Abstract

We introduce what is believed to be a novel concept by which several sensors with automatic target recognition (ATR) capability collaborate to recognize objects. Such an approach would be suitable for netted systems in which the sensors and platforms can coordinate to optimize end-to-end performance. We use correlation filtering techniques to facilitate the development of the concept, although other ATR algorithms may be easily substituted. Essentially, a self-configuring geometry of netted platforms is proposed that positions the sensors optimally with respect to each other, and takes into account the interactions among the sensor, the recognition algorithms, and the classes of the objects to be recognized. We show how such a paradigm optimizes overall performance, and illustrate the collaborative ATR scheme for recognizing targets in synthetic aperture radar imagery by using viewing position as a sensor parameter.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. V. K. Vijaya Kumar, "Tutorial survey of composite filter designs for optical correlators," Appl. Opt. 31, 4773-4801 (1992).
  2. D. Casasent, "Unified synthetic discriminant function computational formulation," Appl. Opt. 23, 1620-1627 (1984).
  3. A. Mahalanobis and A. J. Van Nevel, "A collaborative network of correlation filters for object recognition," in Optical Information Systems, B. Javidi and D. Psaltis, eds., Proc. SPIE 5202, 219-226 (2003).
    [CrossRef]
  4. R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley 1973).
  5. A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, and J. Epperson, "Unconstrained Correlation Filters," Appl. Opt. 33, 3751-3759 (1994).
  6. B. V. K. Vijaya Kumar, "Minimum variance synthetic discriminant functions," J. Opt. Soc. Am. A 3, 1579-1584 (1986).
  7. J. Figue and Ph. Refregier, "Optimality of trade-off filters," Appl. Opt. 32, 1933-1935 (1993).
  8. MSTAR/IU public release data set, Veda Incorporated, www.mbvlab.wpafb.af.mil/public/mbvdata.
  9. A. Mahalanobis, D. W. Carlson, and B. V. K. Vijaya Kumar, "Evaluation of MACH and DCCF correlation filters for SAR ATR using the MSTAR public database," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 460-469 (1998).
  10. A. Mahalanobis and B. V. K. Vijaya Kumar, "Important differences between distance classifier correlation filters and Fisher linear discriminant functions," in Automatic Target Recognition VIII, F. A. Sadjadi, ed., Proc. SPIE 3371, 263-274 (1998).
    [CrossRef]
  11. T. D. Ross, S. W. Worrell, V. J. Velten, J. C. Mossing, and M. L. Bryant, "Standard SAR ATR evaluation experiments using the MSTAR public release data set," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 566-575 (1998).
    [CrossRef]

2003 (1)

A. Mahalanobis and A. J. Van Nevel, "A collaborative network of correlation filters for object recognition," in Optical Information Systems, B. Javidi and D. Psaltis, eds., Proc. SPIE 5202, 219-226 (2003).
[CrossRef]

1998 (3)

A. Mahalanobis, D. W. Carlson, and B. V. K. Vijaya Kumar, "Evaluation of MACH and DCCF correlation filters for SAR ATR using the MSTAR public database," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 460-469 (1998).

A. Mahalanobis and B. V. K. Vijaya Kumar, "Important differences between distance classifier correlation filters and Fisher linear discriminant functions," in Automatic Target Recognition VIII, F. A. Sadjadi, ed., Proc. SPIE 3371, 263-274 (1998).
[CrossRef]

T. D. Ross, S. W. Worrell, V. J. Velten, J. C. Mossing, and M. L. Bryant, "Standard SAR ATR evaluation experiments using the MSTAR public release data set," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 566-575 (1998).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1986 (1)

1984 (1)

Bryant, M. L.

T. D. Ross, S. W. Worrell, V. J. Velten, J. C. Mossing, and M. L. Bryant, "Standard SAR ATR evaluation experiments using the MSTAR public release data set," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 566-575 (1998).
[CrossRef]

Carlson, D. W.

A. Mahalanobis, D. W. Carlson, and B. V. K. Vijaya Kumar, "Evaluation of MACH and DCCF correlation filters for SAR ATR using the MSTAR public database," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 460-469 (1998).

