Abstract

We introduce what is to our knowledge a new nonlinear shift-invariant classifier called the polynomial distance classifier correlation filter (PDCCF). The underlying theory extends the original linear distance classifier correlation filter [Appl. Opt. 35, 3127 (1996)] to include nonlinear functions of the input pattern. This new filter provides a framework (for combining different classification filters) that takes advantage of the individual filter strengths. In this new filter design, all filters are optimized jointly. We demonstrate the advantage of the new PDCCF method using simulated and real multi-class synthetic aperture radar images.

© 2003 Optical Society of America

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  6. A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
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  7. D. L. Flannery, J. L. Horner, “Fourier optical signal processors,” Proc. IEEE 77, 1511–1527 (1989).
    [CrossRef]
  8. A. Mahalanobis, A. Forman, M. Bower, N. Day, R. F. Cherry, “A quadratic distance classifier for multi-class SAR ATR using correlation filters,” in Ultrahigh Resolution Radar, R. S. Vickers, ed. Proc. SPIE1875, 84–95 (1993).
    [CrossRef]
  9. K. Fukunaga, Statistical Pattern Recognition (Academic, San Diego, Calif., 1990).
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  12. A. VanderLugt, F. B. Rotz, “The use of film nonlinearities in optical spatial filtering,” Appl. Opt. 1, 215–222 (1970).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, “Performance of the MACH/DCCF algorithms on the 10-class public release MSTAR data set,” in Algorithms for Synthetic Aperture Radar Imagery VI, E. G. Zelnio, ed. Proc. SPIE3721, 285–291 (1999).
    [CrossRef]
  24. A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, A. Ezekiel, “Correlation ATR performance using Xpatch (synthetic) training data,” in Algorithms for Synthetic Aperture Radar Imagery VII, E. G. Zelnio, ed. Proc. SPIE4053, 340–343 (2000).
    [CrossRef]
  25. A. Mahalanobis, A. V. Forman, N. Day, M. Bower, R. Cherry, “Multiclass SAR ATR using shift-invariant correlation filters,” Pattern Recogn. 27, 619–626 (1994).
    [CrossRef]
  26. A. Mahalanobis, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance-classifier correlation filters for multiclass target recognition,” Appl. Opt. 35, 3127–3133 (1996).
    [CrossRef] [PubMed]
  27. L. M. Kaplan, R. M. E. Asika, K. N. Namuduri, “Effect of signal-to-clutter ratio on template-based ATR,” in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed. Proc. SPIE3370, 408–419 (1998).
    [CrossRef]
  28. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, New York, 1993).
  29. W. H. Beyer, CRC Standards Mathematical Tables and Formulae (CRC Press, Boca Raton, Florida, 1991).
  30. M. Alkanhal, B. V. K. Vijaya Kumar, A. Mahalanobis, “Combining multiple correlators using neural networks,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds. Proc. SPIE3073, 398–403 (1997).
    [CrossRef]
  31. K. Al-Ghoneim, “Learning ranks for pattern recognition,” Ph.D. dissertation (Carnegie Mellon University, Pittsburgh, 1996).
  32. K. S. Fu, “A step towards unification of syntactic and statistical pattern recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 200–205 (1983).
  33. E. Mandler, J. Schuermann, “Combining the classification results of independent classifiers based on the Dempster/Shafer theory of evidence,” in Pattern Recognition and Artificial Intelligence: Towards an Integration, E. S. Gelsema, L. N. Kanal, eds. (North-Holland, Amsterdam, 1988), pp. 381–393.
  34. T. K. Ho, J. J. Hull, S. N. Srihari, “Decision combination in multiple classifier systems,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 66–75 (1994).
    [CrossRef]
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2000 (1)

B. V. K. Vijaya Kumar, A. Mahalanobis, A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
[CrossRef]

1996 (1)

1994 (4)

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
[CrossRef] [PubMed]

A. Mahalanobis, A. V. Forman, N. Day, M. Bower, R. Cherry, “Multiclass SAR ATR using shift-invariant correlation filters,” Pattern Recogn. 27, 619–626 (1994).
[CrossRef]

T. K. Ho, J. J. Hull, S. N. Srihari, “Decision combination in multiple classifier systems,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 66–75 (1994).
[CrossRef]

Ph. Réfrégier, V. Laude, “Nonlinear joint transform correlation: an optimal solution for adaptive image discrimination and input noise robustness,” Opt. Lett. 19, 405–407 (1994).

