Abstract

Correlation filters have traditionally been designed without much attention given to the issue of the training images within a class or the relative spatial position between classes. We examine the impact of training-set registration on correlation-filter performance and develop techniques for centering the training images from a class that result in improved performance. We also show that it is beneficial to adjust the spatial position of the classes relative to one another. Although the proposed techniques are relevant for many types of correlation filter, we limit our discussion to algorithms for the maximum average correlation height filter and the distance classifier correlation filter.

© 2000 Optical Society of America

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References

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  1. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
    [CrossRef]
  2. D. O. North, “An analysis of the factors which determine signal/noise discrimination in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1963).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. A. Mahalanobis, B. V. K. Vijaya Kumar, S. R. F. Sims, “Distance classifier correlation filters for multi-class target recognition,” Appl. Opt. 35, 3127–3133 (1996).
    [CrossRef] [PubMed]
  10. Three-class public MSTAR data set (CD version), released for the Defense Advanced Research Projects Agency by Veda Incorporated, the Dayton Group, 1997; for more information see the URL https://www.mbvlab.wpafb.af.mil/public/sdms/main.htm .

1996 (1)

1994 (1)

1992 (1)

1990 (1)

1987 (1)

1986 (1)

1980 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
[CrossRef]

1963 (1)

D. O. North, “An analysis of the factors which determine signal/noise discrimination in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1963).
[CrossRef]

Casasent, D.

Epperson, J.

Hester, C. F.

Mahalanobis, A.

North, D. O.

D. O. North, “An analysis of the factors which determine signal/noise discrimination in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1963).
[CrossRef]

Réfrégier, Ph.

Sims, S. R. F.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
[CrossRef]

Vijaya Kumar, B. V. K.

Appl. Opt. (5)

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory 10, 139–145 (1964).
[CrossRef]

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

Opt. Lett. (1)

Proc. IEEE (1)

D. O. North, “An analysis of the factors which determine signal/noise discrimination in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1963).
[CrossRef]

Other (1)

Three-class public MSTAR data set (CD version), released for the Defense Advanced Research Projects Agency by Veda Incorporated, the Dayton Group, 1997; for more information see the URL https://www.mbvlab.wpafb.af.mil/public/sdms/main.htm .

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Figures (2)

Fig. 1
Fig. 1

Average of BTR70 training images between 135° and 180° (a) without registration and (b) after registration.

Fig. 2
Fig. 2

Relative position of class mean images of the BTR70, T72, and BMP for cluster number 4 (a) before optimization and (b) after optimization to account for maximum possible confusion.

Tables (2)

Tables Icon

Table 1 Comparison of λmax Values Before and After Numerical Optimization to Adjust the Relative Position of Class Means to Accommodate Worst-Case Class Separation

Tables Icon

Table 2 Results of Testing the Three-Class Automatic Target Recognition Using the MSTAR Data Set (a) Without Optimization and (b) after Registration of Training Images and Optimization of the Relative Position of Class Means

Equations (23)

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mN=1Ni=1Nxi,
σN2=1Ni=1Nxi-mNTxi-mN=1Ni=1NxiTxi-mNTmN.
σN+12=1N+1i=1N+1xiTxi-mN+1TmN+1=1N+1i=1N+1xiTxi-1N+12×i=1Nxi+xN+1Ti=1Nxi+xN+1.
N+12σN+12=N+1i=1NxiTxi+N+1xN+1TxN+1-N2mNTmN+2NmNTxN+1+xN+1TxN+1=N i=1NxiTxi-N2mNTmN+i=1NxiTxi+N+1xN+1TxN+1-xN+1TxN+1-2NmNTxN+1.
σN+12=N2N+12 σN2+NN+12×1Ni=1NxiTxi+xN+1TxN+1-2mNTxN+1.
ΨN+1=xN+1TxN+1-2mN+1TxN+1.
Jh=h+m1-m2m1-m2+hh+Sh.
Jh=m1-m2+S-1m1-m2.
Jh=m1+S-1m1+m2+S-1m2-2m1+S-1m2.
maxm1+S-1m2=maxm1+h2=maxi,jkl m1k, lh2k+i, l+j=maxi,jg12i, j,
Jh=h+Thh+Sh
h=S-1Ea,
S-1EE+S-1Ea=λmax·S-1Ea,
E+S-1Ea=λmaxa,
ASM=h+Sh=a+E+S-1Ea=λmax · a+a=λmax,
h+Th=a+E+S-1EE+S-1Ea=a+·λmax · λmax · a=λmax2.
Jh=h+Thh+Sh=λmax2λmax=λmax.
ϕik, l=exp-2πj kai+lbid-1.
Θ=a1b1a2b2aCbC.
mik, lϕik, l=mik, lexp-2πj kai+lbid-1
E+S-1E=e1+S-1e1e1+S-1e2 e1+S-1eCe2+S-1e1e2+S-1e2 e2+S-1eC   eC+S-1e1eC+S-1e2 eC+S-1eC,
TraceE+SE=i=1Cei+S-1ei=i=1Cmi-μ+S-1mi-μ.
Ψk+1=mk+1+S-1mk+1-2μk+S-1mk+1,  1kC.

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