis, eds., Proc. SPIE, 3466, 56–64 (1998).
[CrossRef]

Maloney, W. T.

McAulay, A. D.

A. D. McAulay, “Optical correlator for improving images distorted by atmospheric turbulence,” in Advances in Optical Information Processing IX, D. R. Pape, ed., Proc. SPIE, 4046, 41–47 (2000).
[CrossRef]

Nasrabadi, N. M.

W. Li, N. M. Nasrabadi, “Invariant object recognition based on network of cascade RCE nets,” Int. J. Pattern Recognition and Artificial Intelligence, 7, 815–829 (1993).
[CrossRef]

Psaltis, D.

Réfrégier, P.

Schonfeld, D.

Towghi, N.

Turin, J. L.

J. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory IT-6, 311–329 (1960).
[CrossRef]

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory, 19, 139–145 (1964).

Wang, J.

Wernick, M. N.

Willett, P.

Young, R. C. D.

Zi-Liang, P.

Appl. Opt. (8)

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory, 19, 139–145 (1964).

Int. J. Pattern Recognition and Artificial Intelligence (1)

W. Li, N. M. Nasrabadi, “Invariant object recognition based on network of cascade RCE nets,” Int. J. Pattern Recognition and Artificial Intelligence, 7, 815–829 (1993).
[CrossRef]

IRE Trans. Inf. Theory (1)

J. L. Turin, “An introduction to matched filters,” IRE Trans. Inf. Theory IT-6, 311–329 (1960).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Lett. (3)

Other (6)

A. D. McAulay, “Optical correlator for improving images distorted by atmospheric turbulence,” in Advances in Optical Information Processing IX, D. R. Pape, ed., Proc. SPIE, 4046, 41–47 (2000).
[CrossRef]

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

F. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, New York, 1972).

A. Mahalanobis, “Review of correlation filters and their application for scene matching,” in Optoelectronic Devices and Systems for Processing; Critical Reviews of Optical Science Technology, B. Javidi, K. M. Johnson, eds., CR65, SPIE Press, 240–260 (1996).

A. Mahalanobis, “Processing of multi-sensor data using correlation filters,” Algorithms, Devices, and Systems for Optical Information Processing II, B. Javidi, D. Psaltis, eds., Proc. SPIE, 3466, 56–64 (1998).
[CrossRef]

S. Haykin, Neural Networks: a Comprehensive Foundation (Prentice Hall, Englewood Cliffs, New Jersey1998).

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Figures (8)

Fig. 1
Fig. 1

Set of true-class training targets with different out-of-plane rotational distortions from 0 to 90 deg with increments of 10 deg. Zero deg (target No. 1) represents the front view of the car.

Fig. 2
Fig. 2

(a) Input scene used to generate the ROC curves with one true training target and a false object. The additive noise has a standard deviation of 0.8. (b) ROC of the proposed receiver compared with the matched filters by use of a true-class training target. (c) ROC of the proposed receiver compared with the matched filters by use of a true-class nontraining target.

Fig. 3
Fig. 3

(a) Untrained true-class target used in the simulations with a rotation angle of 25 degrees (referred as target No. 15). (b) False object.

Fig. 4
Fig. 4

(a) True-class training target with 10 deg out-of-plane rotation without illumination distortion, a true-class nontraining target with 25 deg out-of-plane rotation (target No. 15) without illumination distortion, and a false object. (b) Same scene with noise added with a mean of 0.5 and a standard deviation of 0.7. (c) Receiver output.

Fig. 5
Fig. 5

(a) True-class training target with 10 deg out-of-plane rotation and illumination distortion of 0.7, a true-class nontraining target with 25 deg out-of-plane rotation (target No. 15) and illumination distortion of 1.3, and a 100% illuminated false object. (b) Same scene with noise added with a mean of 0.5 and a standard deviation of 0.7. (c) Receiver output.

Fig. 6
Fig. 6

(a) True-class training target with 10 deg out-of-plane rotation and 1.3 illumination distortion, a true-class nontraining target with 25 deg out-of-plane rotation (target No. 15) and 0.7 illumination distortion, and a 100% illuminated false object. (b) Same scene with noise added with a mean of 0.5 and a standard deviation of 0.7. (c) Receiver output.

Fig. 7
Fig. 7

(a) True-class training target having 10 deg out-of-plane rotation, 1.2 illumination distortion, and down sampled by half; a true-class nontraining target having 25 deg. out-of-plane rotation (target No. 15), 0.8 illumination distortion, and down sampled by half; and a 100% illuminated false object. (b) Same scene with noise added with a mean of zero and a standard deviation of 0.5. (c) Receiver output.

Fig. 8
Fig. 8

(a) True-class training target with 10 deg out-of-plane rotation and 1.2 illumination distortion, a true class nontraining target with 25 deg out-of-plane rotation (target No. 15) and 0.8 illumination distortion, and a 100% illuminated false object. (b) Same scene with noise added with a mean of zero and a standard deviation of 0.5. (c) Receiver output with the illumination not considered.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

st=art-tj+nt.
Hj : st=art-tj+nt.
Hj : stm=artm-tj+ntm,
Hji : stm=aritm-tj+ntm, m1, M,
Pstm/Hj=1Ni=1N12πσ21/2 exp-stm-μ-aritm-tj2/2σ2,
Ps/Hj=m:wtm-tj=11Ni=1N12πσ21/2×exp-stm-μ-aritm-tj2/2σ2 ×m:wtm-tj=012πσ21/2 exp-stm-μ2/2σ2,
logPs/Hj=m:wtm-tj=1logi=1N12πσ2×exp-stm-μ-aritm-tj2/2σ2+m:wtm-tj=0log12πσ2exp-stm-μ2/2σ2.
Ps/Hja=0,
Ps/Hjμ=0,
Ps/Hjσ2=0.
âj=m=1Mi=1Nstm-μritm-tjwtm-tji=1N Ei,
Ei=m=1Mritmwitm2,
Ps/HjwO=m:wtm-tj=0log12πσ2×exp-stm-μ2/2σ2.
μˆj=1Ni=1Nm=1Mstm1-wtm-tjMio,
σˆj2=1Ni=1Nstm-μˆj2Mio.
âj=m=1Mi=1Nstm-1Nl=1Nn=1Mstn1-wtn-tjMloritm-tjwtm-tji=1N Ei.

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