1992 (3)

1989 (2)

B. Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28, 2358–2367 (1989).
[CrossRef] [PubMed]

D. L. Flannery, J. L. Horner, “Fourier optical signal processors,” Proc. IEEE 77, 1511–1527 (1989).
[CrossRef]

1983 (1)

K. S. Fu, “A step towards unification of syntactic and statistical pattern recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 200–205 (1983).

1982 (1)

1980 (1)

1970 (1)

A. VanderLugt, F. B. Rotz, “The use of film nonlinearities in optical spatial filtering,” Appl. Opt. 1, 215–222 (1970).

1966 (1)

1965 (1)

T. M. Cover, “Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition,” IEEE Trans. Electron. Comput. EC-14, 326–334 (1965).
[CrossRef]

Al-Ghoneim, K.

K. Al-Ghoneim, “Learning ranks for pattern recognition,” Ph.D. dissertation (Carnegie Mellon University, Pittsburgh, 1996).

Alkanhal, M.

K. Al-Mashouq, B. V. K. Vijaya Kumar, M. Alkanhal, “Analysis of signal-to-noise ratio of polynomial correlation filters,” in Optical Pattern Recognition X, D. P. Casasent, T. Chao, eds. Proc. SPIE3715, 407–413 (1999).
[CrossRef]

M. Alkanhal, B. V. K. Vijaya Kumar, A. Mahalanobis, “Combining multiple correlators using neural networks,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds. Proc. SPIE3073, 398–403 (1997).
[CrossRef]

Al-Mashouq, K.

K. Al-Mashouq, B. V. K. Vijaya Kumar, M. Alkanhal, “Analysis of signal-to-noise ratio of polynomial correlation filters,” in Optical Pattern Recognition X, D. P. Casasent, T. Chao, eds. Proc. SPIE3715, 407–413 (1999).
[CrossRef]

April, G.

Arsenault, H. H.

Asika, R. M. E.

L. M. Kaplan, R. M. E. Asika, K. N. Namuduri, “Effect of signal-to-clutter ratio on template-based ATR,” in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed. Proc. SPIE3370, 408–419 (1998).
[CrossRef]

Beyer, W. H.

W. H. Beyer, CRC Standards Mathematical Tables and Formulae (CRC Press, Boca Raton, Florida, 1991).

Bower, M.

A. Mahalanobis, A. V. Forman, N. Day, M. Bower, R. Cherry, “Multiclass SAR ATR using shift-invariant correlation filters,” Pattern Recogn. 27, 619–626 (1994).
[CrossRef]

A. Mahalanobis, A. Forman, M. Bower, N. Day, R. F. Cherry, “A quadratic distance classifier for multi-class SAR ATR using correlation filters,” in Ultrahigh Resolution Radar, R. S. Vickers, ed. Proc. SPIE1875, 84–95 (1993).
[CrossRef]

Carlson, D. W.

A. Mahalanobis, D. W. Carlson, B. V. K. Vijaya Kumar, “Evaluation of MACH and DCCF correlation filters for SAR ATR using MSTAR public data base,” in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed. Proc. SPIE3370, 460–469 (1998).
[CrossRef]

A. Mahalanobis, D. W. Carlson, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance classifier correlation filters,” in Hybrid Image and Signal Processing IV, D. P. Casasent, A. G. Tescher, eds. Proc. SPIE2238, 2–13 (1994).
[CrossRef]

Casasent, D.

C. F. Hester, D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
[CrossRef] [PubMed]

D. Casasent, W. Cox, “RI-MINACE filters to augment segmentation of touching objects,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds. Proc. SPIE3073, 354–363 (1997).
[CrossRef]

Cherry, R.