Casasent, D.

Duda, R. O.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley 1973).

Epperson, J.

Figue, J.

Hart, P. E.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley 1973).

Kumar, B. V. K. Vijaya

A. Mahalanobis and B. V. K. Vijaya Kumar, "Important differences between distance classifier correlation filters and Fisher linear discriminant functions," in Automatic Target Recognition VIII, F. A. Sadjadi, ed., Proc. SPIE 3371, 263-274 (1998).
[CrossRef]

A. Mahalanobis, D. W. Carlson, and B. V. K. Vijaya Kumar, "Evaluation of MACH and DCCF correlation filters for SAR ATR using the MSTAR public database," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 460-469 (1998).

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, and J. Epperson, "Unconstrained Correlation Filters," Appl. Opt. 33, 3751-3759 (1994).

B. V. K. Vijaya Kumar, "Tutorial survey of composite filter designs for optical correlators," Appl. Opt. 31, 4773-4801 (1992).

B. V. K. Vijaya Kumar, "Minimum variance synthetic discriminant functions," J. Opt. Soc. Am. A 3, 1579-1584 (1986).

Mahalanobis, A.

A. Mahalanobis and A. J. Van Nevel, "A collaborative network of correlation filters for object recognition," in Optical Information Systems, B. Javidi and D. Psaltis, eds., Proc. SPIE 5202, 219-226 (2003).
[CrossRef]

A. Mahalanobis and B. V. K. Vijaya Kumar, "Important differences between distance classifier correlation filters and Fisher linear discriminant functions," in Automatic Target Recognition VIII, F. A. Sadjadi, ed., Proc. SPIE 3371, 263-274 (1998).
[CrossRef]

A. Mahalanobis, D. W. Carlson, and B. V. K. Vijaya Kumar, "Evaluation of MACH and DCCF correlation filters for SAR ATR using the MSTAR public database," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 460-469 (1998).

A. Mahalanobis, B. V. K. Vijaya Kumar, S. Song, S. R. F. Sims, and J. Epperson, "Unconstrained Correlation Filters," Appl. Opt. 33, 3751-3759 (1994).

Mossing, J. C.

T. D. Ross, S. W. Worrell, V. J. Velten, J. C. Mossing, and M. L. Bryant, "Standard SAR ATR evaluation experiments using the MSTAR public release data set," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 566-575 (1998).
[CrossRef]

Refregier, Ph.

Ross, T. D.

T. D. Ross, S. W. Worrell, V. J. Velten, J. C. Mossing, and M. L. Bryant, "Standard SAR ATR evaluation experiments using the MSTAR public release data set," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 566-575 (1998).
[CrossRef]

Sims, S. R. F.

Song, S.

Van Nevel, A. J.

A. Mahalanobis and A. J. Van Nevel, "A collaborative network of correlation filters for object recognition," in Optical Information Systems, B. Javidi and D. Psaltis, eds., Proc. SPIE 5202, 219-226 (2003).
[CrossRef]

Velten, V. J.

T. D. Ross, S. W. Worrell, V. J. Velten, J. C. Mossing, and M. L. Bryant, "Standard SAR ATR evaluation experiments using the MSTAR public release data set," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 566-575 (1998).
[CrossRef]

Worrell, S. W.

T. D. Ross, S. W. Worrell, V. J. Velten, J. C. Mossing, and M. L. Bryant, "Standard SAR ATR evaluation experiments using the MSTAR public release data set," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 566-575 (1998).
[CrossRef]

Appl. Opt. (4)

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

Proc. SPIE (3)

A. Mahalanobis and A. J. Van Nevel, "A collaborative network of correlation filters for object recognition," in Optical Information Systems, B. Javidi and D. Psaltis, eds., Proc. SPIE 5202, 219-226 (2003).
[CrossRef]

A. Mahalanobis and B. V. K. Vijaya Kumar, "Important differences between distance classifier correlation filters and Fisher linear discriminant functions," in Automatic Target Recognition VIII, F. A. Sadjadi, ed., Proc. SPIE 3371, 263-274 (1998).
[CrossRef]

T. D. Ross, S. W. Worrell, V. J. Velten, J. C. Mossing, and M. L. Bryant, "Standard SAR ATR evaluation experiments using the MSTAR public release data set," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 566-575 (1998).
[CrossRef]

Other (3)

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley 1973).

