Abstract

A new distortion-invariant optical correlation filter to produce easily detectable correlation peaks in the presence of noise and clutter and to provide better intraclass recognition is presented. The basic ideas of the minimum variance synthetic discriminant function correlation filter (which minimizes noise variance in the output correlation peak/plane) and the minimum average correlation energy filter (which minimizes the average correlation plane energy over all the training images) are unified in a new filter that produces sharp correlation peaks while maintaining an acceptable signal-to-noise ratio in the correlation plane output. This new minimum noise and correlation energy filter approach introduces the concept of using the spectral envelope of the training images and the noise power spectrum to obtain a tight bound to the energy minimization problem that is associated with distortion-invariant filters in noise while allowing the user a variable parameter to adjust depending on the noise or clutter that is expected. We present the mathematical basis for the minimum noise and correlation energy filter and the initial simulation results.

© 1992 Optical Society of America

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References

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  1. A. B. VanderLugt, “Signal detection by complex matched spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
    [CrossRef]
  2. D. Casasent, “Unified synthetic discriminant function computational formulation,” Appl. Opt. 23, 1620–1627 (1984).
    [CrossRef] [PubMed]
  3. B. V. K. Vijaya Kumar, “Minimum variance synthetic discriminant functions,” J. Opt. Soc. Am. A 3, 1579–1584 (1986).
    [CrossRef]
  4. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987).
    [CrossRef] [PubMed]
  5. D. Casasent, G. Ravichandran, “Advanced distortion invariant MACE filters,” Appl. Opt. (to be published).
  6. D. Casasent, G. Ravichandran, “Modified MACE filters for distortion-invariant recognition of relocatable targets,” in Airborne Reconnaissance XIII, P. A. Henkel, F. R. LaGesse, W. W. Schurter, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1156, 177–187 (1989).
  7. A. M. S. I. Sudharsanan, M. K. Sundaresan, “Unified framework for the synthesis of synthetic discriminant function with reduced noise variance and sharp correlation structure,” Opt. Eng. 29, 1021–1028 (1990).
    [CrossRef]
  8. P. Refregier, “Filter design for optical pattern recognition: multi-criteria optimization approach,” Opt. Lett. 15, 854–856 (1990).
    [CrossRef] [PubMed]
  9. B. V. K. Kumar Vijaya, A. Mahalanobis, “Alternate interpretation for minimum variance synthetic discriminant functions,” Appl. Opt. 25, 2484–2485 (1986).
    [CrossRef]
  10. D. Casasent, G. Ravichandran, S. Bollapragada, “Gaussian-MACE filters,” Appl. Opt. 30, 5176 (1991).
    [CrossRef] [PubMed]

1991 (1)

1990 (2)

A. M. S. I. Sudharsanan, M. K. Sundaresan, “Unified framework for the synthesis of synthetic discriminant function with reduced noise variance and sharp correlation structure,” Opt. Eng. 29, 1021–1028 (1990).
[CrossRef]

P. Refregier, “Filter design for optical pattern recognition: multi-criteria optimization approach,” Opt. Lett. 15, 854–856 (1990).
[CrossRef] [PubMed]

1987 (1)

1986 (2)

1984 (1)

1964 (1)

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

Bollapragada, S.

Casasent, D.

D. Casasent, G. Ravichandran, S. Bollapragada, “Gaussian-MACE filters,” Appl. Opt. 30, 5176 (1991).
[CrossRef] [PubMed]

A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filters,” Appl. Opt. 26, 3633–3640 (1987).
[CrossRef] [PubMed]

D. Casasent, “Unified synthetic discriminant function computational formulation,” Appl. Opt. 23, 1620–1627 (1984).
[CrossRef] [PubMed]

D. Casasent, G. Ravichandran, “Modified MACE filters for distortion-invariant recognition of relocatable targets,” in Airborne Reconnaissance XIII, P. A. Henkel, F. R. LaGesse, W. W. Schurter, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1156, 177–187 (1989).

D. Casasent, G. Ravichandran, “Advanced distortion invariant MACE filters,” Appl. Opt. (to be published).

Mahalanobis, A.

Ravichandran, G.

D. Casasent, G. Ravichandran, S. Bollapragada, “Gaussian-MACE filters,” Appl. Opt. 30, 5176 (1991).
[CrossRef] [PubMed]

D. Casasent, G. Ravichandran, “Advanced distortion invariant MACE filters,” Appl. Opt. (to be published).

D. Casasent, G. Ravichandran, “Modified MACE filters for distortion-invariant recognition of relocatable targets,” in Airborne Reconnaissance XIII, P. A. Henkel, F. R. LaGesse, W. W. Schurter, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1156, 177–187 (1989).

Refregier, P.

Sudharsanan, A. M. S. I.

A. M. S. I. Sudharsanan, M. K. Sundaresan, “Unified framework for the synthesis of synthetic discriminant function with reduced noise variance and sharp correlation structure,” Opt. Eng. 29, 1021–1028 (1990).
[CrossRef]

Sundaresan, M. K.

A. M. S. I. Sudharsanan, M. K. Sundaresan, “Unified framework for the synthesis of synthetic discriminant function with reduced noise variance and sharp correlation structure,” Opt. Eng. 29, 1021–1028 (1990).
[CrossRef]

VanderLugt, A. B.

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

Vijaya, B. V. K. Kumar

Vijaya Kumar, B. V. K.

