Abstract

The essence of character recognition is a comparison between the unknown character and a set of reference patterns. Usually, these reference patterns are all possible characters themselves, the whole alphabet in the case of letter characters. Obviously, N analog measurements are highly redundant, since only K = log2N binary decisions are enough to identify one out of N characters. Therefore, we devised K reference patterns accordingly. These patterns, called principal components, are found by digital image processing, but used in an optical analog computer. We will explain the concept of principal components, and we will describe experiments with several optical character recognition systems, based on this concept.

© 1979 Optical Society of America

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References

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  1. E. Goldberg, German Patent (1932).
  2. A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964); see also J. W. Goodman: Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 177–184.
    [CrossRef]
  3. A. W. Lohmann, “Several Optical Correlation Methods,” in Proceedings of IEEE Conference on Optical Computing, Washington, D.C. (IEEE, New York, 1975), IEEE Catalog 75 EH 0941-5c, p. 142.
  4. D. Casasent, D. Psaltis, in Progress in Optics, Vol. 16, E. Wolf, Ed. (1978).
    [CrossRef]
  5. L. P. Horwitz, G. L. Shelton, Proc. Inst. Radio Eng. 49, 175 (1961).
  6. S. Lowenthal, A. Werts, C. R. Acad. Sci. Ser. B: 266, 542 (1968); A. W. Lohmann, Appl. Opt. 7, 561 (1968); A. W. Lohmann, H. W. Werlich, Appl. Opt. 10, 670 (1971).
    [CrossRef] [PubMed]
  7. W. T. Maloney, Appl. Opt. 10, 2554 (1971).
    [CrossRef] [PubMed]
  8. J. D. Armitage, A. W. Lohmann, Appl. Opt. 4, 461 (1965).
    [CrossRef]
  9. H. J. Caulfield, W. T. Maloney, Appl. Opt. 8, 2354 (1969); P. S. Naidu, Opt. Commun. 12, 287 (1974).
    [CrossRef] [PubMed]
  10. B. Braunecker, A. W. Lohmann, Opt. Commun. 11, 141 (1974).
    [CrossRef]
  11. J. Fleuret, H. Maitre, Opt. Commun. 17, 64 (1976).
    [CrossRef]
  12. P. J. Dhrymes, Econometrics (Springer, New York, 1974), pp. 1–20.
  13. R. W. Hamming, Bell Syst. Tech. J. 29, 147 (1950); W. W. Peterson, Error Correcting Codes (Wiley, New York, 1961).
  14. W. H. Lee, in Progress in Optics, 16, 121 (1978); W. J. Dallas, in Topics in Applied Physics, B. R. Frieden, Ed., in press (Springer, New York).
    [CrossRef]
  15. P. Chavel, S. Lowenthal, J. Opt. Soc. Am. 66, 14 (1976); A. W. Lohmann, Appl. Opt. 16, 261 (1977); W. T. Rhodes, Appl. Opt. 16, 265 (1977); A. W. Lohmann, W. T. Rhodes, Appl. Opt. 17, 1141 (1978); W. Stoner, Appl. Opt. 17, 2454 (1978).
    [CrossRef] [PubMed]
  16. B. Braunecker, R. Hauck, W. T. Rhodes, Appl. Opt. 18, 44 (1979).
    [CrossRef] [PubMed]
  17. P. Chavel, S. Lowenthal, J. Opt. Soc. Am. 68, 559, 721 (1978).
    [CrossRef]
  18. B. Braunecker, R. Hauck, A. W. Lohmann, Photogr. Sci. Eng. 21, 278 (1977).
  19. B. Braunecker, R. Hauck, Opt. Commun. 20, 234 (1977).
    [CrossRef]
  20. B. Braunecker, R. Hauck, K. Reuter, Nucl. Instrum. Methods 150, 321 (1978).
    [CrossRef]
  21. R. Hauck, Diplomarbeit, Physical Institute Erlangen-Nürnberg (1976).
  22. M. Z. Nashed, Generalized Inverses and Applications (Academic, New York, 1976).

