Abstract

A novel method is presented for optimization of quadratic correlation filters (QCFs) for shift-invariant target detection in imagery. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense, the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. For example, multiple correlators work in parallel to optimize jointly the QCF performance metric and produce a single combined output, which leads to considerable simplification of the postprocessing scheme. In addition, QCFs also yield better performance than their linear counterparts for comparable throughput requirements. The primary application considered is target detection in infrared imagery for surveillance applications. In the current approach, the class-separation metric is formulated as a Rayleigh quotient that is maximized by the QCF solution. It is shown that the proposed method results in considerable improvement in performance compared with a previously reported QCF design approach and many other detection techniques. The results of independent tests and evaluations at the U.S. Army’s Night Vision Laboratory are also presented.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. A. Chan, S. Z. Der, N. M. Nasrabadi, “Neural based target detectors for multi-band infrared imagery,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 1–36.
  2. J. H. Friedman, “Greedy function approximation: a gradient boosting machine,” Ann. Stat. 29, 1189–1232 (2001).
    [CrossRef]
  3. H. Drucker, C. J. C. Burges, L. Kaufman, A. Smola, V. Vapnik, “Support vector regression machines,” Adv. Neural Inf. Process. Syst. 9, 155–161 (1997).
  4. B. Bhanu, J. Ahn, “A system for model-based recognition of articulated objects,” in Proceedings of the Fourteenth International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), Vol. 2, pp. 1812–1815.
  5. S. Z. Der, Q. Zheng, R. Chellappa, B. Redman, H. Mahmoud, “View based recognition of military vehicles in ladar imagery using CAD model matching,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 151–187.
  6. B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
    [CrossRef]
  7. 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]
  8. A. Mahalanobis, B. V. K. Vijaya Kumar, “Polynomial filters for higher order correlation and multi-input information fusion,” in Optoelectronic Information Processing, B. Javidi, P. Refregier, eds., Vol. PM54 of SPIE Press Monographs (SPIE Press, Bellingham, Wash., 1997), pp. 221–231.
  9. G. Gheen, “A general class of invariant quadratic filters for optical pattern recognition,” Proc. SPIE 2237, 19–26 (1994).
    [CrossRef]
  10. D. Weber, D. P. Casasent, “Quadratic filters for object classification and detection,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 2–13 (1997).
    [CrossRef]
  11. A. Mahalanobis, R. R. Muise, S. R. Stanfill, A. Van Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron., to be published.
  12. X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
    [CrossRef]
  13. S. R. F. Sims, A. Mahalanobis, “Performance evaluation of quadratic correlation filters for target detection and discrimination in infrared imagery,” Opt. Eng. (to be published).

2001

J. H. Friedman, “Greedy function approximation: a gradient boosting machine,” Ann. Stat. 29, 1189–1232 (2001).
[CrossRef]

1997

H. Drucker, C. J. C. Burges, L. Kaufman, A. Smola, V. Vapnik, “Support vector regression machines,” Adv. Neural Inf. Process. Syst. 9, 155–161 (1997).

1994

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]

G. Gheen, “A general class of invariant quadratic filters for optical pattern recognition,” Proc. SPIE 2237, 19–26 (1994).
[CrossRef]

1992

Ahn, J.

B. Bhanu, J. Ahn, “A system for model-based recognition of articulated objects,” in Proceedings of the Fourteenth International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), Vol. 2, pp. 1812–1815.

Bhanu, B.

B. Bhanu, J. Ahn, “A system for model-based recognition of articulated objects,” in Proceedings of the Fourteenth International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), Vol. 2, pp. 1812–1815.

Burges, C. J. C.

H. Drucker, C. J. C. Burges, L. Kaufman, A. Smola, V. Vapnik, “Support vector regression machines,” Adv. Neural Inf. Process. Syst. 9, 155–161 (1997).

Casasent, D. P.

D. Weber, D. P. Casasent, “Quadratic filters for object classification and detection,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 2–13 (1997).
[CrossRef]

Chan, L. A.

L. A. Chan, S. Z. Der, N. M. Nasrabadi, “Neural based target detectors for multi-band infrared imagery,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 1–36.

Chellappa, R.

S. Z. Der, Q. Zheng, R. Chellappa, B. Redman, H. Mahmoud, “View based recognition of military vehicles in ladar imagery using CAD model matching,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 151–187.

Chen, J.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

Der, S. Z.

S. Z. Der, Q. Zheng, R. Chellappa, B. Redman, H. Mahmoud, “View based recognition of military vehicles in ladar imagery using CAD model matching,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 151–187.

L. A. Chan, S. Z. Der, N. M. Nasrabadi, “Neural based target detectors for multi-band infrared imagery,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 1–36.

Donoho, D. L.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

Drucker, H.

H. Drucker, C. J. C. Burges, L. Kaufman, A. Smola, V. Vapnik, “Support vector regression machines,” Adv. Neural Inf. Process. Syst. 9, 155–161 (1997).

