Abstract

The problem investigated is that of a human observer having to distinguish between certain specified geometrical forms corrupted by speckle—an idealization of the problem of a scientist studying a synthetic aperture radar map. Specifically, the cases of two simple alternative forms and of two and four orientations of a simple form have been considered. A theoretical model is developed for the observer’s decision process by analogy with optimal receiver theory, and the probability of a correct decision is related to form parameters like size, contrast, and looks. These calculations are verified by psychophysical experiments using computer-simulated pictures.

© 1981 Optical Society of America

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References

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  1. J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).
  2. J. W. Goodman, J. Opt. Soc. Am. 66, 1145 (1976).
    [CrossRef]
  3. J. C. Dainty, Ed., Laser Speckle and Related Phenomena (Springer, Berlin, 1975).
  4. J. C. Dainty, Opt. Acta 18, 327 (1971).
    [CrossRef]
  5. N. George, J. S. Bennett, B. D. Guenther, C. R. Christensen, J. Opt. Soc. Am. 66, 1282 (1976).
    [CrossRef]
  6. A. Kozma, C. R. Christensen, J. Opt. Soc. Am. 66, 1257 (1976).
    [CrossRef]
  7. R. D. Harger, Synthetic Aperture Radar Systems: Theory and Design (Academic, New York, 1970).
  8. W. M. Brown, IEEE Trans. Aerosp. Electron. Syst. AES-3, 217 (1976).
    [CrossRef]
  9. L. J. Porcello, N. G. Massey, R. B. Innes, J. M. Marks, J. Opt. Soc. Am. 66, 1305 (1976).
    [CrossRef]
  10. V. N. Korwar, J. R. Pierce, Appl. Opt. 20, 312 (1981).
    [CrossRef] [PubMed]
  11. J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965).
  12. T. W. Bernard, A Symposium on Sampled Images (Perkin-Elmer, Norwalk, Conn., 1971).
  13. J. W. Wulfech, J. H. Taylor, Eds., Form Discrimination as Related to Military Problems, Publication 561, NAS-NRC (U.S. GPO, Washington, D.C., 1957).
  14. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
  15. T. N. Cornsweet, Visual Perception (Academic, New York, 1970).
  16. F. Radcliff, M. K. Hartline, W. H. Miller, J. Opt. Soc. Am. 53, 110 (1963).
    [CrossRef]
  17. H. Helson, J. Opt. Soc. Am. 53, 179 (1963).
    [CrossRef]
  18. L. D. Harmon, B. Julesz, Science 180, 1194 (1973).
    [CrossRef] [PubMed]
  19. V. N. Korwar, Ph.D. Thesis, California Institute of Technology, Pasadena (1980).
  20. J. W. Goodman, Proc. IEEE 53, 1688 (1965).
    [CrossRef]
  21. W. J. Dixon, F. J. Massey, Introduction to Statistical Analysis (McGraw-Hill, New York, 1969).
  22. B. D. Guenther, C. R. Christensen, A. Jain, at IEEE Computer Society Conference on Pattern Recognition and Image Processing, 78CH1318-5C (1978).

1981 (1)

1976 (5)

1973 (1)

L. D. Harmon, B. Julesz, Science 180, 1194 (1973).
[CrossRef] [PubMed]

1971 (1)

J. C. Dainty, Opt. Acta 18, 327 (1971).
[CrossRef]

1965 (1)

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

1963 (2)

1962 (1)

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Bennett, J. S.

Bernard, T. W.

T. W. Bernard, A Symposium on Sampled Images (Perkin-Elmer, Norwalk, Conn., 1971).

Brown, W. M.

W. M. Brown, IEEE Trans. Aerosp. Electron. Syst. AES-3, 217 (1976).
[CrossRef]

Christensen, C. R.

N. George, J. S. Bennett, B. D. Guenther, C. R. Christensen, J. Opt. Soc. Am. 66, 1282 (1976).
[CrossRef]

A. Kozma, C. R. Christensen, J. Opt. Soc. Am. 66, 1257 (1976).
[CrossRef]

B. D. Guenther, C. R. Christensen, A. Jain, at IEEE Computer Society Conference on Pattern Recognition and Image Processing, 78CH1318-5C (1978).

Cornsweet, T. N.

T. N. Cornsweet, Visual Perception (Academic, New York, 1970).

Dainty, J. C.

J. C. Dainty, Opt. Acta 18, 327 (1971).
[CrossRef]

Dixon, W. J.

W. J. Dixon, F. J. Massey, Introduction to Statistical Analysis (McGraw-Hill, New York, 1969).

George, N.

Goodman, J. W.

Gordon, E. I.

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Guenther, B. D.

N. George, J. S. Bennett, B. D. Guenther, C. R. Christensen, J. Opt. Soc. Am. 66, 1282 (1976).
[CrossRef]

B. D. Guenther, C. R. Christensen, A. Jain, at IEEE Computer Society Conference on Pattern Recognition and Image Processing, 78CH1318-5C (1978).

