Abstract

Most modern pattern recognition filters used in target detection require a clutter-noise estimate to perform efficiently in realistic situations. Markovian and autoregressive models are proposed as an alternative to the white-noise model that has so far been the most widely used. Simulations by use of the Wiener filter and involving real clutter scenes show that both the Markovian and the autoregressive models perform considerably better than the white-noise model. The results also show that both models are general enough to yield similar results with different types of real scenes.

© 2002 Optical Society of America

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References

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2001 (1)

1999 (2)

V. Laude, A. Grunnet-Jepsen, S. Tonda, “Input image spectral density estimation for real-time adaption of correlation filters,” Opt. Eng. 38, 672–676 (1999).
[CrossRef]

S. Tan, R. C. D. Young, J. D. Richardson, C. R. Chatwin, “A pattern recognition Wiener filter for realistic clutter backgrounds,” Opt. Commun. 172, 193–202 (1999).
[CrossRef]

1998 (1)

S. R. DeGraaf, “SAR imaging via Modern 2-D spectral estimation methods,” IEEE Trans. Image Process. 7, 729–761 (1998).
[CrossRef]

1996 (3)

P. Réfrégier, F. Goudail, T. Gaidon, “Optimal location of random targets in random background: random Markov fields modelization,” Opt. Commun. 128, 211–215 (1996).
[CrossRef]

R. Paget, D. Longstaff, “A nonparametric multiscale Markov random field model for synthesising natural textures, Fourth International Symposium on Signal Processing and its Applications,” 2, 744–747 (1996).

E. Marom, H. Inbar, “New interpretations of Wiener filters for image recognition,” J. Opt. Soc. Am. A 13, 1325–1330 (1996).
[CrossRef]

1995 (1)

1994 (2)

1992 (3)

J. Mao, A. K. Jain, “Texture classification and segmentation using multiresolution simultaneous autoregressive models,” Pattern Recogn. 25, 173–188 (1992).
[CrossRef]

J. W. Modestino, J. Zhang, “A Markov random field model-based approach to image interpretation, IEEE Trans. Pattern Anal. Mach. Intell. 14, 606–615 (1992).
[CrossRef]

C. S. Won, H. Derin, Unsupervised segmentation of noisy and textured images using Markov random fields, CVGIP: Graph. Models Image Process. 54, 308–328 (1992).
[CrossRef]

1991 (2)

1990 (2)

1989 (2)

B. Gidas, “A renormalization group approach to image processing problems,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 164–180 (1989).
[CrossRef]

H. Derin, P. A. Kelly, “Discrete-index Markov-type random fields,” Proc. IEEE 77, 1485–1510 (1989).
[CrossRef]

1986 (1)

1984 (1)

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984).
[CrossRef] [PubMed]

1983 (2)

R. L. Kashyap, R. Chellappa, “Estimation and choice of neighbors in spatial-interaction models of images,” IEEE Trans. Inf. Theory IT-29, 60–72 (1983).
[CrossRef]

G. R. Cross, A. K. Jain, “Markov random field texture models,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 25–39 (1983).
[CrossRef]

1982 (2)

J. H. McClellan, “Multidimensional spectral estimation,” Proc. IEEE 70, 1029–1039 (1982).
[CrossRef]

F. R. Hansen, H. Elliott, “Image segmentation using simple Markov random field models,” Comput. Graph. Image Process. 20, 101–132 (1982).
[CrossRef]

1981 (1)

A. K. Jain, “Advances in mathematical models for image processing,” Proc. IEEE 69, 502–528 (1981).
[CrossRef]

1980 (1)

M. Hassner, J. Slansky, “The use of Markov random fields as models of texture,” Comput. Graph. Image Process. 12, 357–370 (1980).
[CrossRef]

1972 (1)

J. W. Woods, “Two-dimensional discrete Markovian fields,” IEEE Trans. Inf. Theory IT-18, 232–240 (1972).
[CrossRef]

Birch, P.

Blackledge, J. M.

J. M. Blackledge, Quantitative Coherent Imaging (Academic, London, 1989).

Budgett, D.

Carlson, D. W.

Chao, T. S.

H. Zhou, T. S. Chao, “MACH filter synthesizing for detecting targets in cluttered environment for gray-scale optical correlator,” in Optical Pattern Recognition X, D. P. Casasent, T.-H. Chao, eds. SPIE3715, 394–398 (1999).

Chatwin, C.

Chatwin, C. R.

S. Tan, R. C. D. Young, J. D. Richardson, C. R. Chatwin, “A pattern recognition Wiener filter for realistic clutter backgrounds,” Opt. Commun. 172, 193–202 (1999).
[CrossRef]

Chellappa, R.