MSTAR/IU public release data set, Veda Incorporated, www.mbvlab.wpafb.af.mil/public/mbvdata.

A. Mahalanobis, D. W. Carlson, and B. V. K. Vijaya Kumar, "Evaluation of MACH and DCCF correlation filters for SAR ATR using the MSTAR public database," in Algorithms for Synthetic Aperture Radar Imagery V, E. G. Zelnio, ed., Proc. SPIE 3370, 460-469 (1998).

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 (9)

Fig. 1
Fig. 1

(Color online) Sensors can fly toward the object at optimum angles if its orientation is known. Otherwise, the sensors may search for the correct 2-bit code by flying around the object at a relative angular separation of θ 1 θ 2 or α 1 α 2 , depending on whether it is believed to belong to class 1 or class 2.

Fig. 2
Fig. 2

Typical SAR images of (a) T72 and (b) BTR from the public domain MSTAR database.

Fig. 3
Fig. 3

Behavior of the MSM shows that the 0° view of the T72 is most separable from the view of the BTR at about 130°.

Fig. 4
Fig. 4

Separation metric depicted here as a function of all possible combinations of the viewing angles of both targets. This 2D array of values characterizes the separability of the two classes as a function of the angular position of the sensors. The best separation between the two classes occurs when class 1 (T72) at θ 1 = 30 ° is compared to class 2 (BTR) at α 1 = 130 ° . The next best separation occurs at θ 2 = 130 ° and α 2 = 40 ° .

Fig. 5
Fig. 5

(Color online) Optimum viewing geometry for ATR1 and ATR2 depends on the target class. Under the hypothesis that the object belongs to class 1, the platforms should form an angular separation of θ 1 θ 2 . Conversely, for a confirmed class 2 hypothesis, the platforms should maintain an angular separation of α 1 α 2 .

Fig. 6
Fig. 6

Search for maxima in the 3D hypercube can be accomplished by using the 1D and 2D components that compare two classes at a time. Only terms that contain m θ k are combined to compute J k = ( m θ k ) T D - 1 m θ k + i k C α i α k ( m θ k ) T D - 1 m θ i and find the angle where the maximum occurs with respect to the kth class.

Fig. 7
Fig. 7

Two ATR case yields better probability of correct decision in the presence of noise than the single ATR case.

Fig. 8
Fig. 8

(Color online) Sample SAR images of the three target classes from the public domain MSTAR data set.

Fig. 9
Fig. 9

Intergrated approach to automatic target recognition using the processing algorithm to determine the sensing geometry.

Tables (4)

Tables Icon

Table 1 Simple 3-Bit Binary Code to Represent Eight Classes

Tables Icon

Table 2 Optimization of the 3D MSM Function Yields the Optimum Combination of Angles for the Three Platforms to Recognize the Three Classes

Tables Icon

Table 3 Performance of Three ATRs Operating Independently

Tables Icon

Table 4 Performance of Three Coded ATRs Using Collaboration

Equations (30)