A. Mahalanobis, A. V. Forman, N. Day, M. Bower, R. Cherry, “Multiclass SAR ATR using shift-invariant correlation filters,” Pattern Recogn. 27, 619–626 (1994).
[CrossRef]

Cherry, R. F.

A. Mahalanobis, A. Forman, M. Bower, N. Day, R. F. Cherry, “A quadratic distance classifier for multi-class SAR ATR using correlation filters,” in Ultrahigh Resolution Radar, R. S. Vickers, ed. Proc. SPIE1875, 84–95 (1993).
[CrossRef]

Cover, T. M.

T. M. Cover, “Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition,” IEEE Trans. Electron. Comput. EC-14, 326–334 (1965).
[CrossRef]

Cox, W.

D. Casasent, W. Cox, “RI-MINACE filters to augment segmentation of touching objects,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds. Proc. SPIE3073, 354–363 (1997).
[CrossRef]

Day, N.

A. Mahalanobis, A. V. Forman, N. Day, M. Bower, R. Cherry, “Multiclass SAR ATR using shift-invariant correlation filters,” Pattern Recogn. 27, 619–626 (1994).
[CrossRef]

A. Mahalanobis, A. Forman, M. Bower, N. Day, R. F. Cherry, “A quadratic distance classifier for multi-class SAR ATR using correlation filters,” in Ultrahigh Resolution Radar, R. S. Vickers, ed. Proc. SPIE1875, 84–95 (1993).
[CrossRef]

Duda, R.

R. Duda, P. Hart, D. Stork, Pattern Classification (Wiley, New York, 2000).

Epperson, J. F.

Ezekiel, A.

A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, A. Ezekiel, “Correlation ATR performance using Xpatch (synthetic) training data,” in Algorithms for Synthetic Aperture Radar Imagery VII, E. G. Zelnio, ed. Proc. SPIE4053, 340–343 (2000).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, New York, 1993).

Flannery, D. L.

D. L. Flannery, J. L. Horner, “Fourier optical signal processors,” Proc. IEEE 77, 1511–1527 (1989).
[CrossRef]

Forman, A.

A. Mahalanobis, A. Forman, M. Bower, N. Day, R. F. Cherry, “A quadratic distance classifier for multi-class SAR ATR using correlation filters,” in Ultrahigh Resolution Radar, R. S. Vickers, ed. Proc. SPIE1875, 84–95 (1993).
[CrossRef]

Forman, A. V.

A. Mahalanobis, A. V. Forman, N. Day, M. Bower, R. Cherry, “Multiclass SAR ATR using shift-invariant correlation filters,” Pattern Recogn. 27, 619–626 (1994).
[CrossRef]

Fu, K. S.

K. S. Fu, “A step towards unification of syntactic and statistical pattern recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 5, 200–205 (1983).

Fukunaga, K.

K. Fukunaga, Statistical Pattern Recognition (Academic, San Diego, Calif., 1990).

Goodman, J. W.

Hart, P.

R. Duda, P. Hart, D. Stork, Pattern Classification (Wiley, New York, 2000).

Hester, C. F.

Ho, T. K.

T. K. Ho, J. J. Hull, S. N. Srihari, “Decision combination in multiple classifier systems,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 66–75 (1994).
[CrossRef]

Horner, J. L.

D. L. Flannery, J. L. Horner, “Fourier optical signal processors,” Proc. IEEE 77, 1511–1527 (1989).
[CrossRef]

Hsu, Y. N.

Hull, J. J.

T. K. Ho, J. J. Hull, S. N. Srihari, “Decision combination in multiple classifier systems,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 66–75 (1994).
[CrossRef]

Javidi, B.

Kaplan, L. M.

L. M. Kaplan, R. M. E. Asika, K. N. Namuduri, “Effect of signal-to-clutter ratio on template-based ATR,” in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed. Proc. SPIE3370, 408–419 (1998).
[CrossRef]

Laude, V.

Mahalanobis, A.