Appl. Opt. (4)

IEEE Trans. Inf. Theory (1)

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

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

Opt. Eng. (1)

A. M. S. I. Sudharsanan, M. K. Sundaresan, “Unified framework for the synthesis of synthetic discriminant function with reduced noise variance and sharp correlation structure,” Opt. Eng. 29, 1021–1028 (1990).
[CrossRef]

Opt. Lett. (1)

Other (2)

D. Casasent, G. Ravichandran, “Advanced distortion invariant MACE filters,” Appl. Opt. (to be published).

D. Casasent, G. Ravichandran, “Modified MACE filters for distortion-invariant recognition of relocatable targets,” in Airborne Reconnaissance XIII, P. A. Henkel, F. R. LaGesse, W. W. Schurter, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1156, 177–187 (1989).

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Figures (10)

Fig. 1
Fig. 1

Effect of the MACE preprocessor on signal and noise.

Fig. 2
Fig. 2

Energy envelope used by the MICE filter.

Fig. 3
Fig. 3

Effect of MICE preprocessor on signal and noise.

Fig. 4
Fig. 4

Missile launcher (32 × 32) imagery.

Fig. 5
Fig. 5

Effect of the MVMACE preprocessor on signal and noise.

Fig. 6
Fig. 6

Effect of the MINACE preprocessor on signal and noise.

Fig. 7
Fig. 7

Correlation plane generated by the MACE filter with a true class training image.

Fig. 8
Fig. 8

Correlation plane generated by the MACE filter with a true class nontraining image.

Fig. 9
Fig. 9

Correlation plane generated by the MINACE filter with a true class training image,

Fig. 10
Fig. 10

Correlation plane generated by the MINACE filter with a true class nontraining image.

Tables (4)

Tables Icon

Table I MICE Filter Simulation Results

Tables Icon

Table II MINACE Filter Tests for ZSU-23 at a Depression Angle of 70°

Tables Icon

Table III MINACE Filter Tests for SA-13 at a Depression Angle of 70°

Tables Icon

Table IV MINACE Filter Tests for SCUD-B at a Depression Angle of 30°

Equations (31)

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E i = u v H ( u , v ) 2 X i ( u , v ) 2 = u v H ( u , v ) 2 D i ( u , v )             i = 1 , 2 , , N T ,
E = ( 1 / N T ) i = 1 N T E i = u v { H ( u , v ) 2 [ ( 1 / N T ) i = 1 N T D i ( u , v ) ] } = u v H ( u , v ) 2 D ( u , v ) .
H * ( u , v ) X i ( u , v ) = u i             i = 1 , 2 , , N T .
E = H + [ ( 1 / N T ) i = 1 N T D i ] H = H + DH ,
H = D - 1 X ( X + D - 1 X ) - 1 u .
H = D - 1 / 2 [ Y ( Y + Y ) - 1 u ] ,
Y i = D - 1 / 2 X i .
E max > E i             for i = 1 , 2 , , N T             ( for all H ) ,
E max = i = 1 N T E i ,
E max = u v H ( u , v ) 2 T ( u , v ) ,
u v H ( u , v ) 2 T ( u , v ) > u v H ( u , v ) 2 D i ( u , v )             for i = 1 , 2 , N T [ for all H ( u , v ) ] .
H ( u , v ) 2 T ( u , v ) > H ( u , v ) 2 D i ( u , v )             for i = 1 , 2 , , N T [ for all H ( u , v ) ]
T ( u , v ) > D i ( u , v ) ,             i = 1 , 2 , , N T .
T ( u , v ) = max [ D 1 ( u , v ) , D 2 ( u , v ) , , D N T ( u , v ) ] ,
T ( k , k ) = max [ D 1 ( k , k ) , D 2 ( k , k ) , , D N T ( k , k ) ] ,
E = H + TH ,
H + X = u
Φ = H + TH - 2 λ 1 ( H + X 1 - u 1 ) - - 2 λ N T ( H + X N T - u N T ) ,
H = T - 1 X ( X + T - 1 X ) - 1 u .
E c = H + ( D i + N ) H = H + D i H + H + NH = E i + E n ,
E max i > E n ,             E max i > E i             ( for all H ) ,
E max i = u v H ( u , v ) 2 T i ( u , v ) .
u v H ( u , v ) 2 T i ( u , v ) > u v H ( u , v ) 2 D i ( u , v ) , u v H ( u , v ) 2 T i ( u , v ) > u v H ( u , v ) 2 N ( u , v ) ,             [ for all H ( u , v ) ] .
H ( u , v ) 2 T i ( u , v ) > H ( u , v ) 2 D i ( u , v ) , H ( u , v ) 2 T i ( u , v ) > H ( u , v ) 2 N ( u , v )             [ for all H ( u , v ) ] ,
T i ( u , v ) = max [ D i ( u , v ) , N ( u , v ) ] .
E max i = H + T i H ,
H = T i - 1 X ( X + T i - 1 X ) - 1 u .
E max > E max i             i = 1 , 2 , , N T ( for all H ) ,
H = T - 1 X ( X + T - 1 X ) - 1 u ,
T ( k , k ) = max [ T 1 ( k , k ) , T 2 ( k , k ) , , T N T ( k , k ) ] .
T ( k , k ) = max [ D 1 ( k , k ) , D 2 ( k , k ) , , D N T ( k , k ) , N ( k , k ) ] ,

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