Abstract

Automatic target detection and recognition in images often is attempted by use of a linear correlation filter (matched filter), whose output is interpreted by a single pointwise detector (detection based on only one point). I examine a technique for significantly improving the performance of this target detection approach by supplementing the pointwise detector with several neighborhood correlation peak detectors (detection based on a domain of many points extending over much of the peak). The neighborhood detectors extract peak shape information through a moment analysis of correlation plane peaks. I describe the design of statistically quasi-optimal correlation peak discriminators based on second-order geometric moments.

© 1999 Optical Society of America

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References

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  1. G. Schils, D. Sweeney, “Optical processor for recognition of three-dimensional targets viewed from any direction,” J. Opt. Soc. Am. A 5, 1309–1321 (1988).
    [CrossRef]
  2. T. Walsh, M. Giles, “Statistical filtering of time-sequenced peak correlation responses for distortion invariant recognition of multiple input objects,” Opt. Eng. 29, 1052–1064 (1990).
    [CrossRef]
  3. H. Caulfield, “Optical processing of optical correlation plane data,” in Optical Pattern Recognition, H.-K. Liu, ed., Proc. SPIE1053, 93–95 (1989).
    [CrossRef]
  4. W. Crowe, “Optical morphological processing of optical correlator signals,” in Photonics for Processors, Neural Networks, and Memories, J. Horner, B. Javidi, S. Kowel, W. Miceli, eds., Proc. SPIE2026, 297–301 (1993).
    [CrossRef]
  5. D. Montera, S. Rogers, D. Ruck, M. Oxley, “Object tracking through adaptive correlation,” Opt. Eng. 33, 294–302 (1994).
    [CrossRef]
  6. B. Gutmann, T. Wolf, H. Weber, J. Ferrè-Borrull, S. Bosch, S. Vallmitjana, “Improvement of the discrimination capability of correlation techniques by the use of fuzzy logic,” in Vision Systems: New Image Processing Techniques, P. Réfrégier, ed., Proc. SPIE2785, 83–94 (1996).
  7. B. Draayer, G. Carhart, M. Giles, “Optimum classification of correlation-plane data by Bayesian decision theory,” Appl. Opt. 33, 3034–3049 (1994).
    [CrossRef] [PubMed]
  8. J. Booth, “Automatic post processing of correlation planeimagery,” in Optical Pattern Recognition VI, D. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 108–116 (1995).
    [CrossRef]
  9. P. Miller, R. Caprari, “Demonstration of improved automatic target recognition system performance by moment analysis of correlation peaks,” Appl. Opt. 38, 1325–1331 (1999).
    [CrossRef]
  10. M.-K. Hu, “Pattern recognition by moment invariants,” Proc. IRE 49, 1428 (1961).
  11. M.-K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).
  12. R. Prokop, A. Reeves, “A survey of moment-based techniques for unoccluded object representation and recognition,” CVGIP: Graph. Models Image Process. 54, 438–460 (1992).
    [CrossRef]
  13. L. Wang, G. Healey, “Illumination and geometry invariant recognition of texture in color images,” in Proceedings of the 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 419–424.
  14. H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, Mass., 1980).
  15. H. Poor, An Introduction to Signal Detection and Estimation, 2nd ed. (Springer-Verlag, New York, 1994).
    [CrossRef]
  16. C. Helstrom, Elements of Signal Detection and Estimation (Prentice-Hall, Englewood Cliffs, N.J., 1995).

1999 (1)

1994 (2)

D. Montera, S. Rogers, D. Ruck, M. Oxley, “Object tracking through adaptive correlation,” Opt. Eng. 33, 294–302 (1994).
[CrossRef]

B. Draayer, G. Carhart, M. Giles, “Optimum classification of correlation-plane data by Bayesian decision theory,” Appl. Opt. 33, 3034–3049 (1994).
[CrossRef] [PubMed]

1992 (1)

R. Prokop, A. Reeves, “A survey of moment-based techniques for unoccluded object representation and recognition,” CVGIP: Graph. Models Image Process. 54, 438–460 (1992).
[CrossRef]

1990 (1)

T. Walsh, M. Giles, “Statistical filtering of time-sequenced peak correlation responses for distortion invariant recognition of multiple input objects,” Opt. Eng. 29, 1052–1064 (1990).
[CrossRef]

1988 (1)

1962 (1)

M.-K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).

1961 (1)

M.-K. Hu, “Pattern recognition by moment invariants,” Proc. IRE 49, 1428 (1961).

Booth, J.

J. Booth, “Automatic post processing of correlation planeimagery,” in Optical Pattern Recognition VI, D. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 108–116 (1995).
[CrossRef]

Bosch, S.

B. Gutmann, T. Wolf, H. Weber, J. Ferrè-Borrull, S. Bosch, S. Vallmitjana, “Improvement of the discrimination capability of correlation techniques by the use of fuzzy logic,” in Vision Systems: New Image Processing Techniques, P. Réfrégier, ed., Proc. SPIE2785, 83–94 (1996).