B. V. K. Vijaya Kumar, A. Mahalanobis, A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance-classifier correlation filters for multiclass target recognition,” Appl. Opt. 35, 3127–3133 (1996).
[CrossRef] [PubMed]

A. Mahalanobis, A. V. Forman, N. Day, M. Bower, R. Cherry, “Multiclass SAR ATR using shift-invariant correlation filters,” Pattern Recogn. 27, 619–626 (1994).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
[CrossRef] [PubMed]

A. Mahalanobis, B. V. K. Vijaya Kumar, “Polynomial filters for higher order and multi-input information fusion,” in 11th Euro American Opto-Electronic Information Processing Workshop, Spain, June1997, pp. 221–231.

A. Mahalanobis, D. W. Carlson, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance classifier correlation filters,” in Hybrid Image and Signal Processing IV, D. P. Casasent, A. G. Tescher, eds. Proc. SPIE2238, 2–13 (1994).
[CrossRef]

A. Mahalanobis, A. Forman, M. Bower, N. Day, R. F. Cherry, “A quadratic distance classifier for multi-class SAR ATR using correlation filters,” in Ultrahigh Resolution Radar, R. S. Vickers, ed. Proc. SPIE1875, 84–95 (1993).
[CrossRef]

M. Alkanhal, B. V. K. Vijaya Kumar, A. Mahalanobis, “Combining multiple correlators using neural networks,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds. Proc. SPIE3073, 398–403 (1997).
[CrossRef]

A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, “Performance of the MACH/DCCF algorithms on the 10-class public release MSTAR data set,” in Algorithms for Synthetic Aperture Radar Imagery VI, E. G. Zelnio, ed. Proc. SPIE3721, 285–291 (1999).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance classifier correlation filters for distortion tolerance, discrimination, and clutter rejection,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds. Proc. SPIE2026, 325–337 (1993).
[CrossRef]

A. Mahalanobis, D. W. Carlson, B. V. K. Vijaya Kumar, “Evaluation of MACH and DCCF correlation filters for SAR ATR using MSTAR public data base,” in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed. Proc. SPIE3370, 460–469 (1998).
[CrossRef]

A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, A. Ezekiel, “Correlation ATR performance using Xpatch (synthetic) training data,” in Algorithms for Synthetic Aperture Radar Imagery VII, E. G. Zelnio, ed. Proc. SPIE4053, 340–343 (2000).
[CrossRef]

Mandler, E.

E. Mandler, J. Schuermann, “Combining the classification results of independent classifiers based on the Dempster/Shafer theory of evidence,” in Pattern Recognition and Artificial Intelligence: Towards an Integration, E. S. Gelsema, L. N. Kanal, eds. (North-Holland, Amsterdam, 1988), pp. 381–393.

Namuduri, K. N.

L. M. Kaplan, R. M. E. Asika, K. N. Namuduri, “Effect of signal-to-clutter ratio on template-based ATR,” in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed. Proc. SPIE3370, 408–419 (1998).
[CrossRef]

Ortiz, L.

A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, “Performance of the MACH/DCCF algorithms on the 10-class public release MSTAR data set,” in Algorithms for Synthetic Aperture Radar Imagery VI, E. G. Zelnio, ed. Proc. SPIE3721, 285–291 (1999).
[CrossRef]

A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, A. Ezekiel, “Correlation ATR performance using Xpatch (synthetic) training data,” in Algorithms for Synthetic Aperture Radar Imagery VII, E. G. Zelnio, ed. Proc. SPIE4053, 340–343 (2000).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, New York, 1993).

Réfrégier, Ph.

Rotz, F. B.

A. VanderLugt, F. B. Rotz, “The use of film nonlinearities in optical spatial filtering,” Appl. Opt. 1, 215–222 (1970).

Schuermann, J.

E. Mandler, J. Schuermann, “Combining the classification results of independent classifiers based on the Dempster/Shafer theory of evidence,” in Pattern Recognition and Artificial Intelligence: Towards an Integration, E. S. Gelsema, L. N. Kanal, eds. (North-Holland, Amsterdam, 1988), pp. 381–393.

