Abstract

The laboratory realization of smart matched spatial filters (specifically snythetic discriminant functions) is considered and studied via computer simulation. The realization of these distortion-invariant correlator functions by computer-generated hologram and other methods is considered. Multiclass filters are addressed in this work. Phase-only filters and filters with a quantized number of amplitude and phase levels are considered. Phase-only filters are found to perform well for some imagery, but filters with some amplitude response are preferable. We also considered the number of phase and magnitude levels required and found four levels of each to be adequate.

© 1986 Optical Society of America

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References

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  1. D. Casasent, “Unified Synthetic Discriminant Function Computational Formulation,” Appl. Opt. 23, 1620 (1984).
    [CrossRef] [PubMed]
  2. B. V. K. Vijaya Kumar, E. Pochapsky, D. Casasent, “Optimality Considerations in Modified Matched Spatial Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 519, 85 (1984).
  3. W. T. Chang, D. Casasent, D. Fetterly, “SDF Control of Correlation Plane Structure for 3-D Object Representation and Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 507, 9 (1984).
  4. D. Casasent, W. Rozzi, D. Fetterly, “Projection Synthetic Discriminant Function Performance,” Opt. Eng. 23, 716 (1984).
    [CrossRef]
  5. D. Casasent, W. Rozzi, D. Fetterly, “Correlation Synthetic Discriminant Functions for Object Recognition and Classification in High Clutter,” Proc. Soc. Photo-Opt. Instrum. Eng. 575, (Aug.1985).
  6. D. Casasent, W. T. Chang, “Correlation Synthetic Discriminant Functions,” Appl. Opt. 25, 2343 (1986).
    [CrossRef] [PubMed]
  7. J. Horner, P. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
    [CrossRef] [PubMed]
  8. P. Gianino, J. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695 (1984).
    [CrossRef]
  9. J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
    [CrossRef]
  10. J. L. Horner, H. O. Bartelt, “Two-Bit Correlation,” Appl. Opt. 24, 2889 (1985).
    [CrossRef] [PubMed]
  11. H. Bartelt, J. Horner, “Improving Binary Phase Correlation Filters Using Iterative Techniques,” Appl. Opt. 24, 2894 (1985).
    [CrossRef] [PubMed]
  12. H. J. Caulfield, “Linear Combinations of Filters for Character Recognition: a Unified Treatment,” Appl. Opt. 19, 3877 (1980); Y. N. Hsu, H. H. Arsenault, “Optical Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4016 (1982).
    [CrossRef] [PubMed]
  13. A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 5129 (1981).
    [CrossRef]

1986 (1)

1985 (3)

J. L. Horner, H. O. Bartelt, “Two-Bit Correlation,” Appl. Opt. 24, 2889 (1985).
[CrossRef] [PubMed]

H. Bartelt, J. Horner, “Improving Binary Phase Correlation Filters Using Iterative Techniques,” Appl. Opt. 24, 2894 (1985).
[CrossRef] [PubMed]

D. Casasent, W. Rozzi, D. Fetterly, “Correlation Synthetic Discriminant Functions for Object Recognition and Classification in High Clutter,” Proc. Soc. Photo-Opt. Instrum. Eng. 575, (Aug.1985).

1984 (7)

P. Gianino, J. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695 (1984).
[CrossRef]

J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
[CrossRef]

B. V. K. Vijaya Kumar, E. Pochapsky, D. Casasent, “Optimality Considerations in Modified Matched Spatial Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 519, 85 (1984).

W. T. Chang, D. Casasent, D. Fetterly, “SDF Control of Correlation Plane Structure for 3-D Object Representation and Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 507, 9 (1984).

D. Casasent, W. Rozzi, D. Fetterly, “Projection Synthetic Discriminant Function Performance,” Opt. Eng. 23, 716 (1984).
[CrossRef]

J. Horner, P. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
[CrossRef] [PubMed]

D. Casasent, “Unified Synthetic Discriminant Function Computational Formulation,” Appl. Opt. 23, 1620 (1984).
[CrossRef] [PubMed]

1981 (1)

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 5129 (1981).
[CrossRef]

1980 (1)

Bartelt, H.

Bartelt, H. O.

Butler, S.

J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
[CrossRef]

Casasent, D.

D. Casasent, W. T. Chang, “Correlation Synthetic Discriminant Functions,” Appl. Opt. 25, 2343 (1986).
[CrossRef] [PubMed]

D. Casasent, W. Rozzi, D. Fetterly, “Correlation Synthetic Discriminant Functions for Object Recognition and Classification in High Clutter,” Proc. Soc. Photo-Opt. Instrum. Eng. 575, (Aug.1985).

B. V. K. Vijaya Kumar, E. Pochapsky, D. Casasent, “Optimality Considerations in Modified Matched Spatial Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 519, 85 (1984).

W. T. Chang, D. Casasent, D. Fetterly, “SDF Control of Correlation Plane Structure for 3-D Object Representation and Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 507, 9 (1984).