1979 (1)

1978 (3)

P. Chavel, S. Lowenthal, J. Opt. Soc. Am. 68, 559, 721 (1978).
[CrossRef]

W. H. Lee, in Progress in Optics, 16, 121 (1978); W. J. Dallas, in Topics in Applied Physics, B. R. Frieden, Ed., in press (Springer, New York).
[CrossRef]

B. Braunecker, R. Hauck, K. Reuter, Nucl. Instrum. Methods 150, 321 (1978).
[CrossRef]

1977 (2)

B. Braunecker, R. Hauck, A. W. Lohmann, Photogr. Sci. Eng. 21, 278 (1977).

B. Braunecker, R. Hauck, Opt. Commun. 20, 234 (1977).
[CrossRef]

1976 (2)

1974 (1)

B. Braunecker, A. W. Lohmann, Opt. Commun. 11, 141 (1974).
[CrossRef]

1971 (1)

1969 (1)

1968 (1)

S. Lowenthal, A. Werts, C. R. Acad. Sci. Ser. B: 266, 542 (1968); A. W. Lohmann, Appl. Opt. 7, 561 (1968); A. W. Lohmann, H. W. Werlich, Appl. Opt. 10, 670 (1971).
[CrossRef] [PubMed]

1965 (1)

1964 (1)

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964); see also J. W. Goodman: Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 177–184.
[CrossRef]

1961 (1)

L. P. Horwitz, G. L. Shelton, Proc. Inst. Radio Eng. 49, 175 (1961).

1950 (1)

R. W. Hamming, Bell Syst. Tech. J. 29, 147 (1950); W. W. Peterson, Error Correcting Codes (Wiley, New York, 1961).

Armitage, J. D.

Braunecker, B.

B. Braunecker, R. Hauck, W. T. Rhodes, Appl. Opt. 18, 44 (1979).
[CrossRef] [PubMed]

B. Braunecker, R. Hauck, K. Reuter, Nucl. Instrum. Methods 150, 321 (1978).
[CrossRef]

B. Braunecker, R. Hauck, A. W. Lohmann, Photogr. Sci. Eng. 21, 278 (1977).

B. Braunecker, R. Hauck, Opt. Commun. 20, 234 (1977).
[CrossRef]

B. Braunecker, A. W. Lohmann, Opt. Commun. 11, 141 (1974).
[CrossRef]

Casasent, D.

D. Casasent, D. Psaltis, in Progress in Optics, Vol. 16, E. Wolf, Ed. (1978).
[CrossRef]

Caulfield, H. J.

Chavel, P.

Dhrymes, P. J.

P. J. Dhrymes, Econometrics (Springer, New York, 1974), pp. 1–20.

Fleuret, J.

J. Fleuret, H. Maitre, Opt. Commun. 17, 64 (1976).
[CrossRef]

Goldberg, E.

E. Goldberg, German Patent (1932).

Hamming, R. W.

R. W. Hamming, Bell Syst. Tech. J. 29, 147 (1950); W. W. Peterson, Error Correcting Codes (Wiley, New York, 1961).

Hauck, R.

B. Braunecker, R. Hauck, W. T. Rhodes, Appl. Opt. 18, 44 (1979).
[CrossRef] [PubMed]

B. Braunecker, R. Hauck, K. Reuter, Nucl. Instrum. Methods 150, 321 (1978).
[CrossRef]

B. Braunecker, R. Hauck, Opt. Commun. 20, 234 (1977).
[CrossRef]

B. Braunecker, R. Hauck, A. W. Lohmann, Photogr. Sci. Eng. 21, 278 (1977).

R. Hauck, Diplomarbeit, Physical Institute Erlangen-Nürnberg (1976).

Horwitz, L. P.

L. P. Horwitz, G. L. Shelton, Proc. Inst. Radio Eng. 49, 175 (1961).

Lee, W. H.

W. H. Lee, in Progress in Optics, 16, 121 (1978); W. J. Dallas, in Topics in Applied Physics, B. R. Frieden, Ed., in press (Springer, New York).
[CrossRef]

Lohmann, A. W.

