Abstract

The correlation of several 1-D projections of a 2-D image are considered for pattern recognition. A theoretical analysis and SNR comparison to 2-D correlations are provided with successful simulated results that show that the use of two or three 1-D correlations can identify and discriminate the 26 characters in the alphabet. Several possible 1-D optical correlators to implement projection correlations are described.

© 1988 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Casasent, W. T. Chang, “Correlation Synthetic Discriminant Functions,” Appl. Opt. 25, 2343 (1986).
    [CrossRef] [PubMed]
  2. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum Average Correlation Energy (MACE) Filters,” Appl. Opt. 26, 3633 (1987).
    [CrossRef] [PubMed]
  3. Y. N. Hsu, H. H. Arsenault, “Optical Pattern Recognition Using Circular Harmonic Expansion,” Appl. Opt. 21, 4016 (1982).
    [CrossRef] [PubMed]
  4. K. Mersereau, G. M. Morris, “Scale, Rotation, and Shift Invariant Image Recognition,” Appl. Opt. 25, 2338 (1986).
    [CrossRef] [PubMed]
  5. F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983), pp. 264–270.
  6. S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983), pp. 1–50.
  7. A. Rosenfeld, A. C. Kak, Digital Picture Processing I (Academic, New York, 1982), pp. 365–369.
  8. D. Ros, I. Juvells, S. Vallmitajana, J. R. De F. Moneo, “A Simplified Method for the Automatic Alignment of Images Affected by a Random Noise,” Opt. Acta 31, 1151 (1984).
    [CrossRef]
  9. K. T. Ma, G. Kusic, “An Algorithm for Distortion Analysis in Two-Dimensional Patterns Using Its Projections,” in Proceedings, Seventh New England Bioengineering Conference (1979), p. 177.
  10. P. Breuer, M. Vajita, “Structural Character Recognition by Forming Projections,” Probl. Control Inf. Theory 4, 339 (1975).
  11. D. Casasent, J. Lambert, “General I and Q Data Processing on a Multichannel AO System,” Appl. Opt. 25, 3217 (1986).
    [CrossRef] [PubMed]

1987 (1)

1986 (3)

1984 (1)

D. Ros, I. Juvells, S. Vallmitajana, J. R. De F. Moneo, “A Simplified Method for the Automatic Alignment of Images Affected by a Random Noise,” Opt. Acta 31, 1151 (1984).
[CrossRef]

1982 (1)

1975 (1)

P. Breuer, M. Vajita, “Structural Character Recognition by Forming Projections,” Probl. Control Inf. Theory 4, 339 (1975).

Arsenault, H. H.

Breuer, P.

P. Breuer, M. Vajita, “Structural Character Recognition by Forming Projections,” Probl. Control Inf. Theory 4, 339 (1975).

Casasent, D.

Chang, W. T.

Deans, S. R.

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983), pp. 1–50.

Hsu, Y. N.

Juvells, I.

D. Ros, I. Juvells, S. Vallmitajana, J. R. De F. Moneo, “A Simplified Method for the Automatic Alignment of Images Affected by a Random Noise,” Opt. Acta 31, 1151 (1984).
[CrossRef]

Kak, A. C.

A. Rosenfeld, A. C. Kak, Digital Picture Processing I (Academic, New York, 1982), pp. 365–369.

Kusic, G.

K. T. Ma, G. Kusic, “An Algorithm for Distortion Analysis in Two-Dimensional Patterns Using Its Projections,” in Proceedings, Seventh New England Bioengineering Conference (1979), p. 177.

Lambert, J.

Ma, K. T.

K. T. Ma, G. Kusic, “An Algorithm for Distortion Analysis in Two-Dimensional Patterns Using Its Projections,” in Proceedings, Seventh New England Bioengineering Conference (1979), p. 177.

Mahalanobis, A.

Mersereau, K.

Moneo, J. R. De F.

D. Ros, I. Juvells, S. Vallmitajana, J. R. De F. Moneo, “A Simplified Method for the Automatic Alignment of Images Affected by a Random Noise,” Opt. Acta 31, 1151 (1984).
[CrossRef]

Morris, G. M.

Ros, D.