R. L. Kashyap, R. Chellappa, “Estimation and choice of neighbors in spatial-interaction models of images,” IEEE Trans. Inf. Theory IT-29, 60–72 (1983).
[CrossRef]

R. Chellappa, A. Jain, Markov Random Field-Theory and Applications (Academic, San Diego, Calif., 1993).

Claret-Tournier, F.

Cross, G. R.

G. R. Cross, A. K. Jain, “Markov random field texture models,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 25–39 (1983).
[CrossRef]

DeGraaf, S. R.

S. R. DeGraaf, “SAR imaging via Modern 2-D spectral estimation methods,” IEEE Trans. Image Process. 7, 729–761 (1998).
[CrossRef]

Derin, H.

C. S. Won, H. Derin, Unsupervised segmentation of noisy and textured images using Markov random fields, CVGIP: Graph. Models Image Process. 54, 308–328 (1992).
[CrossRef]

H. Derin, P. A. Kelly, “Discrete-index Markov-type random fields,” Proc. IEEE 77, 1485–1510 (1989).
[CrossRef]

Elliott, H.

F. R. Hansen, H. Elliott, “Image segmentation using simple Markov random field models,” Comput. Graph. Image Process. 20, 101–132 (1982).
[CrossRef]

Gaidon, T.

P. Réfrégier, F. Goudail, T. Gaidon, “Optimal location of random targets in random background: random Markov fields modelization,” Opt. Commun. 128, 211–215 (1996).
[CrossRef]

Geman, D.

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984).
[CrossRef] [PubMed]

Geman, S.

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984).
[CrossRef] [PubMed]

Gidas, B.

B. Gidas, “A renormalization group approach to image processing problems,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 164–180 (1989).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1993).

Goudail, F.

P. Réfrégier, F. Goudail, T. Gaidon, “Optimal location of random targets in random background: random Markov fields modelization,” Opt. Commun. 128, 211–215 (1996).
[CrossRef]

Grunnet-Jepsen, A.

V. Laude, A. Grunnet-Jepsen, S. Tonda, “Input image spectral density estimation for real-time adaption of correlation filters,” Opt. Eng. 38, 672–676 (1999).
[CrossRef]

Haindl, M.

M. Haindl, “Texture synthesis,” CWI Quaterly 4, 305–331 (1991).

Hansen, F. R.

F. R. Hansen, H. Elliott, “Image segmentation using simple Markov random field models,” Comput. Graph. Image Process. 20, 101–132 (1982).
[CrossRef]

Hassebrook, L.

Hassner, M.

M. Hassner, J. Slansky, “The use of Markov random fields as models of texture,” Comput. Graph. Image Process. 12, 357–370 (1980).
[CrossRef]

Inbar, H.

Jain, A.

R. Chellappa, A. Jain, Markov Random Field-Theory and Applications (Academic, San Diego, Calif., 1993).

Jain, A. K.

J. Mao, A. K. Jain, “Texture classification and segmentation using multiresolution simultaneous autoregressive models,” Pattern Recogn. 25, 173–188 (1992).
[CrossRef]

G. R. Cross, A. K. Jain, “Markov random field texture models,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 25–39 (1983).
[CrossRef]

A. K. Jain, “Advances in mathematical models for image processing,” Proc. IEEE 69, 502–528 (1981).
[CrossRef]

Kashyap, R. L.

R. L. Kashyap, R. Chellappa, “Estimation and choice of neighbors in spatial-interaction models of images,” IEEE Trans. Inf. Theory IT-29, 60–72 (1983).
[CrossRef]

Kelly, P. A.

H. Derin, P. A. Kelly, “Discrete-index Markov-type random fields,” Proc. IEEE 77, 1485–1510 (1989).
[CrossRef]

Koukoulas, T.

Laude, V.

V. Laude, A. Grunnet-Jepsen, S. Tonda, “Input image spectral density estimation for real-time adaption of correlation filters,” Opt. Eng. 38, 672–676 (1999).
[CrossRef]

Li, S. Z.

S. Z. Li, Markov Random Fields Modeling in Computer Vision (Springer-Verlag, Berlin, 1995).

Longstaff, D.

R. Paget, D. Longstaff, “A nonparametric multiscale Markov random field model for synthesising natural textures, Fourth International Symposium on Signal Processing and its Applications,” 2, 744–747 (1996).

Mahalanobis, A.

Manolakis, D.

J. Proakis, D. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1996).

Mao, J.

J. Mao, A. K. Jain, “Texture classification and segmentation using multiresolution simultaneous autoregressive models,” Pattern Recogn. 25, 173–188 (1992).
[CrossRef]

Marom, E.

Marple, S. L.

S. L. Marple, Digital Spectral Analysis with ApplicationsPrentice-Hall, Englewood Cliffs, N.J., 1987).

McClellan, J. H.