D. Casasent, W. Rozzi, D. Fetterly, “Projection Synthetic Discriminant Function Performance,” Opt. Eng. 23, 716 (1984).
[CrossRef]

D. Casasent, “Unified Synthetic Discriminant Function Computational Formulation,” Appl. Opt. 23, 1620 (1984).
[CrossRef] [PubMed]

Caulfield, H. J.

Chang, W. T.

D. Casasent, W. T. Chang, “Correlation Synthetic Discriminant Functions,” Appl. Opt. 25, 2343 (1986).
[CrossRef] [PubMed]

W. T. Chang, D. Casasent, D. Fetterly, “SDF Control of Correlation Plane Structure for 3-D Object Representation and Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 507, 9 (1984).

Fetterly, D.

D. Casasent, W. Rozzi, D. Fetterly, “Correlation Synthetic Discriminant Functions for Object Recognition and Classification in High Clutter,” Proc. Soc. Photo-Opt. Instrum. Eng. 575, (Aug.1985).

W. T. Chang, D. Casasent, D. Fetterly, “SDF Control of Correlation Plane Structure for 3-D Object Representation and Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 507, 9 (1984).

D. Casasent, W. Rozzi, D. Fetterly, “Projection Synthetic Discriminant Function Performance,” Opt. Eng. 23, 716 (1984).
[CrossRef]

Gianino, P.

J. Horner, P. Gianino, “Phase-Only Matched Filtering,” Appl. Opt. 23, 812 (1984).
[CrossRef] [PubMed]

P. Gianino, J. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695 (1984).
[CrossRef]

Horner, J.

Horner, J. L.

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 5129 (1981).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 5129 (1981).
[CrossRef]

Pochapsky, E.

B. V. K. Vijaya Kumar, E. Pochapsky, D. Casasent, “Optimality Considerations in Modified Matched Spatial Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 519, 85 (1984).

Riggins, J.

J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
[CrossRef]

Rozzi, W.

D. Casasent, W. Rozzi, D. Fetterly, “Correlation Synthetic Discriminant Functions for Object Recognition and Classification in High Clutter,” Proc. Soc. Photo-Opt. Instrum. Eng. 575, (Aug.1985).

D. Casasent, W. Rozzi, D. Fetterly, “Projection Synthetic Discriminant Function Performance,” Opt. Eng. 23, 716 (1984).
[CrossRef]

Vijaya Kumar, B. V. K.

B. V. K. Vijaya Kumar, E. Pochapsky, D. Casasent, “Optimality Considerations in Modified Matched Spatial Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 519, 85 (1984).

Appl. Opt. (6)

Opt. Eng. (3)

D. Casasent, W. Rozzi, D. Fetterly, “Projection Synthetic Discriminant Function Performance,” Opt. Eng. 23, 716 (1984).
[CrossRef]

P. Gianino, J. Horner, “Additional Properties of the Phase-Only Correlation Filter,” Opt. Eng. 23, 695 (1984).
[CrossRef]

J. Riggins, S. Butler, “Simulation of Synthetic Discriminant Function Optical Implementation,” Opt. Eng. 23, 721 (1984).
[CrossRef]

Proc. IEEE (1)

A. V. Oppenheim, J. S. Lim, “The Importance of Phase in Signals,” Proc. IEEE 69, 5129 (1981).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

D. Casasent, W. Rozzi, D. Fetterly, “Correlation Synthetic Discriminant Functions for Object Recognition and Classification in High Clutter,” Proc. Soc. Photo-Opt. Instrum. Eng. 575, (Aug.1985).

B. V. K. Vijaya Kumar, E. Pochapsky, D. Casasent, “Optimality Considerations in Modified Matched Spatial Filters,” Proc. Soc. Photo-Opt. Instrum. Eng. 519, 85 (1984).

W. T. Chang, D. Casasent, D. Fetterly, “SDF Control of Correlation Plane Structure for 3-D Object Representation and Recognition,” Proc. Soc. Photo-Opt. Instrum. Eng. 507, 9 (1984).

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Figures (4)

Fig. 1
Fig. 1

Typical true class 1 [images (a) and (b)] and false class 2 [images (c) and (d)] imagery showing broadside [images (b) and (d)] and 40° aspect views [images (a) and (c)] data.

Fig. 2
Fig. 2

Typical true (a) and false (b) class-correlation plane outputs for a phase-only pSDF with binary image data.

Fig. 3
Fig. 3

Typical true (a) and false (b) class-correlation plane outputs for a phase-only pSDF with edge-enhanced image data.

Fig. 4
Fig. 4

Typical true-class cSDF correlation plane pattern using a filter with a quantized number of magnitude and phase levels.

Tables (1)

Tables Icon

Table I Phase-Only Filter and Selected Quantized (Number of Amplitude and Phase Levels) Filter Performance for Projection Synthetic Discriminant Functions and for Correlation Synthetic Discriminant Functions

Equations (7)

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

h ( x , y ) = a m v m ( x , y ) ,
a = P - 1 u ,
J ( h ) = h T R T h h T R F h .
R T h = λ R F h ,
N = N F + 0.25 ( N T - N F ) .
H ( u , v ) = H ( u , v ) exp [ j ϕ ( u , v ) ] .
t ( x , y ) = exp [ j ϕ ( x , y ) ] .

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