Sicoranza, G. L.

G. L. Sicoranza, “Quadratic filters for signal processing,” Proc. IEEE 80, 1263–1285 (1992).
[CrossRef]

Sims, S. R. F.

A. Mahalanobis, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance-classifier correlation filters for multiclass target recognition,” Appl. Opt. 35, 3127–3133 (1996).
[CrossRef] [PubMed]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
[CrossRef] [PubMed]

A. Mahalanobis, D. W. Carlson, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance classifier correlation filters,” in Hybrid Image and Signal Processing IV, D. P. Casasent, A. G. Tescher, eds. Proc. SPIE2238, 2–13 (1994).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance classifier correlation filters for distortion tolerance, discrimination, and clutter rejection,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds. Proc. SPIE2026, 325–337 (1993).
[CrossRef]

Song, S.

Srihari, S. N.

T. K. Ho, J. J. Hull, S. N. Srihari, “Decision combination in multiple classifier systems,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 66–75 (1994).
[CrossRef]

Stork, D.

R. Duda, P. Hart, D. Stork, Pattern Classification (Wiley, New York, 2000).

Takessian, A.

B. V. K. Vijaya Kumar, A. Mahalanobis, A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
[CrossRef]

Tang, Q.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, New York, 1993).

VanderLugt, A.

A. VanderLugt, F. B. Rotz, “The use of film nonlinearities in optical spatial filtering,” Appl. Opt. 1, 215–222 (1970).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University, New York, 1993).

Vijaya Kumar, B. V. K.

B. V. K. Vijaya Kumar, A. Mahalanobis, A. Takessian, “Optimal tradeoff circular harmonic function correlation filter methods providing controlled in-plane rotation,” IEEE Trans. Image Process. 9, 1025–1034 (2000).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance-classifier correlation filters for multiclass target recognition,” Appl. Opt. 35, 3127–3133 (1996).
[CrossRef] [PubMed]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, J. F. Epperson, “Unconstrained correlation filters,” Appl. Opt. 33, 3751–3759 (1994).
[CrossRef] [PubMed]

B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
[CrossRef]

M. Alkanhal, B. V. K. Vijaya Kumar, A. Mahalanobis, “Combining multiple correlators using neural networks,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds. Proc. SPIE3073, 398–403 (1997).
[CrossRef]

A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, “Performance of the MACH/DCCF algorithms on the 10-class public release MSTAR data set,” in Algorithms for Synthetic Aperture Radar Imagery VI, E. G. Zelnio, ed. Proc. SPIE3721, 285–291 (1999).
[CrossRef]

A. Mahalanobis, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance classifier correlation filters for distortion tolerance, discrimination, and clutter rejection,” in Photonics for Processors, Neural Networks, and Memories, J. L. Horner, B. Javidi, S. T. Kowel, W. J. Miceli, eds. Proc. SPIE2026, 325–337 (1993).
[CrossRef]

K. Al-Mashouq, B. V. K. Vijaya Kumar, M. Alkanhal, “Analysis of signal-to-noise ratio of polynomial correlation filters,” in Optical Pattern Recognition X, D. P. Casasent, T. Chao, eds. Proc. SPIE3715, 407–413 (1999).
[CrossRef]

A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, A. Ezekiel, “Correlation ATR performance using Xpatch (synthetic) training data,” in Algorithms for Synthetic Aperture Radar Imagery VII, E. G. Zelnio, ed. Proc. SPIE4053, 340–343 (2000).
[CrossRef]

A. Mahalanobis, D. W. Carlson, B. V. K. Vijaya Kumar, “Evaluation of MACH and DCCF correlation filters for SAR ATR using MSTAR public data base,” in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed. Proc. SPIE3370, 460–469 (1998).
[CrossRef]

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K. Al-Mashouq, B. V. K. Vijaya Kumar, M. Alkanhal, “Analysis of signal-to-noise ratio of polynomial correlation filters,” in Optical Pattern Recognition X, D. P. Casasent, T. Chao, eds. Proc. SPIE3715, 407–413 (1999).
[CrossRef]