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

g ( n ) = k = 1 N h ( k ) x ( k + n ) .
y = h T x = g ( 0 ) = k = 1 N h ( k ) x ( k ) .
[ x 1 1 x N 1 x 1 2 x N 2 x 1 8 x N 8 ] T X
h 1 = [ 0 1 0 1 ]         [   1 1   ] u 1 ,
h 1 = X ( X T X ) - 1 u 1 .
H ( k , l ) = M ( k , l ) S ( k , l ) ,
M x θ ( k , l ) = 1 N i = 1 N X i ( k , l ) S x θ ( k , l ) = i = 1 N X i ( k , l ) - M x θ ( k , l ) 2 , M y α ( k , l ) = 1 N i = 1 N Y i ( k , l ) S y α ( k , l ) = i = 1 N Y i ( k , l ) - M y α ( k , l ) 2 .
H 1 ( k , l ) = M x θ ( k , l ) - M y α ( k , l ) S x θ ( k , l ) + S y α ( k , l ) .
Q ( θ , α ) = k l [ M x θ ( k , l ) - M y α ( k , l ) ] * H 1 ( k , l ) 2 = k l M x θ ( k , l ) - M y α ( k , l ) 2 S x θ ( k , l ) + S y α ( k , l ) .
H 2 ( k , l ) = M y α ( k , l ) - M x θ ( k , l ) S x θ ( k , l ) + S y α ( k , l ) .
h 3 = ( j = 1 8 S j θ j ) - 1 ( - i = 1 4 m i θ i + j = 5 8 m j θ j ) ,
Q 3 ( Θ ) = ( j = 5 8 m j θ j - i = 1 4 m i θ i ) T ( j = 1 8 S j θ j ) - 1 × ( j = 5 8 m j θ j - i = 1 4 m i θ i ) .
Q ( Θ ) = ( i = 1 C α i m θ i ) T ( j = 1 C S θ j ) - 1 ( k = 1 C α k m θ k ) ,
J ( Θ ) = ( i = 1 C α i m θ i ) T D - 1 ( k = 1 C α k m θ i ) .
J k = ( m θ k ) T D - 1 m θ k + i k C α i α k ( m θ k ) T D - 1 m θ i .
P C 1 = 0.5 { P ( ω 1 [ 1 ] ) + P ( ω 2 [ 0 ] ) } = 0.5 { P ( [ 1 ] ω 1 ) P ( [ 1 ] ω 1 ) + P ( [ 1 ] ω 2 ) + P ( [ 0 ] ω 2 ) P ( [ 0 ] ω 1 ) + P ( [ 0 ] ω 2 ) } ,
P C 2 = 0.5 { P ( ω 1 [ 1 , 0 ] ) + P ( ω 2 [ 0 , 1 ] ) } = 0.5 { P ( [ 1 , 0 ] ω 1 ) P ( [ 1 , 0 ] ω 1 ) + P ( [ 1 , 0 ] ω 2 ) + P ( [ 0 , 1 ] ω 2 ) P ( [ 0 , 1 ] ω 1 ) + P ( [ 0 , 1 ] ω 2 ) } .
P C 1 = p p + q .
P C 2 = P ( ω 1 [ 1 , 0 ] ) = P ( ω 2 [ 0 , 1 ] ) = p 2 p 2 + q 2 = p p + ( q 2 p ) .
p 2 p 2 + q 2 > p p + q ,
y = h T x + h T v ,
P ( [ 1 ] ω 1 ) = P ( y > T ω 1 )
= 1 2 π σ 1 2 T exp [ ( y - μ 1 ) σ 1 2 ] d y .
P ( [ 0 ] ω 2 ) = P ( y < T ω 2 )
= 1 2 π σ 2 2 - T exp [ ( y - μ 2 ) σ 2 2 ] d y .
P ( [ 1 , 0 ] ω 1 ) = 1 2 π C 1 T T exp [ 0.5 ( z μ 1 ) T × C 1 1 ( z μ 1 ) ] d z ,
P ( [ 0 , 1 ] ω 2 ) = 1 2 π C 2 T T exp [ 0.5 ( z μ 2 ) T × C 2 1 ( z μ 2 ) ] d z ,
μ 1 = [ h 1 T m 1 h 2 T m 1 ] , μ 2 = [ h 1 T m 2 h 2 T m 2 ] ,
C 1 = [ h 1 T h 2 T ] R 1 [ h 1 h 1 ] + σ 2 [ h 1 T h 1 0 0 h 2 T h 2 ] , and
C 2 = [ h 1 T h 2 T ] R 2 [ h 1 h 1 ] + σ 2 [ h 1 T h 1 0 0 h 2 T h 2 ] .

Metrics