D. Ros, I. Juvells, S. Vallmitajana, J. R. De F. Moneo, “A Simplified Method for the Automatic Alignment of Images Affected by a Random Noise,” Opt. Acta 31, 1151 (1984).
[CrossRef]

Rosenfeld, A.

A. Rosenfeld, A. C. Kak, Digital Picture Processing I (Academic, New York, 1982), pp. 365–369.

Vajita, M.

P. Breuer, M. Vajita, “Structural Character Recognition by Forming Projections,” Probl. Control Inf. Theory 4, 339 (1975).

Vallmitajana, S.

D. Ros, I. Juvells, S. Vallmitajana, J. R. De F. Moneo, “A Simplified Method for the Automatic Alignment of Images Affected by a Random Noise,” Opt. Acta 31, 1151 (1984).
[CrossRef]

Vijaya Kumar, B. V. K.

Yu, F. T. S.

F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983), pp. 264–270.

Appl. Opt. (5)

Opt. Acta (1)

D. Ros, I. Juvells, S. Vallmitajana, J. R. De F. Moneo, “A Simplified Method for the Automatic Alignment of Images Affected by a Random Noise,” Opt. Acta 31, 1151 (1984).
[CrossRef]

Probl. Control Inf. Theory (1)

P. Breuer, M. Vajita, “Structural Character Recognition by Forming Projections,” Probl. Control Inf. Theory 4, 339 (1975).

Other (4)

K. T. Ma, G. Kusic, “An Algorithm for Distortion Analysis in Two-Dimensional Patterns Using Its Projections,” in Proceedings, Seventh New England Bioengineering Conference (1979), p. 177.

F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983), pp. 264–270.

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983), pp. 1–50.

A. Rosenfeld, A. C. Kak, Digital Picture Processing I (Academic, New York, 1982), pp. 365–369.

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 (10)

Fig. 1
Fig. 1

Examples of (a) 1-D projection and (b) the Fourier transform slice it is equivalent to.

Fig. 2
Fig. 2

Equivalence of 1-D projection correlations and projections of the 2-D correlation pattern: (a) horizontal and vertical projections of a 2-D image; (b) horizontal and vertical projections of the 2-D correlation pattern.

Fig. 3
Fig. 3

Comparison of a projection correlation and an integrated 2-D correlation: (a) input character C image; (b) 2-D correlation; (c) vertical projection correlation; and (d) vertically integrated 2-D correlation.

Fig. 4
Fig. 4

Zero-mean projection correlations: (a) vertical projection correlation and (b) horizontal projection correlation.

Fig. 5
Fig. 5

Noisy projection and 2-D correlations: (a) noisy input; (b) 2-D correlation input; and (c) horizontal projection correlation.

Fig. 6
Fig. 6

Projection cross-correlation results: (a) input data; (b) horizontal projection correlations with a filter of C; and (c) 45° diagonal projection correlations with a filter of C.

Fig. 7
Fig. 7

Noisy projection cross-correlation results: (a) noisy input data; (b) horizontal projection correlation with a filter of C; and (c) 45° diagonal projection correlation with a filter of C.

Fig. 8
Fig. 8

Multichannel AO space-integrating projection correlator.

Fig. 9
Fig. 9

Multichannel AO time-integrating projection correlator.

Fig. 10
Fig. 10

Use of multiple projections to identify multiple objects and resolve ambiguities when two objects have the same horizontal and vertical coordinates.

Equations (7)

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

p θ ( r ) = ( x , y ) δ ( r - x cos θ - y sin θ ) d x d y ,
P θ ( ρ ) = - 0 π f ( r 0 , θ 0 ) exp [ - j 2 π ρ r 0 cos ( θ 0 - θ ) ] r 0 d θ 0 d r 0 .
c θ ( r ) = P f ( ρ ) P g * ( ρ ) exp ( j 2 π ρ r ) d ρ = C f , g ( ρ , θ ) exp ( j 2 π ρ r ) d ρ = c f , g ( x , y ) δ ( r - x cos θ - y sin θ ) d x d y .
s x ( y ) = s ( x , y ) d x , s y ( x ) = s ( x , y ) d y ,
r x ( y ) = r ( x , y ) d x , r y ( x ) = r ( x , y ) d y .
SNR = peak value ( standard deviation away from the peak ) ,
PSR = peak value average value around the peak .

Metrics