Caprari, R.

Carhart, G.

Caulfield, H.

H. Caulfield, “Optical processing of optical correlation plane data,” in Optical Pattern Recognition, H.-K. Liu, ed., Proc. SPIE1053, 93–95 (1989).
[CrossRef]

Crowe, W.

W. Crowe, “Optical morphological processing of optical correlator signals,” in Photonics for Processors, Neural Networks, and Memories, J. Horner, B. Javidi, S. Kowel, W. Miceli, eds., Proc. SPIE2026, 297–301 (1993).
[CrossRef]

Draayer, B.

Ferrè-Borrull, J.

B. Gutmann, T. Wolf, H. Weber, J. Ferrè-Borrull, S. Bosch, S. Vallmitjana, “Improvement of the discrimination capability of correlation techniques by the use of fuzzy logic,” in Vision Systems: New Image Processing Techniques, P. Réfrégier, ed., Proc. SPIE2785, 83–94 (1996).

Giles, M.

B. Draayer, G. Carhart, M. Giles, “Optimum classification of correlation-plane data by Bayesian decision theory,” Appl. Opt. 33, 3034–3049 (1994).
[CrossRef] [PubMed]

T. Walsh, M. Giles, “Statistical filtering of time-sequenced peak correlation responses for distortion invariant recognition of multiple input objects,” Opt. Eng. 29, 1052–1064 (1990).
[CrossRef]

Goldstein, H.

H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, Mass., 1980).

Gutmann, B.

B. Gutmann, T. Wolf, H. Weber, J. Ferrè-Borrull, S. Bosch, S. Vallmitjana, “Improvement of the discrimination capability of correlation techniques by the use of fuzzy logic,” in Vision Systems: New Image Processing Techniques, P. Réfrégier, ed., Proc. SPIE2785, 83–94 (1996).

Healey, G.

L. Wang, G. Healey, “Illumination and geometry invariant recognition of texture in color images,” in Proceedings of the 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 419–424.

Helstrom, C.

C. Helstrom, Elements of Signal Detection and Estimation (Prentice-Hall, Englewood Cliffs, N.J., 1995).

Hu, M.-K.

M.-K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).

M.-K. Hu, “Pattern recognition by moment invariants,” Proc. IRE 49, 1428 (1961).

Miller, P.

Montera, D.

D. Montera, S. Rogers, D. Ruck, M. Oxley, “Object tracking through adaptive correlation,” Opt. Eng. 33, 294–302 (1994).
[CrossRef]

Oxley, M.

D. Montera, S. Rogers, D. Ruck, M. Oxley, “Object tracking through adaptive correlation,” Opt. Eng. 33, 294–302 (1994).
[CrossRef]

Poor, H.

H. Poor, An Introduction to Signal Detection and Estimation, 2nd ed. (Springer-Verlag, New York, 1994).
[CrossRef]

Prokop, R.

R. Prokop, A. Reeves, “A survey of moment-based techniques for unoccluded object representation and recognition,” CVGIP: Graph. Models Image Process. 54, 438–460 (1992).
[CrossRef]

Reeves, A.

R. Prokop, A. Reeves, “A survey of moment-based techniques for unoccluded object representation and recognition,” CVGIP: Graph. Models Image Process. 54, 438–460 (1992).
[CrossRef]

Rogers, S.

D. Montera, S. Rogers, D. Ruck, M. Oxley, “Object tracking through adaptive correlation,” Opt. Eng. 33, 294–302 (1994).
[CrossRef]

Ruck, D.

D. Montera, S. Rogers, D. Ruck, M. Oxley, “Object tracking through adaptive correlation,” Opt. Eng. 33, 294–302 (1994).
[CrossRef]

Schils, G.

Sweeney, D.

Vallmitjana, S.

B. Gutmann, T. Wolf, H. Weber, J. Ferrè-Borrull, S. Bosch, S. Vallmitjana, “Improvement of the discrimination capability of correlation techniques by the use of fuzzy logic,” in Vision Systems: New Image Processing Techniques, P. Réfrégier, ed., Proc. SPIE2785, 83–94 (1996).

Walsh, T.

T. Walsh, M. Giles, “Statistical filtering of time-sequenced peak correlation responses for distortion invariant recognition of multiple input objects,” Opt. Eng. 29, 1052–1064 (1990).
[CrossRef]

Wang, L.

L. Wang, G. Healey, “Illumination and geometry invariant recognition of texture in color images,” in Proceedings of the 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 419–424.

Weber, H.

B. Gutmann, T. Wolf, H. Weber, J. Ferrè-Borrull, S. Bosch, S. Vallmitjana, “Improvement of the discrimination capability of correlation techniques by the use of fuzzy logic,” in Vision Systems: New Image Processing Techniques, P. Réfrégier, ed., Proc. SPIE2785, 83–94 (1996).

Wolf, T.