J. H. McClellan, “Multidimensional spectral estimation,” Proc. IEEE 70, 1029–1039 (1982).
[CrossRef]

Modestino, J. W.

J. W. Modestino, J. Zhang, “A Markov random field model-based approach to image interpretation, IEEE Trans. Pattern Anal. Mach. Intell. 14, 606–615 (1992).
[CrossRef]

Paget, R.

R. Paget, D. Longstaff, “A nonparametric multiscale Markov random field model for synthesising natural textures, Fourth International Symposium on Signal Processing and its Applications,” 2, 744–747 (1996).

Proakis, J.

J. Proakis, D. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1996).

Réfrégier, P.

Richardson, J. D.

S. Tan, R. C. D. Young, J. D. Richardson, C. R. Chatwin, “A pattern recognition Wiener filter for realistic clutter backgrounds,” Opt. Commun. 172, 193–202 (1999).
[CrossRef]

Sims, S. R. F.

Slansky, J.

M. Hassner, J. Slansky, “The use of Markov random fields as models of texture,” Comput. Graph. Image Process. 12, 357–370 (1980).
[CrossRef]

Song, S.

Tan, S.

P. Birch, S. Tan, R. Young, T. Koukoulas, F. Claret-Tournier, D. Budgett, C. Chatwin, “Experimental implementation of a Wiener filter in a hybrid digital-optical correlator,” Opt. Lett. 26, 494–496 (2001).
[CrossRef]

S. Tan, R. C. D. Young, J. D. Richardson, C. R. Chatwin, “A pattern recognition Wiener filter for realistic clutter backgrounds,” Opt. Commun. 172, 193–202 (1999).
[CrossRef]

Tonda, S.

V. Laude, A. Grunnet-Jepsen, S. Tonda, “Input image spectral density estimation for real-time adaption of correlation filters,” Opt. Eng. 38, 672–676 (1999).
[CrossRef]

Vijaya Kumar, B. V. K.

Wiener, N.

N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, (Wiley, New York, 1949).

Won, C. S.

C. S. Won, H. Derin, Unsupervised segmentation of noisy and textured images using Markov random fields, CVGIP: Graph. Models Image Process. 54, 308–328 (1992).
[CrossRef]

Woods, J. W.

J. W. Woods, “Two-dimensional discrete Markovian fields,” IEEE Trans. Inf. Theory IT-18, 232–240 (1972).
[CrossRef]

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1993).

Young, R.

Young, R. C. D.

S. Tan, R. C. D. Young, J. D. Richardson, C. R. Chatwin, “A pattern recognition Wiener filter for realistic clutter backgrounds,” Opt. Commun. 172, 193–202 (1999).
[CrossRef]

Zhang, J.

J. W. Modestino, J. Zhang, “A Markov random field model-based approach to image interpretation, IEEE Trans. Pattern Anal. Mach. Intell. 14, 606–615 (1992).
[CrossRef]

Zhou, H.

H. Zhou, T. S. Chao, “MACH filter synthesizing for detecting targets in cluttered environment for gray-scale optical correlator,” in Optical Pattern Recognition X, D. P. Casasent, T.-H. Chao, eds. SPIE3715, 394–398 (1999).

A nonparametric multiscale Markov random field model for synthesising natural textures, Fourth International Symposium on Signal Processing and its Applications (1)

R. Paget, D. Longstaff, “A nonparametric multiscale Markov random field model for synthesising natural textures, Fourth International Symposium on Signal Processing and its Applications,” 2, 744–747 (1996).

Appl. Opt. (2)

Comput. Graph. Image Process. (2)

M. Hassner, J. Slansky, “The use of Markov random fields as models of texture,” Comput. Graph. Image Process. 12, 357–370 (1980).
[CrossRef]

F. R. Hansen, H. Elliott, “Image segmentation using simple Markov random field models,” Comput. Graph. Image Process. 20, 101–132 (1982).
[CrossRef]

CVGIP: Graph. Models Image Process. (1)

C. S. Won, H. Derin, Unsupervised segmentation of noisy and textured images using Markov random fields, CVGIP: Graph. Models Image Process. 54, 308–328 (1992).
[CrossRef]

CWI Quaterly (1)

M. Haindl, “Texture synthesis,” CWI Quaterly 4, 305–331 (1991).

IEEE Trans. Image Process. (1)

S. R. DeGraaf, “SAR imaging via Modern 2-D spectral estimation methods,” IEEE Trans. Image Process. 7, 729–761 (1998).
[CrossRef]

IEEE Trans. Inf. Theory (2)

J. W. Woods, “Two-dimensional discrete Markovian fields,” IEEE Trans. Inf. Theory IT-18, 232–240 (1972).
[CrossRef]

R. L. Kashyap, R. Chellappa, “Estimation and choice of neighbors in spatial-interaction models of images,” IEEE Trans. Inf. Theory IT-29, 60–72 (1983).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (4)