Elad, M.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

Epperson, J. F.

Flesia, A. G.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

Friedman, J.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

Friedman, J. H.

J. H. Friedman, “Greedy function approximation: a gradient boosting machine,” Ann. Stat. 29, 1189–1232 (2001).
[CrossRef]

Gheen, G.

G. Gheen, “A general class of invariant quadratic filters for optical pattern recognition,” Proc. SPIE 2237, 19–26 (1994).
[CrossRef]

Huo, X.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

Kaufman, L.

H. Drucker, C. J. C. Burges, L. Kaufman, A. Smola, V. Vapnik, “Support vector regression machines,” Adv. Neural Inf. Process. Syst. 9, 155–161 (1997).

Mahalanobis, A.

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 correlation and multi-input information fusion,” in Optoelectronic Information Processing, B. Javidi, P. Refregier, eds., Vol. PM54 of SPIE Press Monographs (SPIE Press, Bellingham, Wash., 1997), pp. 221–231.

A. Mahalanobis, R. R. Muise, S. R. Stanfill, A. Van Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron., to be published.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

S. R. F. Sims, A. Mahalanobis, “Performance evaluation of quadratic correlation filters for target detection and discrimination in infrared imagery,” Opt. Eng. (to be published).

Mahmoud, H.

S. Z. Der, Q. Zheng, R. Chellappa, B. Redman, H. Mahmoud, “View based recognition of military vehicles in ladar imagery using CAD model matching,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 151–187.

Muise, R. R.

A. Mahalanobis, R. R. Muise, S. R. Stanfill, A. Van Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron., to be published.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

Nasrabadi, N. M.

L. A. Chan, S. Z. Der, N. M. Nasrabadi, “Neural based target detectors for multi-band infrared imagery,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 1–36.

Popescu, B.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

Redman, B.

S. Z. Der, Q. Zheng, R. Chellappa, B. Redman, H. Mahmoud, “View based recognition of military vehicles in ladar imagery using CAD model matching,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 151–187.

Sims, S. R. F.

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]

S. R. F. Sims, A. Mahalanobis, “Performance evaluation of quadratic correlation filters for target detection and discrimination in infrared imagery,” Opt. Eng. (to be published).

Smola, A.

H. Drucker, C. J. C. Burges, L. Kaufman, A. Smola, V. Vapnik, “Support vector regression machines,” Adv. Neural Inf. Process. Syst. 9, 155–161 (1997).

Song, S.

Stanfill, S. R.

A. Mahalanobis, R. R. Muise, S. R. Stanfill, A. Van Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron., to be published.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

Van Nevel, A.

A. Mahalanobis, R. R. Muise, S. R. Stanfill, A. Van Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron., to be published.

Vapnik, V.

H. Drucker, C. J. C. Burges, L. Kaufman, A. Smola, V. Vapnik, “Support vector regression machines,” Adv. Neural Inf. Process. Syst. 9, 155–161 (1997).

Vijaya Kumar, B. V. K.

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]

A. Mahalanobis, B. V. K. Vijaya Kumar, “Polynomial filters for higher order correlation and multi-input information fusion,” in Optoelectronic Information Processing, B. Javidi, P. Refregier, eds., Vol. PM54 of SPIE Press Monographs (SPIE Press, Bellingham, Wash., 1997), pp. 221–231.

Weber, D.

D. Weber, D. P. Casasent, “Quadratic filters for object classification and detection,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 2–13 (1997).
[CrossRef]

Zheng, Q.

S. Z. Der, Q. Zheng, R. Chellappa, B. Redman, H. Mahmoud, “View based recognition of military vehicles in ladar imagery using CAD model matching,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 151–187.

Adv. Neural Inf. Process. Syst.

H. Drucker, C. J. C. Burges, L. Kaufman, A. Smola, V. Vapnik, “Support vector regression machines,” Adv. Neural Inf. Process. Syst. 9, 155–161 (1997).

Ann. Stat.

J. H. Friedman, “Greedy function approximation: a gradient boosting machine,” Ann. Stat. 29, 1189–1232 (2001).
[CrossRef]

Appl. Opt.

Proc. SPIE

G. Gheen, “A general class of invariant quadratic filters for optical pattern recognition,” Proc. SPIE 2237, 19–26 (1994).
[CrossRef]

Other

D. Weber, D. P. Casasent, “Quadratic filters for object classification and detection,” in Optical Pattern Recognition VIII, D. P. Casasent, T.-H. Chao, eds., Proc. SPIE3073, 2–13 (1997).
[CrossRef]

A. Mahalanobis, R. R. Muise, S. R. Stanfill, A. Van Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron., to be published.