B. Gutmann, T. Wolf, H. Weber, J. Ferrè-Borrull, S. Bosch, S. Vallmitjana, “Improvement of the discrimination capability of correlation techniques by the use of fuzzy logic,” in Vision Systems: New Image Processing Techniques, P. Réfrégier, ed., Proc. SPIE2785, 83–94 (1996).

Appl. Opt. (2)

CVGIP: Graph. Models Image Process. (1)

R. Prokop, A. Reeves, “A survey of moment-based techniques for unoccluded object representation and recognition,” CVGIP: Graph. Models Image Process. 54, 438–460 (1992).
[CrossRef]

IRE Trans. Inf. Theory (1)

M.-K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Inf. Theory IT-8, 179–187 (1962).

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

T. Walsh, M. Giles, “Statistical filtering of time-sequenced peak correlation responses for distortion invariant recognition of multiple input objects,” Opt. Eng. 29, 1052–1064 (1990).
[CrossRef]

D. Montera, S. Rogers, D. Ruck, M. Oxley, “Object tracking through adaptive correlation,” Opt. Eng. 33, 294–302 (1994).
[CrossRef]

Proc. IRE (1)

M.-K. Hu, “Pattern recognition by moment invariants,” Proc. IRE 49, 1428 (1961).

Other (8)

L. Wang, G. Healey, “Illumination and geometry invariant recognition of texture in color images,” in Proceedings of the 1996 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 419–424.

H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, Mass., 1980).

H. Poor, An Introduction to Signal Detection and Estimation, 2nd ed. (Springer-Verlag, New York, 1994).
[CrossRef]

C. Helstrom, Elements of Signal Detection and Estimation (Prentice-Hall, Englewood Cliffs, N.J., 1995).

B. Gutmann, T. Wolf, H. Weber, J. Ferrè-Borrull, S. Bosch, S. Vallmitjana, “Improvement of the discrimination capability of correlation techniques by the use of fuzzy logic,” in Vision Systems: New Image Processing Techniques, P. Réfrégier, ed., Proc. SPIE2785, 83–94 (1996).

J. Booth, “Automatic post processing of correlation planeimagery,” in Optical Pattern Recognition VI, D. Casasent, T.-H. Chao, eds., Proc. SPIE2490, 108–116 (1995).
[CrossRef]

H. Caulfield, “Optical processing of optical correlation plane data,” in Optical Pattern Recognition, H.-K. Liu, ed., Proc. SPIE1053, 93–95 (1989).
[CrossRef]

W. Crowe, “Optical morphological processing of optical correlator signals,” in Photonics for Processors, Neural Networks, and Memories, J. Horner, B. Javidi, S. Kowel, W. Miceli, eds., Proc. SPIE2026, 297–301 (1993).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Contours of correlation plane peaks formed by filter 46. The peaks at the left all result from targets to which the correlation filter is tuned. The peaks at the right all result from clutter patterns in the input image. Notice that target peaks have a better consistency of shape and orientation among themselves than do clutter peaks, which vary quite erratically.

Fig. 2
Fig. 2

Histograms of target correlation peaks (filled circles), clutter correlation peaks (open circles), and their associated receiver operating characteristics (ROC’s), for angle, eccentricity, and trace parameters, and their combination into a composite parameter, for correlation filter 46.

Fig. 3
Fig. 3

Graph of the detection effectiveness measure function η(P fa, P d) [Eq. (8)], which is used in the choice of a detector operating point on the ROC.

Equations (14)

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

m=D px, ydxdy.
cx=1m D xpx, ydxdy,  cy=1m D ypx, ydxdy.
Ixx=1m Dx-cx2px, ydxdy,  Iyy=1m Dy-cy2px, ydxdy,  Iyx=Ixy=1m Dx-cxy-cypx, ydxdy.
I11=1/2Ixx+Iyy+Ixx-Iyy2+4Ixy21/2,  I22=1/2Ixx+Iyy-Ixx-Iyy2+4Ixy21/2.
angle θ=arctanI11-Ixx/Ixy+π,
eccentricity e=1-I22/I111/2,
trace t=Ixx+Iyy=I11+I22,
ηPfa, Pd ln0.005+0.995Pfaln0.005×1+exp-0.5/0.06Pd0.41+exp-Pd-0.5/0.06,
pθ, e, t|target=12π3/2σθ_tσe_tσt_t exp-θt-μθ_t2σθ_t-e-μe_t2σe_t2-t-μt_t2σt_t2.
pθ, e, t|clutter=12π3/2σθ_cσe_cσt_c×exp-θc-μθ_c2σθ_c2-e-μe_c2σe_c2-t-μt_c2σt_c2.
Lθ, e, tpθ, e, t|targetpθ, e, t|clutter.
δθ, e, t1Lθ, e, tτ0Lθ, e, t<τ,
δθ, e, t=1cθ, e, tτ0cθ, e, t<τ,
composite cθ, e, t-θt-μθ_t2σθ_t2-e-μe_t2σe_t2-t-μt_t2σt_t2+θc-μθ_c2σθ_c2+e-μe_c2σe_c2+t-μt_c2σt_c2,

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