B. Braunecker, R. Hauck, A. W. Lohmann, Photogr. Sci. Eng. 21, 278 (1977).

B. Braunecker, A. W. Lohmann, Opt. Commun. 11, 141 (1974).
[CrossRef]

J. D. Armitage, A. W. Lohmann, Appl. Opt. 4, 461 (1965).
[CrossRef]

A. W. Lohmann, “Several Optical Correlation Methods,” in Proceedings of IEEE Conference on Optical Computing, Washington, D.C. (IEEE, New York, 1975), IEEE Catalog 75 EH 0941-5c, p. 142.

Lowenthal, S.

P. Chavel, S. Lowenthal, J. Opt. Soc. Am. 68, 559, 721 (1978).
[CrossRef]

P. Chavel, S. Lowenthal, J. Opt. Soc. Am. 66, 14 (1976); A. W. Lohmann, Appl. Opt. 16, 261 (1977); W. T. Rhodes, Appl. Opt. 16, 265 (1977); A. W. Lohmann, W. T. Rhodes, Appl. Opt. 17, 1141 (1978); W. Stoner, Appl. Opt. 17, 2454 (1978).
[CrossRef] [PubMed]

S. Lowenthal, A. Werts, C. R. Acad. Sci. Ser. B: 266, 542 (1968); A. W. Lohmann, Appl. Opt. 7, 561 (1968); A. W. Lohmann, H. W. Werlich, Appl. Opt. 10, 670 (1971).
[CrossRef] [PubMed]

Maitre, H.

J. Fleuret, H. Maitre, Opt. Commun. 17, 64 (1976).
[CrossRef]

Maloney, W. T.

Nashed, M. Z.

M. Z. Nashed, Generalized Inverses and Applications (Academic, New York, 1976).

Psaltis, D.

D. Casasent, D. Psaltis, in Progress in Optics, Vol. 16, E. Wolf, Ed. (1978).
[CrossRef]

Reuter, K.

B. Braunecker, R. Hauck, K. Reuter, Nucl. Instrum. Methods 150, 321 (1978).
[CrossRef]

Rhodes, W. T.

Shelton, G. L.

L. P. Horwitz, G. L. Shelton, Proc. Inst. Radio Eng. 49, 175 (1961).

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964); see also J. W. Goodman: Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 177–184.
[CrossRef]

Werts, A.

S. Lowenthal, A. Werts, C. R. Acad. Sci. Ser. B: 266, 542 (1968); A. W. Lohmann, Appl. Opt. 7, 561 (1968); A. W. Lohmann, H. W. Werlich, Appl. Opt. 10, 670 (1971).
[CrossRef] [PubMed]

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

R. W. Hamming, Bell Syst. Tech. J. 29, 147 (1950); W. W. Peterson, Error Correcting Codes (Wiley, New York, 1961).

C. R. Acad. Sci. Ser. B (1)

S. Lowenthal, A. Werts, C. R. Acad. Sci. Ser. B: 266, 542 (1968); A. W. Lohmann, Appl. Opt. 7, 561 (1968); A. W. Lohmann, H. W. Werlich, Appl. Opt. 10, 670 (1971).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964); see also J. W. Goodman: Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 177–184.
[CrossRef]

J. Opt. Soc. Am. (2)

Nucl. Instrum. Methods (1)

B. Braunecker, R. Hauck, K. Reuter, Nucl. Instrum. Methods 150, 321 (1978).
[CrossRef]

Opt. Commun. (3)

B. Braunecker, A. W. Lohmann, Opt. Commun. 11, 141 (1974).
[CrossRef]

J. Fleuret, H. Maitre, Opt. Commun. 17, 64 (1976).
[CrossRef]

B. Braunecker, R. Hauck, Opt. Commun. 20, 234 (1977).
[CrossRef]

Photogr. Sci. Eng. (1)

B. Braunecker, R. Hauck, A. W. Lohmann, Photogr. Sci. Eng. 21, 278 (1977).

Proc. Inst. Radio Eng. (1)

L. P. Horwitz, G. L. Shelton, Proc. Inst. Radio Eng. 49, 175 (1961).

Progress in Optics (1)

W. H. Lee, in Progress in Optics, 16, 121 (1978); W. J. Dallas, in Topics in Applied Physics, B. R. Frieden, Ed., in press (Springer, New York).
[CrossRef]

Other (6)

R. Hauck, Diplomarbeit, Physical Institute Erlangen-Nürnberg (1976).

M. Z. Nashed, Generalized Inverses and Applications (Academic, New York, 1976).

E. Goldberg, German Patent (1932).

A. W. Lohmann, “Several Optical Correlation Methods,” in Proceedings of IEEE Conference on Optical Computing, Washington, D.C. (IEEE, New York, 1975), IEEE Catalog 75 EH 0941-5c, p. 142.