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[CrossRef]

A. Mahalanobis, D. W. Carlson, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance classifier correlation filters,” in Hybrid Image and Signal Processing IV, D. P. Casasent, A. G. Tescher, eds. Proc. SPIE2238, 2–13 (1994).
[CrossRef]

A. Mahalanobis, D. W. Carlson, B. V. K. Vijaya Kumar, “Evaluation of MACH and DCCF correlation filters for SAR ATR using MSTAR public data base,” in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed. Proc. SPIE3370, 460–469 (1998).
[CrossRef]

A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, “Performance of the MACH/DCCF algorithms on the 10-class public release MSTAR data set,” in Algorithms for Synthetic Aperture Radar Imagery VI, E. G. Zelnio, ed. Proc. SPIE3721, 285–291 (1999).
[CrossRef]

A. Mahalanobis, L. Ortiz, B. V. K. Vijaya Kumar, A. Ezekiel, “Correlation ATR performance using Xpatch (synthetic) training data,” in Algorithms for Synthetic Aperture Radar Imagery VII, E. G. Zelnio, ed. Proc. SPIE4053, 340–343 (2000).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Schematic of correlation filtering.

Fig. 2
Fig. 2

Block diagram of the DCCF recognition process. The DCCF transform is determined from training images of all classes. This figure is adapted from Ref. 22.

Fig. 3
Fig. 3

Block diagram of the PDCCF recognition process. The PDCCF transform is obtained from training images of all classes.

Fig. 4
Fig. 4

Training images of size 64 × 64 of T72 and M1A1 tanks shown at different aspect angles; the background value is 100. The maximum value is 255.

Fig. 5
Fig. 5

Test images of size 64 × 64 of T72 and M1A1 tanks shown at different aspect angles; the background is real clutter.

Fig. 6
Fig. 6

Log distance ratio for the T72 and the M1A1 training images when using the DCCF (i.e., PDCCF with ϕ = {1}).

Fig. 7
Fig. 7

Log distance ratio for the T72 and the M1A1 test images when using the DCCF (i.e., PDCCF with ϕ = {1}).

Fig. 8
Fig. 8

Log distance ratio for the two test classes when using the PDCCF with different sets of ϕ.

Fig. 9
Fig. 9

Effect of using different sets of ϕ with the PDCCF.

Fig. 10
Fig. 10

Performance of two-term PDCCF with the training set using the MSE-then-total and the total-then-MSE approaches. The first term corresponds to the first order while the second one corresponds to r.

Fig. 11
Fig. 11

Performance of two-term PDCCF on the test set with ϕ = {1, r}.

Fig. 12
Fig. 12

Performances of a two-term PDCCF using the independent design approach. Also shown is the performance of a one-term PDCCF with ϕ = {r}.

Fig. 13
Fig. 13

Performances of the two-term PDCCF with different combination methods using the joint and independent designs.

Fig. 14
Fig. 14

SAR targets of size 64 × 64 at different aspect angles.

Fig. 15
Fig. 15

Error rate as a function of ϕ for different bins. Points with circles represent powers included in the final power set.

Tables (8)

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Table 1 Performance of the PDCCFa

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Table 2 MSTAR Target Database Used in the Performance Evaluation

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Table 3 Error Rates of Different Binsa

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Table 4 Confusion Matrix Showing the Results of the DCCFa

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Table 5 Confusion Matrix Showing the Results of the PDCCFa

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Table 6 Error Rate of Each Bin for the DCCFa

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Table 7 Confusion Matrix Showing the Results of the DCCFa

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Table 8 Confusion Matrix Showing the Results of the PDCCFa

Equations (57)