X. Huo, M. Elad, A. G. Flesia, R. R. Muise, S. R. Stanfill, J. Friedman, B. Popescu, J. Chen, A. Mahalanobis, D. L. Donoho, “Optimal reduced-rank quadratic classifiers using the Fukunaga-Koontz transform with applications to automated target recognition,” in Automatic Target Recognition XIII, F. A. Sadjadi, ed., Proc. SPIE5094, 59–72 (2003).
[CrossRef]

S. R. F. Sims, A. Mahalanobis, “Performance evaluation of quadratic correlation filters for target detection and discrimination in infrared imagery,” Opt. Eng. (to be published).

L. A. Chan, S. Z. Der, N. M. Nasrabadi, “Neural based target detectors for multi-band infrared imagery,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 1–36.

B. Bhanu, J. Ahn, “A system for model-based recognition of articulated objects,” in Proceedings of the Fourteenth International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), Vol. 2, pp. 1812–1815.

S. Z. Der, Q. Zheng, R. Chellappa, B. Redman, H. Mahmoud, “View based recognition of military vehicles in ladar imagery using CAD model matching,” in Image Recognition and Classification: Algorithms, Systems, and Applications, B. Javidi, ed. (Marcel Dekker, New York, 2002), pp. 151–187.

A. Mahalanobis, B. V. K. Vijaya Kumar, “Polynomial filters for higher order correlation and multi-input information fusion,” in Optoelectronic Information Processing, B. Javidi, P. Refregier, eds., Vol. PM54 of SPIE Press Monographs (SPIE Press, Bellingham, Wash., 1997), pp. 221–231.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Typical eigenvalues of (R 1 + R 2)-1(R 1 - R 2) range between -1 and 1. The eigenvectors that correspond to eigenvalues with large magnitudes are included in the coefficient matrix.

Fig. 2
Fig. 2

Efficient QCF architecture is realized by shaping the columns of coefficient matrix T into 2-D masks, correlating them in parallel with the input image, and adding the squared magnitude output of all the branches.

Fig. 3
Fig. 3

Typical IR image frame used for evaluating target detection performance.

Fig. 4
Fig. 4

Typical training images of the six target classes.

Fig. 5
Fig. 5

Each 20 × 40 kernel in this image is a RQ QCF basis function. The first 33 represent clutter whereas the last 33 represent targets. These are implemented as parallel filters in the architecture in Fig. 2 to obtain the RQ QCF output.

Fig. 6
Fig. 6

(a) Input scene is processed by the (b) RQ QCF to produce the output. A strong (bright) response is observed at the location of the target. Dark regions represent where structured clutter has been strongly suppressed.

Fig. 7
Fig. 7

Comparison of the receiver operating characteristic curves shows that the RQ QCF method performs better for target detection than the TBF QCFs designed by use of the FKT.

Fig. 8
Fig. 8

Results of independent tests taken by the NVESD on the challenging Vision-2 set show that the RQ QCF achieves better performance than most other algorithms tested to date.

Equations (28)

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

y=xTTx=i=1Nj=1N tijxixj.
T=i=1NqiqiT,
ϕ=xTTx.
E1ϕ-E2ϕ=i=1NqiR1-R2qiT,
E1ϕ+E2ϕ=i=1NqiR1+R2qiT.
Jq= E1ϕ-E2ϕE1ϕ+E2ϕ= i=1NqiR1-R2qiTi=1NqiR1+R2qiT.
R1+R2-1R1-R2qi=λiqi.
R1-R2qi=λiR1+R2qi R1qi1-λi=R2qi1+λi R2-1R1qi=qi1+λi1-λi =qiγi.
E1ϕE2ϕ= i=1NqiTR1qii=1NqiTR2qi.
qiTR1-R2qi=λiqiTR1+R2qi
qiTR1-R2qiqiTR1+R2qi=λi.
E1ϕ-E2ϕE1ϕ+E2ϕ=Jqi= qiR1-R2qiTqiR1+R2qiT=λi.
E1ϕ1-λi1+λi =E2ϕ.
E1ϕ-E2ϕ=E1ϕ1- 1-λi1+λi.
E1ϕ-E2ϕE1ϕ=1- 1-λi1+λi= 2λi1+λi.
T=i=1N1qiqiT-i=1N2pipiT,
y=zTTz=zTFFTz=vTv,
νim, n=xm, nfim, n, 1iN,
ym, n=i=1N |νim, n|2=i=1N |xm, nfim, n|2.
ym, n= i=1N2 |xm, nfim, n|2- i=1N1 |xm, ngim, n|2,
Rˆ2=α · R2+β · RS,
i=1N xi22>i=1N xi4
A-1Bqi=λiqi, Q=q1q2 Λ qNT.
QAQT=I, QBQT=Δ,
i=1NqiTR1+R2qi=traceQR1+R2QT, i=1NqiTR1-R2qi=traceQR1-R2QT.
QR1+R2QT=I, QR1-R2QT=Δ.
i=1NqiTR+Rqi=traceQR1+R2QT=traceI=N, i=1NqiTR-Rqi=traceQR1-R2QT=traceΔ=i=1N λi,
Jq= 1Ni=1N λi.

Metrics