D. Casasent, D. Psaltis, in Progress in Optics, Vol. 16, E. Wolf, Ed. (1978).
[CrossRef]

P. J. Dhrymes, Econometrics (Springer, New York, 1974), pp. 1–20.

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Figures (6)

Fig. 1
Fig. 1

Direct correlators: (A) for coherent amplitude signals; (I) for incoherent intensity signals; (P) for incoherent spatial power spectra, where SOU, OBJ, REF, DET, and DFU denote, respectively, the light source, the object, the reference pattern, the detector, and the moving diffuser.

Fig. 2
Fig. 2

Correlation by spatial filtering: (A) for coherent amplitude signals; (I) for incoherent intensity signals; (P) for incoherent spatial power spectra, where FILT denotes the spatial filter.

Fig. 3
Fig. 3

Incoherent spatial filtering: (a) test set of N = 16 alphanumerical object patterns; (b) K = 4 PC spatial filter pairs v ˜ k ± * calculated from the pattern set of (a) and plotted using a gray level coding technique; (c) histogram of the NK = 64 measured correlation signals.

Fig. 4
Fig. 4

Incoherent direct correlation: (a) K = 4 PC-mask pairs calculated from the pattern set of Fig. 3(a) and plotted using a binary pulse width coding technique; (b) histogram of the NK = 64 measured correlation signals.

Fig. 5
Fig. 5

Incoherent direct correlation with x-rays: (a) experimental setup: A point source illuminates both object and reference masks. The intensity is measured as a function of the rotation angle of object vs reference mask by a multichannel analyzer; (b) object mask: eight different patterns are obtained by rotating this mask to different angular orientations (differing by π/4); (c) PC-mask: two different PC-patterns are obtained at different angular positions of this mask (rotated by π/8); (d) results: the counting rate as a function of angle φ modulated by the ternary code sequence (0,1), (0,2), (1,0) ….

Fig. 6
Fig. 6

Test set of 64 Chinese characters.

Equations (48)

