Abstract

A technique for multiclass optical pattern recognition of different perspective views of an object is described. Each multiclass representation of an object is described as an orthonormal basis function expansion, and a single averaged matched spatial filter is then produced from a weighted linear combination of these functions. The technique is demonstrated for a terminal missile guidance application using IR tank imagery.

© 1980 Optical Society of America

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References

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  1. D. Casasent, M. Saverino, Proc. Soc. Photo-Opt. Instrum. Eng. 118, 11 (1977);D. Casasent, AIAA J., in press.
  2. J. Upatnieks, Final Report, Battelle Task 0489 (1977).
  3. K. Leib et al., Appl. Opt. 17, 2892 (1978).
    [CrossRef] [PubMed]
  4. A. Gara, Appl. Opt. 16, 149 (1977).
    [CrossRef] [PubMed]
  5. A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  6. D. Casasent, A. Furman, Appl. Opt. 16, 1652, 1662 (1977).
    [CrossRef] [PubMed]
  7. R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  8. C. Christensen, J. Upatnieks, B. Guenther, U.S. Army Missile Research and Development Command, Technical Report T-79-18 (1979).
  9. H. J. Caulfield, W. T. Maloney, Appl. Opt. 8, 2354 (1964).
    [CrossRef]
  10. H. J. Caulfield, D. Casasent, Opt. Eng. (March, in press 1980).
  11. N. Ahmed, K. Rao, Orthogonal Transforms for Digital Signal Processing (Springer, Heidelberg, 1975).
    [CrossRef]
  12. J. Wozencraft, I. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965).
  13. D. Bode, P. Bratt, Proc. Soc. Photo-Opt. Instrum. Eng. 95, (1976).
  14. Proceedings, SPIE Conference on IR Technology (1977), Vol. 124.
  15. Proceedings, SPIE Conference on Airborne Reconnaissance 4, Washington, D.C. (1979), Vol. 175.
  16. C. Hester, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 77, 201 (1979).
  17. M. Svedlow et al., IEEE Aerosp. Electron. Syst. AES-14, 141 (1978).
    [CrossRef]
  18. W. K. Pratt, IEEE Aerosp. Electron. Syst. AES-10, 353 (1974).
    [CrossRef]
  19. D. Casasent, D. Munoz, Proc. Soc. Photo-Opt. Instrum. Eng. 58, 201 (1979).

1979

C. Hester, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 77, 201 (1979).

D. Casasent, D. Munoz, Proc. Soc. Photo-Opt. Instrum. Eng. 58, 201 (1979).

1978

M. Svedlow et al., IEEE Aerosp. Electron. Syst. AES-14, 141 (1978).
[CrossRef]

K. Leib et al., Appl. Opt. 17, 2892 (1978).
[CrossRef] [PubMed]

1977

A. Gara, Appl. Opt. 16, 149 (1977).
[CrossRef] [PubMed]

D. Casasent, A. Furman, Appl. Opt. 16, 1652, 1662 (1977).
[CrossRef] [PubMed]

D. Casasent, M. Saverino, Proc. Soc. Photo-Opt. Instrum. Eng. 118, 11 (1977);D. Casasent, AIAA J., in press.

Proceedings, SPIE Conference on IR Technology (1977), Vol. 124.

1976

D. Bode, P. Bratt, Proc. Soc. Photo-Opt. Instrum. Eng. 95, (1976).

1974

W. K. Pratt, IEEE Aerosp. Electron. Syst. AES-10, 353 (1974).
[CrossRef]

1964

H. J. Caulfield, W. T. Maloney, Appl. Opt. 8, 2354 (1964).
[CrossRef]

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Ahmed, N.

N. Ahmed, K. Rao, Orthogonal Transforms for Digital Signal Processing (Springer, Heidelberg, 1975).
[CrossRef]

Bode, D.

D. Bode, P. Bratt, Proc. Soc. Photo-Opt. Instrum. Eng. 95, (1976).

Bratt, P.

D. Bode, P. Bratt, Proc. Soc. Photo-Opt. Instrum. Eng. 95, (1976).

Casasent, D.

C. Hester, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 77, 201 (1979).

D. Casasent, D. Munoz, Proc. Soc. Photo-Opt. Instrum. Eng. 58, 201 (1979).

D. Casasent, M. Saverino, Proc. Soc. Photo-Opt. Instrum. Eng. 118, 11 (1977);D. Casasent, AIAA J., in press.

D. Casasent, A. Furman, Appl. Opt. 16, 1652, 1662 (1977).
[CrossRef] [PubMed]

H. J. Caulfield, D. Casasent, Opt. Eng. (March, in press 1980).

Caulfield, H. J.

H. J. Caulfield, W. T. Maloney, Appl. Opt. 8, 2354 (1964).
[CrossRef]

H. J. Caulfield, D. Casasent, Opt. Eng. (March, in press 1980).

Christensen, C.

C. Christensen, J. Upatnieks, B. Guenther, U.S. Army Missile Research and Development Command, Technical Report T-79-18 (1979).

Duda, R.

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Furman, A.