G. R. Cross, A. K. Jain, “Markov random field texture models,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 25–39 (1983).
[CrossRef]

J. W. Modestino, J. Zhang, “A Markov random field model-based approach to image interpretation, IEEE Trans. Pattern Anal. Mach. Intell. 14, 606–615 (1992).
[CrossRef]

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984).
[CrossRef] [PubMed]

B. Gidas, “A renormalization group approach to image processing problems,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 164–180 (1989).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

P. Réfrégier, F. Goudail, T. Gaidon, “Optimal location of random targets in random background: random Markov fields modelization,” Opt. Commun. 128, 211–215 (1996).
[CrossRef]

S. Tan, R. C. D. Young, J. D. Richardson, C. R. Chatwin, “A pattern recognition Wiener filter for realistic clutter backgrounds,” Opt. Commun. 172, 193–202 (1999).
[CrossRef]

Opt. Eng. (1)

V. Laude, A. Grunnet-Jepsen, S. Tonda, “Input image spectral density estimation for real-time adaption of correlation filters,” Opt. Eng. 38, 672–676 (1999).
[CrossRef]

Opt. Lett. (5)

Pattern Recogn. (1)

J. Mao, A. K. Jain, “Texture classification and segmentation using multiresolution simultaneous autoregressive models,” Pattern Recogn. 25, 173–188 (1992).
[CrossRef]

Proc. IEEE (3)

J. H. McClellan, “Multidimensional spectral estimation,” Proc. IEEE 70, 1029–1039 (1982).
[CrossRef]

H. Derin, P. A. Kelly, “Discrete-index Markov-type random fields,” Proc. IEEE 77, 1485–1510 (1989).
[CrossRef]

A. K. Jain, “Advances in mathematical models for image processing,” Proc. IEEE 69, 502–528 (1981).
[CrossRef]

Other (8)

H. Zhou, T. S. Chao, “MACH filter synthesizing for detecting targets in cluttered environment for gray-scale optical correlator,” in Optical Pattern Recognition X, D. P. Casasent, T.-H. Chao, eds. SPIE3715, 394–398 (1999).

S. Z. Li, Markov Random Fields Modeling in Computer Vision (Springer-Verlag, Berlin, 1995).

N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, (Wiley, New York, 1949).

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1993).

J. M. Blackledge, Quantitative Coherent Imaging (Academic, London, 1989).

S. L. Marple, Digital Spectral Analysis with ApplicationsPrentice-Hall, Englewood Cliffs, N.J., 1987).

J. Proakis, D. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1996).

R. Chellappa, A. Jain, Markov Random Field-Theory and Applications (Academic, San Diego, Calif., 1993).

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Figures (8)

Fig. 1
Fig. 1

Example of choice for the set of nearest neighbors. The black pixel represents the center, the gray ones its chosen nearest neighbors.

Fig. 2
Fig. 2

MK noise effects used in the WF. WN is white noise. MKN1 is obtained with the set of neighbors of Figure 1(a), with a = -2 and b = 4. MKN2 is obtained with the set of neighbors of Figure 1(a) with a = -2 and b = 32. MKN3 is obtained with the set of neighbors of Figure 1(b), with a = -2 and b = 32.

Fig. 3
Fig. 3

Input scenes used to evaluate the performance of the various noise models incorporated in the WF.

Fig. 4
Fig. 4

Comparison results between white noise and the different MK noise effects. The PCE value obtained with white noise is normalized to 1.

Fig. 5
Fig. 5

Correlation planes for (a) WN and (b) MKN3 when the target is in bck1.

Fig. 6
Fig. 6

Different possible regions of support for an AR model.

Fig. 7
Fig. 7

Clutter scenes and their respective power spectra estimated by the AR model.

Fig. 8
Fig. 8

Comparison results between white noise and the different AR noise models. The PCE value obtained with white noise is normalized to 1.

Equations (12)

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

ix, y=rx, y+nx, y,
rˆx, y=ix, y  hx, y.
e=rx, y-rˆx, y2,
HRWFu, v=|Ru, v|2|Ru, v|2+|Nu, v|2.
HPRWFu, v=Ru, v*|Ru, v|2+|Nu, v|2,
HPRWFu, v=1Ru, v×|Ru, v|2|Ru, v|2+|Nu, v|2
HPRWFu, v=1Ru, v×HRWFu, v.
pxi/Ωi=expxiT1+expT,
T=a+i=1Nbini,
T=a+b i=1Nni.
xi, j=-m,nP,Pbmnxi-m, j-n,
PSDu, v=C1+m,nP,Pbmnexp-i2πmu+nv2,

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