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( A ) : u v = u ( x + x ) v * ( x ) d x , ( I ) : u 2 * v 2 = u ( x + x ) 2 v ( x ) 2 d x , ( P ) : u ˜ 2 v ˜ 2 = u ˜ ( ν + ν ) 2 v ˜ ( ν ) 2 d ν ,
u ˜ ( ν ) = u ( x ) exp ( - 2 π i ν x ) d x .
u v = u ( x + x ) v * ( x ) d x = u ˜ ( ν ) v ˜ * ( ν ) exp ( + 2 π i ν x ) d ν = u ( x ) v ˜ * ( ν ) exp [ + 2 π i ν ( x - x ) ] d ν d x .
O F = O ( x + x ) F * ( x ) d x = I ( x ) .
F k ( x ) = O k ( x ) / [ O k ( x ) 2 d x ] 1 / 2             ( k = 1 , 2 N ) .
I n k ( 0 ) = C n k < C n n             ( k = 1 , 2 N ; but k n ) .
F k ( x ) = j = 1 N γ j k O j ( x ) ( j , k = 1 , 2 N ) , I n k ( 0 ) = O n ( x ) F k * ( x ) d x ,
I n k ( 0 ) 2 = δ n k in case A or I n k ( 0 ) = δ n k in cases I and P } .
O n ( x ) ( n = 1 , 2 N = 2 K )             F k ( x ) ( k = 1 , 2 K ) , I n k ( 0 ) = O n ( x ) F k * ( x ) d x ,
I n k ( 0 ) 2 = B n k in case A or I n k ( 0 ) = B n k in cases I and P , B n k = zero or one } .
O n ( x ) = m = 1 M O n ( m / W ) sinc ( x - m / W ) ,
F k ( x ) = m = 1 M F k ( m / W ) sinc ( x - m / W ) .
I n k ( 0 ) = m = 1 M O n ( m / W ) F k * ( m / W ) ,
O _ + · F _ k = I k *             ( k = 1 K )
E _ k = O _ · γ k ,
γ k = ( O _ + · O _ ) - 1 · I k * ,
F _ k = O _ # · I k * = O _ · ( O _ + · O _ ) - 1 · I k * ,
O _ + · G _ r = ( r = 1 R ) .
H _ k = r = 1 R g r k G _ r = G _ · g k
δ I n k * = δ _ O _ n + · F _ k = δ _ O _ n + · O _ # · I k * .
σ k 2 = ( 1 / N ) n = 1 N δ I n k * 2 = ( 1 / N ) δ I k T · δ I k * .
σ k 2 = ( 1 / N ) F _ k + · δ _ O _ · δ _ O _ + · F _ k = ( 1 / N ) F _ k + · Σ _ 2 · F _ k .
F _ k = E _ k + H _ k ,
H _ k = - λ _ · E _ k = - G _ · ( G _ + Σ _ 2 · G _ ) - 1 · G _ + · Σ _ 2 · E _ k .
σ k 2 = ( 1 / N ) I k T · O _ # + · ( 1 _ - λ _ + ) · Σ _ 2 · ( 1 _ - λ _ ) · O _ # · I k * .
σ k 2 = ( 1 / N ) I k T · O _ # + · Σ _ 2 · O _ # · I k * .
F _ k = Σ _ - 2 · O _ · ( O _ + · Σ _ - 2 · O _ ) - 1 · I k * ,
σ k 2 = ( 1 / N ) I k T · ( O _ + · Σ _ - 2 · O _ ) - 1 · I k * .
R k = 1 K { 1 - [ 1 / ( 2 π ) 1 / 2 σ k ] · - Δ I / 2 + Δ I / 2 exp ( - I k 2 / 2 σ k 2 ) d I k }
F _ k = F _ k + - F _ k -
O m n O m n · ( 1 + α Z )             ( n = 1 N , m = 1 M ) .
σ k 2 = ( 1 / N ) C _ + · F _ k 2 .
F _ k = E _ k + H _ k = E _ k + G _ · g k
σ k 2 = ( 1 / N ) D _ k + A _ · g k 2 ,
δ σ k 2 δ g s k * = ( 1 / N ) m = 1 M A m s * ( D m k + r = 1 R A m r g r k )             ( s = 1 R ) .
m = 1 M r = 1 R A m s * A m r g r k = - m = 1 M A m s * D m k r = 1 R ( m = 1 M A m s * A m r ) g r k = - m = 1 M A m s * D m k } .
A _ + · A _ · g k = - A _ + · D _ k .
g k = - ( A _ + · A _ ) - 1 · A _ + · D _ k .
F _ k = E _ k + G _ · g k = E _ k - G _ · ( A _ + · A _ ) - 1 · A _ + · D _ k .
δ 2 σ k 2 δ g s k * δ g t k = ( 1 / N ) m = 1 M A m s * A m t             ( s , t = 1 R ) .
{ δ 2 σ k 2 δ g s k * δ g t k } = ( 1 / N ) A _ + · A _ .
O ^ _ + · F ^ _ k = I k * .
E ^ k = O ^ # · I k * = O ^ · ( O ^ + · O ^ ) - 1 · I k *
E ˇ   _ k = V _ + · E _ k = V _ + · V _ · O _ · ( O _ + · V _ + · V _ · O _ ) - 1 · I k d * ,
O ˇ + · E k = O _ + · V _ + · E ^ k = O _ + · E ^ _ k = I k * .
H _ k = - G · ( A _ + · A _ ) - 1 · A _ + · D ˇ _ ) k
H ˇ _ k = - G _ · ( A _ + · A _ ) - 1 · G _ + · C _ · C _ + · V _ + · V _ · O _ · ( O _ + · V _ + · V _ · O _ ) - 1 · I k * .
F _ k = E ˇ _ k = Σ _ - 2 · O _ · ( O _ + · Σ _ - 2 · O _ ) - 1 · I k * .

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