Abstract

The task of detection of objects composed of several regions by means of statistical filters is analyzed. The target is assumed to have different unknown mean values in each of its regions. The detection is based on likelihood estimation, after performing an estimation of the actual configuration of the mean values in the target region. A simplified filter that reduces the computational complexity is also proposed. The statistical performance is analyzed theoretically and tested in computer experiments.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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  24. J. Rissanen, Stochastic Complexity in Statistical Inquiry (World Scientific, Singapore, 1989).
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2001

2000

P. Garcı́a-Martinez, H. H. Arsenault, S. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for images degraded by nonoverlapping background noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

1999

1998

1997

1996

D. Prévost, Ph. Lalanne, J. C. Rodier, P. Chavel, “Video-rate simulated annealing for stochastic artificial retinas,” Opt. Commun. 132, 427–431 (1996).
[CrossRef]

F. Goudail, P. Réfrégier, “Optimal detection of a target with random gray levels on a spatially disjoint noise,” Opt. Lett. 21, 495–497 (1996).
[CrossRef] [PubMed]

1995

1994

1993

1989

1964

A. VanderLugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

1960

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

Arsenault, H. H.

P. Garcı́a-Martinez, H. H. Arsenault, S. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for images degraded by nonoverlapping background noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

Casasent, D. P.

Chavel, P.

D. Prévost, Ph. Lalanne, J. C. Rodier, P. Chavel, “Video-rate simulated annealing for stochastic artificial retinas,” Opt. Commun. 132, 427–431 (1996).
[CrossRef]

Chesnaud, C.

P. Réfrégier, F. Goudail, C. Chesnaud, “Statistically independent region models applied to correlation and segmentation techniques,” in 1999 Euro-American Workshop on Optoelectronic Information Processing, Ph. Réfrégier, B. Javidi, eds., Vol. CR74 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1999), pp. 193–224.

Duda, R. O.

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

Evans, M.

M. Evans, N. Hastings, B. Peacock, Statistical Distributions (Wiley, New York, 1993).

Fazlolahi, A.

Fazlollahi, A. H.

Ferreira, C.

Garci´a, J.

Garci´a-Martinez, P.

P. Garcı́a-Martinez, H. H. Arsenault, S. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for images degraded by nonoverlapping background noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

P. Garcı́a-Martinez, D. Mas, J. Garcı́a, C. Ferreira, “Nonlinear morphological correlation: optoelectronic implementation,” Appl. Opt. 37, 2112–2118 (1998).
[CrossRef]

Garthwaite, P. H.

P. H. Garthwaite, I. T. Jolliffe, B. Jones, Statistical Inference (Prentice-Hall, London, 1995).

Goudail, F.

Guérault, F.

Hart, P. E.

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

Hastings, N.

M. Evans, N. Hastings, B. Peacock, Statistical Distributions (Wiley, New York, 1993).

Hereford, J. M.

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time-sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1998).

Horner, J-L.

Ishiguro, M.

Y. Sakamoto, M. Ishiguro, G. Kitagawa, Akaike Information Criterion Statistics (KTK Scientific, Tokyo1986).

Javidi, B.

Jolliffe, I. T.

P. H. Garthwaite, I. T. Jolliffe, B. Jones, Statistical Inference (Prentice-Hall, London, 1995).

Jones, B.

P. H. Garthwaite, I. T. Jolliffe, B. Jones, Statistical Inference (Prentice-Hall, London, 1995).

Kitagawa, G.

Y. Sakamoto, M. Ishiguro, G. Kitagawa, Akaike Information Criterion Statistics (KTK Scientific, Tokyo1986).

Lalanne, Ph.

D. Prévost, Ph. Lalanne, J. C. Rodier, P. Chavel, “Video-rate simulated annealing for stochastic artificial retinas,” Opt. Commun. 132, 427–431 (1996).
[CrossRef]

Li, J.

Mahalanobis, A.

Mas, D.

Oliver, C.

C. Oliver, S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Norwood, Mass., 1998).

Pagé, V.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, Boston1991).

Peacock, B.

M. Evans, N. Hastings, B. Peacock, Statistical Distributions (Wiley, New York, 1993).

Prévost, D.

D. Prévost, Ph. Lalanne, J. C. Rodier, P. Chavel, “Video-rate simulated annealing for stochastic artificial retinas,” Opt. Commun. 132, 427–431 (1996).
[CrossRef]

Quegan, S.

C. Oliver, S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Norwood, Mass., 1998).

Réfrégier, P.

Rhodes, W. T.

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time-sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1998).

Rissanen, J.

J. Rissanen, Stochastic Complexity in Statistical Inquiry (World Scientific, Singapore, 1989).

Rodier, J. C.

D. Prévost, Ph. Lalanne, J. C. Rodier, P. Chavel, “Video-rate simulated annealing for stochastic artificial retinas,” Opt. Commun. 132, 427–431 (1996).
[CrossRef]

Roy, S.

P. Garcı́a-Martinez, H. H. Arsenault, S. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for images degraded by nonoverlapping background noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

Sakamoto, Y.

Y. Sakamoto, M. Ishiguro, G. Kitagawa, Akaike Information Criterion Statistics (KTK Scientific, Tokyo1986).

Sjöberg, H.