D. Casasent, A. Furman, Appl. Opt. 16, 1652, 1662 (1977).
[CrossRef] [PubMed]

Gara, A.

Guenther, B.

C. Christensen, J. Upatnieks, B. Guenther, U.S. Army Missile Research and Development Command, Technical Report T-79-18 (1979).

Hart, P.

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Hester, C.

C. Hester, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 77, 201 (1979).

Jacobs, I.

J. Wozencraft, I. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965).

Leib, K.

Maloney, W. T.

Munoz, D.

D. Casasent, D. Munoz, Proc. Soc. Photo-Opt. Instrum. Eng. 58, 201 (1979).

Pratt, W. K.

W. K. Pratt, IEEE Aerosp. Electron. Syst. AES-10, 353 (1974).
[CrossRef]

Rao, K.

N. Ahmed, K. Rao, Orthogonal Transforms for Digital Signal Processing (Springer, Heidelberg, 1975).
[CrossRef]

Saverino, M.

D. Casasent, M. Saverino, Proc. Soc. Photo-Opt. Instrum. Eng. 118, 11 (1977);D. Casasent, AIAA J., in press.

Svedlow, M.

M. Svedlow et al., IEEE Aerosp. Electron. Syst. AES-14, 141 (1978).
[CrossRef]

Upatnieks, J.

J. Upatnieks, Final Report, Battelle Task 0489 (1977).

C. Christensen, J. Upatnieks, B. Guenther, U.S. Army Missile Research and Development Command, Technical Report T-79-18 (1979).

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Wozencraft, J.

J. Wozencraft, I. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965).

Appl. Opt.

IEEE Aerosp. Electron. Syst.

M. Svedlow et al., IEEE Aerosp. Electron. Syst. AES-14, 141 (1978).
[CrossRef]

W. K. Pratt, IEEE Aerosp. Electron. Syst. AES-10, 353 (1974).
[CrossRef]

IEEE Trans. Inf. Theory

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

D. Casasent, M. Saverino, Proc. Soc. Photo-Opt. Instrum. Eng. 118, 11 (1977);D. Casasent, AIAA J., in press.

D. Casasent, D. Munoz, Proc. Soc. Photo-Opt. Instrum. Eng. 58, 201 (1979).

C. Hester, D. Casasent, Proc. Soc. Photo-Opt. Instrum. Eng. 77, 201 (1979).

D. Bode, P. Bratt, Proc. Soc. Photo-Opt. Instrum. Eng. 95, (1976).

Proceedings, SPIE Conference on IR Technology

Proceedings, SPIE Conference on IR Technology (1977), Vol. 124.

Other

Proceedings, SPIE Conference on Airborne Reconnaissance 4, Washington, D.C. (1979), Vol. 175.

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

C. Christensen, J. Upatnieks, B. Guenther, U.S. Army Missile Research and Development Command, Technical Report T-79-18 (1979).

J. Upatnieks, Final Report, Battelle Task 0489 (1977).

H. J. Caulfield, D. Casasent, Opt. Eng. (March, in press 1980).

N. Ahmed, K. Rao, Orthogonal Transforms for Digital Signal Processing (Springer, Heidelberg, 1975).
[CrossRef]

J. Wozencraft, I. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of optical frequency plane correlator.

Fig. 2
Fig. 2

Typical IR tank imagery used.

Fig. 3
Fig. 3

Reconstruction of average filter.

Fig. 4
Fig. 4

Cross-sectional scans through one cross-correlation peak.

Tables (2)

Tables Icon

Table I Experimentally Obtained Unnormalized Correlation Matrix Rij

Tables Icon

Table II Digitally Computed Coefficients in the Gram-Schmidt Expansion of the Basis Functions

Equations (11)

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f ( x ) = j a j ϕ j ( x ) ,
g ( x ) = j b j ϕ j ( x ) ,
ϕ j ( x ) ϕ i ( x ) d x = δ j i .
f ̂ = ( a 1 , a 2 , . . . , a k ) ,
R f g ( τ ) = f ( x ) g ( x ) = f ( x + τ ) g ( x ) d x = i j a j b j ϕ j ( x + τ ) ϕ i ( x ) d x . R f g ( 0 ) = j a j b j = f ̂ ĝ
ĥ = c 1 f ̂ 1 + c 2 f ̂ 2 = ( c 1 a 11 + c 1 a 12 ) ϕ ̂ 1 + ( c 2 a 21 + c 2 a 22 ) ϕ ̂ 2 .
h ( x ) = j c j ϕ j ( x ) .
R g n h ( 0 ) = R n ( 0 ) = R n = g n h = j b n j c j .
R i j = g i g j
ϕ 1 ( x ) = g 1 ( x ) / k 1 ϕ 2 ( x ) = [ g 2 ( x ) C 12 ϕ 1 ( x ) ] / k 2 ϕ n ( x ) = [ g n ( x ) j = 1 n 1 C n j ϕ j ( x ) ] / k n
h = 0.64 ϕ 1 + 0.60 ϕ 2 + 0.42 ϕ 3 + 0.93 ϕ 4 + 0.57 ϕ 5 + 0.59 ϕ 6 + 1.85 ϕ 7 ,

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