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

Ah=|h+mx-h+my|2=h+mx-mymx-my+h,
ASMx=1Ni=1N |gxi-g¯x|2,
gxi=Xih* g¯x=Mxh*
ASMx=1Ni=1NXih*-Mxh*+Xih*-Mxh*=hT1Ni=1NXi-Mx*Xi-Mxh*=h+Sxh,
Sx=1Ni=1NXi-Mx*Xi-Mx.
Bh=ASMx+ASMy=h+Sxh+h+Syh=h+Sx+Syh=h+Sh,
Jh=AhBh=h+mx-mymx-my+hh+Sh.
h=S-1mx-my.
dx=|H*z-H*mx|2=|H*z|2+|H*mx|2-2z+HH*mx=p+bx-2z+HH*mx,
dy=|H*z-H*my|2=|H*z|2+|H*my|2-2z+HH*my=p+by-2z+HH*my,
hx=HH*mx,
hy=HH*my.
dx=p+bx-2z+hx,
dy=p+by-2z+hy.
LDR=logdxdy,
Ah=1Ci=1C |h+mi-h+m|2=1Ci=1Ch+mi-mmi-m+h=h+Wh,
W=1Ci=1Cmi-mmi-m+
Bh=1Ci=1Ch+Sih=h+Sh,
Jh=AhBh=h+Whh+Sh.
ηi: xk, lxik, l,
gk, l=h1k, lx1k, l,
gk, l=h1k, lx1k, l+h2k, lx2k, l.
gk, l=i=1nhik, lxik, l.
xik, l=xk, li,
mx=mx1mx2mxn, my=my1my2myn
h=h1h2hn.
g¯x0, 0=j=1nhj+mxj=h+mx,
g¯y0, 0=j=1nhj+myj=h+my.
Ah=|g¯x0, 0-g¯y0, 0|2=j=1nhj+mxj-j=1nhj+myj2=|h+mx-h+my|2.
ASMx=1Ni=1N |gxi-g¯x|2,
gxi=j=1nXijhj*g¯x=j=1nMjhj*
ASMx=1Ni=1N |Xi1h1*+Xi2h2*++Xinhn*-Mx1h1*-Mx2h2*--Mxnhn*|2=1Ni=1NXi1-Mx1h1*+Xi2-Mx2h2*++Xin-Mxnhn*+Xi1-Mx1h1*+Xi2-Mx2h2*++Xin-Mxnhn*=k=1nl=1nhk+Sxklhl=h1+h2+hn+Sx11Sx12Sx1nSx21Sx22Sx2nSxn1Sxn2Sxnnh1h2hn=h+Sxh,
Sxkl=1Ni=1NXikXil*-MxkMxl*
Sx=Sx11Sx12Sx1nSx21Sx22Sx2nSxn1Sxn2Sxnn.
Bh=ASMx+ASMy=h+Sxh+h+Syh=h+Sh,
h=S-1mx-my.
h1h2=S11S12S21S22-1mx1-my1mx2-my2.
h1h2=S1100S22-1mx1-my1mx2-my2=S11-100S22-1mx1-my1mx2-my2 h1=S11-1mx1-my1,
 h2=S22-1mx2-my2.
S=S11S12S21S22
S-1=S˜11S˜12S˜21S˜22,
S˜11=S11-S12S22-1S21-1S˜12=-S11-S12S22-1S21-1S12S22-1S˜21=-S22-1S21S11-S12S22-1S21-1S˜22=S22-1+S22-1S21S11-S12S22-1S21-1S12S22-1.
dxi=|Hi*zi-Hi*mxi|2,
dxi=pi+bxi-2zi+HiHi*mxi,
pi=|Hi*zi|2,
bxi=|Hi*mxi|2.
hxi=HiHi*mxi.
dxi=pi+bxi-2zi+hxi.
dx=i=1n dxi.
dx=|gz-g¯x|2=i=1nHi*zi-i=1nHi*mxi2=p+bx-2i=1nHi*zi+i=1nHi*mxi,
FR=m1-m22σ12+σ22,
mk=mk1mk2mkn.
Ah=1Ck=1Ci=1nhi+mki-i=1nhi+mi2=1Ck=1C |h+mk-h+m|2=h+Wh,
W=1Ck=1Cmk-mmk-m+,
h=h1h2hn, m=m1m2mn.
Bh=1Ci=1Ch+Sih
=h+Sh,

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