Harger, R. D.

R. D. Harger, Synthetic Aperture Radar Systems: Theory and Design (Academic, New York, 1970).

Harmon, L. D.

L. D. Harmon, B. Julesz, Science 180, 1194 (1973).
[CrossRef] [PubMed]

Hartline, M. K.

Helson, H.

Innes, R. B.

Jacobs, I. M.

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

Jain, A.

B. D. Guenther, C. R. Christensen, A. Jain, at IEEE Computer Society Conference on Pattern Recognition and Image Processing, 78CH1318-5C (1978).

Julesz, B.

L. D. Harmon, B. Julesz, Science 180, 1194 (1973).
[CrossRef] [PubMed]

Korwar, V. N.

V. N. Korwar, J. R. Pierce, Appl. Opt. 20, 312 (1981).
[CrossRef] [PubMed]

V. N. Korwar, Ph.D. Thesis, California Institute of Technology, Pasadena (1980).

Kozma, A.

Marks, J. M.

Massey, F. J.

W. J. Dixon, F. J. Massey, Introduction to Statistical Analysis (McGraw-Hill, New York, 1969).

Massey, N. G.

Miller, W. H.

Pierce, J. R.

Porcello, L. J.

Radcliff, F.

Rigden, J. D.

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Swets, J. A.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Wozencraft, J. M.

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

Appl. Opt. (1)

IEEE Trans. Aerosp. Electron. Syst. (1)

W. M. Brown, IEEE Trans. Aerosp. Electron. Syst. AES-3, 217 (1976).
[CrossRef]

J. Opt. Soc. Am. (6)

Opt. Acta (1)

J. C. Dainty, Opt. Acta 18, 327 (1971).
[CrossRef]

Proc. IEEE (1)

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[CrossRef]

Proc. IRE (1)

J. D. Rigden, E. I. Gordon, Proc. IRE 50, 2367 (1962).

Science (1)

L. D. Harmon, B. Julesz, Science 180, 1194 (1973).
[CrossRef] [PubMed]

Other (10)

V. N. Korwar, Ph.D. Thesis, California Institute of Technology, Pasadena (1980).

W. J. Dixon, F. J. Massey, Introduction to Statistical Analysis (McGraw-Hill, New York, 1969).

B. D. Guenther, C. R. Christensen, A. Jain, at IEEE Computer Society Conference on Pattern Recognition and Image Processing, 78CH1318-5C (1978).

J. C. Dainty, Ed., Laser Speckle and Related Phenomena (Springer, Berlin, 1975).

R. D. Harger, Synthetic Aperture Radar Systems: Theory and Design (Academic, New York, 1970).

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

T. W. Bernard, A Symposium on Sampled Images (Perkin-Elmer, Norwalk, Conn., 1971).

J. W. Wulfech, J. H. Taylor, Eds., Form Discrimination as Related to Military Problems, Publication 561, NAS-NRC (U.S. GPO, Washington, D.C., 1957).

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

T. N. Cornsweet, Visual Perception (Academic, New York, 1970).

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Figures (3)

Fig. 1
Fig. 1

Forms used in two alternative forms experiments: (a) set 1: U vs O; (b) set 2: O vs S.

Fig. 2
Fig. 2

Forms used in (a) two alternative orientations experiments = set 3; (b) four alternative orientations experiments = set 4.

Fig. 3
Fig. 3

Examples of simulated pictures. Both photographs have J = 3 and 3-dB contrast: (left) L = 34; (right) L = 8.

Tables (4)

Tables Icon

Table I Two Alternative Forms; Set 1 (U and O)

Tables Icon

Table II Two Alternative Forms; Set 2 (O and S)

Tables Icon

Table III Two Orientations; Set 3 (U and R)

Tables Icon

Table IV Four Orientations; Set 4 (U, D, L, R)

Equations (12)

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

p d ( x ) = 1 P 0 M x ( M - 1 ) exp ( - x / P 0 ) Γ ( M ) ( for x > 0 ) ,
p b ( x ) = 1 P 0 M ( 1 + b ) M x ( M - 1 ) exp { - x / [ P 0 ( 1 + b ) ] } Γ ( M ) ( for x > 0 ) ,
x t = P 0 [ M ln ( 1 + b ) ] ( 1 + b b ) .
p ( e b ) = 0 x t p b ( x ) d x ,
p ( e d ) = x t p d ( x ) d x .
p c = 1 - ½ [ p ( e d ) + p ( e b ) ] .
x t P 0 M [ 1 + ( b / 2 ) ] ,
p c 1 - ½ { Q ( b M 2 ( 1 + b ) ) + Q ( b M 2 ) } ,
Q ( x ) = 1 2 π x exp ( - z 2 / 2 ) d z
p c = 0 p b ( x ) d x 0 x p d ( y ) d y ,
p c 1 - Q { b M 2 [ 1 + ( 1 + b ) 2 ] } .
p c = 0 p d ( x ) [ x p b ( y ) d y ] 3 d x .

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