Turin, G. L.

G. 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 filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Vijaya Kumar, B. V. K.

Wang, J.

Willet, P.

Appl. Opt.

IEEE Trans. Inf. Theory

A. VanderLugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

IRE Trans. Inf. Theory

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

J. Opt. Soc. Am. A

Opt. Commun.

P. Garcı́a-Martinez, H. H. Arsenault, S. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for images degraded by nonoverlapping background noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

D. Prévost, Ph. Lalanne, J. C. Rodier, P. Chavel, “Video-rate simulated annealing for stochastic artificial retinas,” Opt. Commun. 132, 427–431 (1996).
[CrossRef]

Opt. Eng.

J. M. Hereford, W. T. Rhodes, “Nonlinear optical image filtering by time-sequential threshold decomposition,” Opt. Eng. 27, 274–279 (1998).

Opt. Lett.

Other

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

P. Réfrégier, F. Goudail, C. Chesnaud, “Statistically independent region models applied to correlation and segmentation techniques,” in 1999 Euro-American Workshop on Optoelectronic Information Processing, Ph. Réfrégier, B. Javidi, eds., Vol. CR74 of SPIE Critical Review Series (SPIE, Bellingham, Wash., 1999), pp. 193–224.

P. H. Garthwaite, I. T. Jolliffe, B. Jones, Statistical Inference (Prentice-Hall, London, 1995).

M. Evans, N. Hastings, B. Peacock, Statistical Distributions (Wiley, New York, 1993).

C. Oliver, S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Norwood, Mass., 1998).

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, Boston1991).

Y. Sakamoto, M. Ishiguro, G. Kitagawa, Akaike Information Criterion Statistics (KTK Scientific, Tokyo1986).

J. Rissanen, Stochastic Complexity in Statistical Inquiry (World Scientific, Singapore, 1989).

M. Abramowitz, I. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U.S. GPO, Washington, D.C., 1972).

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Figures (11)

Fig. 1
Fig. 1

(a) Noise-free image showing three objects with different gray-level combinations. (b) Same image as in (a), but corrupted with exponential noise.

Fig. 2
Fig. 2

Output profiles obtained for (a) one-region MLRT (b) four region MLRT. Input image is shown in Fig. 1(a). Profiles show the maximum of every column in the output MLRT images.

Fig. 3
Fig. 3

Pdf of the difference between the MLRT for four region- and MLRT for one region. The four regions are the same size, taking values of 1, 3, and 20 points per region. Theoretical asymptotic pdf is shown for comparison.

Fig. 4
Fig. 4

Pdf’s at target and background locations obtained with one-region MLRT filter (upper graph) and four-region MLRT filter (lower graph). The mean values for background and target are marked with vertical lines. Note that the separation of the background target remains constant, but the variance of both classes increases, as seen in the overlapping of the pdf’s.

Fig. 5
Fig. 5

Losses in performance when the MLRT is evaluated with an increasing number of regions of equal size for a homogeneous object.

Fig. 6
Fig. 6

Example of the different region configurations for a given number of effective regions. (a) Four-region target model defined by the spatial distribution and the maximum number of regions. (b) Different region configurations with two effective regions. The number of effective regions is defined by the number of distinct gray levels. Every region configuration is defined by four digits, where each digit is the index of the effective region, and the order in the row is the region index in the target definition, using the order in the target model description.

Fig. 7
Fig. 7

Estimated number of regions as a function of the parameter α for different contrasts. The object is formed by two regions of equal size, and the RS-MLRT, filter model is four regions.

Fig. 8
Fig. 8

Estimated number of regions as a function of the parameter α for infinite contrast. Three object configurations are considered.

Fig. 9
Fig. 9

COR curves for one-region MLRT, four-region MLRT, RS-MLRT, and SRS-MLRT. The object is a four-region object with null contrast with the background.

Fig. 10
Fig. 10

Same as Fig. 9, but the object is a one-region object with low contrast with the background.

Fig. 11
Fig. 11

Same as Fig. 9, but the object is a two-region object with low contrast with the background.

Tables (1)

Tables Icon

Table 1 Number of Possible Region Configurations for the First Ten Values of the Maximum Number of Regionsa

Equations (14)

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

l=log p(θr, s)+log p(θB,s),
r=log P(θr, s)+log P(θb, s)-log P(θF, s).
rk(L)=k=0L-1iw(k)log P[θ[k], si]+iblog P(θb, si)-iFlog P(θF, si).
ru(L)=-k=0L-1N(k)log1N(k)ir(k)si-Nblog1Nbibsi+NFlog1NFiFsi,
ru(1)=-N log1Nirsi-Nblog1Nbibsi+NFlog1NFiFsi.
ru(P)(uniform)-ru(L)(uniform)=X/2,
F1=|μ1T-μ1B|2σ1T2+σ1B2.
FP=|μPT-μPB|2σPT2+σPB2=|μ1T-μ1B|2σ1T2+σ1B2+σX2/2,
LRS=arg maxM{ru(M)-αM}.
R=ru(LRS).
αMDL=logN.
LSRS=Pifru(P)-ru(1)>αSRS1otherwise;
RSRS=ru(LSRS).
αSRS=(P-1)α,

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