Abstract

The extent of picture degradation of speckle, in particular in synthetic aperture radar pictures, has been investigated in the cases where an observer has to detect (a) a small feature immersed in a darker background, and (b) a square wave grating. In each case, a theoretical model is developed for the observer’s detection mechanism, and the probability of correct decision is related to relevant picture parameters such as contrast, looks per pixel, and size. These calculations are verified by psychophysical experiments using computer-simulated pictures. Detectability of gratings as a criterion for characterizing picture quality is shown to be far inferior to feature detectability.

© 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, C. R. Christensen, J. S. Bennett, B. D. Guenther, 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. O. Massey, R. B. Innes, J. M. Marks, J. Opt. Soc. Am. 6, 1305 (1976).
    [CrossRef]
  10. T. N. Cornsweet, Visual Perception (Academic, New York, 1970).
  11. F. Radcliff, M. K. Hartline, W. H. Miller, J. Opt. Soc. Am. 53, 110 (1963).
    [CrossRef]
  12. H. Nelson, J. Opt. Soc. Am. 53, 179 (1963).
    [CrossRef]
  13. L. D. Harmon, B. Julesz, Science 180, 1194 (1973).
    [CrossRef] [PubMed]
  14. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
  15. T. W. Bernard, A Symposium on Sampled Images (Perkin-Elmer, Norwalk, 1971).
  16. J. M. Findlay, Vision Res. 9, 157 (1969).
    [CrossRef] [PubMed]
  17. V. N. Korwar, Ph.D. Thesis, California Institute of Technology, Pasadena (1980).
  18. J. W. Goodman, Proc. IEEE 53, 1688 (1965).
    [CrossRef]
  19. E. J. Gumbel, Statistics of Extremes (Columbia U.P., New York, 1958).
  20. G. S. Watson, Ann. Math. Stat. 25, 798 (1954).
    [CrossRef]
  21. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (U.S. GPO, Washington, D.C., 1970).
  22. B. D. Guenther, C. R. Christensen, A. Jain, at IEEE Computer Society Conference on Pattern Recognition and Image Processing, 78CH1318-5C (1978).
  23. W. J. Dixon, F. J. Massey, Introduction to Statistical Analysis (McGraw-Hill, New York, 1969).
  24. F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
    [PubMed]
  25. C. F. Stromeyer, B. Julesz, J. Opt. Soc. Am. 62, 1221 (1972).
    [CrossRef] [PubMed]
  26. R. M. Jones, U. Tulunay-Keesey, J. Opt. Soc. Am. 70, 66 (1980).
    [CrossRef] [PubMed]
  27. J. I. Marcum, P. Swerling, IRE Trans. Inf. Theory IT-6, 59 (1960).
    [CrossRef]

1980 (1)

1976 (5)

1973 (1)

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

1972 (1)

1971 (1)

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

1969 (1)

J. M. Findlay, Vision Res. 9, 157 (1969).
[CrossRef] [PubMed]

1968 (1)

F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
[PubMed]

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).

1960 (1)

J. I. Marcum, P. Swerling, IRE Trans. Inf. Theory IT-6, 59 (1960).
[CrossRef]

1954 (1)

G. S. Watson, Ann. Math. Stat. 25, 798 (1954).
[CrossRef]

Bennett, J. S.

Bernard, T. W.

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

Brown, W. M.

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

Campbell, F. W.

F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
[PubMed]

Christensen, C. R.

N. George, C. R. Christensen, J. S. Bennett, B. D. Guenther, 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).

Findlay, J. M.

J. M. Findlay, Vision Res. 9, 157 (1969).
[CrossRef] [PubMed]

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, C. R. Christensen, J. S. Bennett, B. D. Guenther, 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).

Gumbel, E. J.

E. J. Gumbel, Statistics of Extremes (Columbia U.P., New York, 1958).

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.

Innes, R. B.

L. J. Porcello, N. O. Massey, R. B. Innes, J. M. Marks, J. Opt. Soc. Am. 6, 1305 (1976).
[CrossRef]

Jain, A.

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

Jones, R. M.

Julesz, B.

Korwar, V. N.

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

Kozma, A.

Marcum, J. I.

J. I. Marcum, P. Swerling, IRE Trans. Inf. Theory IT-6, 59 (1960).
[CrossRef]

Marks, J. M.

L. J. Porcello, N. O. Massey, R. B. Innes, J. M. Marks, J. Opt. Soc. Am. 6, 1305 (1976).
[CrossRef]

Massey, F. J.

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

Massey, N. O.

L. J. Porcello, N. O. Massey, R. B. Innes, J. M. Marks, J. Opt. Soc. Am. 6, 1305 (1976).
[CrossRef]

Miller, W. H.

Nelson, H.

Porcello, L. J.

L. J. Porcello, N. O. Massey, R. B. Innes, J. M. Marks, J. Opt. Soc. Am. 6, 1305 (1976).
[CrossRef]

Radcliff, F.

Rigden, J. D.

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

Robson, J. G.

F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
[PubMed]

Stromeyer, C. F.

Swerling, P.

J. I. Marcum, P. Swerling, IRE Trans. Inf. Theory IT-6, 59 (1960).
[CrossRef]

Swets, J. A.

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

Tulunay-Keesey, U.

Watson, G. S.

G. S. Watson, Ann. Math. Stat. 25, 798 (1954).
[CrossRef]

Ann. Math. Stat. (1)

G. S. Watson, Ann. Math. Stat. 25, 798 (1954).
[CrossRef]

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

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

IRE Trans. Inf. Theory (1)

J. I. Marcum, P. Swerling, IRE Trans. Inf. Theory IT-6, 59 (1960).
[CrossRef]

J. Opt. Soc. Am. (8)

J. Physiol. London (1)

F. W. Campbell, J. G. Robson, J. Physiol. London 197, 551 (1968).
[PubMed]

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]

Vision Res. (1)

J. M. Findlay, Vision Res. 9, 157 (1969).
[CrossRef] [PubMed]

Other (10)

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

E. J. Gumbel, Statistics of Extremes (Columbia U.P., New York, 1958).

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (U.S. GPO, Washington, D.C., 1970).

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

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

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

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

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

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).

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Figures (6)

Fig. 1
Fig. 1

Probability density functions pB(x), pG(x) with means MP0 and MP0 (1 + b) and asymptotic distribution ANa(x) of largest of N variables Bi with characteristic largest value xN, all with N = 104,M = 35, b = 1, and P0 = 1.

Fig. 2
Fig. 2

Detection of squares, examples of simulated pictures. Both photographs have L = 1 and 5-dB constrast: (left) D = 4; (right) D = 5.

Fig. 3
Fig. 3

Theoretical and experimental probabilities of error pe (continuous curve) and p ^ e (discrete points) vs M for N = 104, b = 2.16.

Fig. 4
Fig. 4

Detection of gratings, examples of simulated pictures. Both photographs have L = 2, D = 3, H = 40, and 2-dB contrast: (left) V = 6; (right) V = 12.

Fig. 5
Fig. 5

Data points and regression curve: experimental pc vs SNNR: ○, data points with V > H; +, data points with V < H; *, data points with V = H.

Fig. 6
Fig. 6

Detectability of D = 6 squares vs detectability of D = 2 gratings in pictures with L = 12 and 1-dB contrast. There are four squares, one in each quadrant of the 200 × 200 photograph on the left; the photograph on the right is a 100 × 100 grating.

Tables (3)

Tables Icon

Table I Detection of D * D Square in 100 * 100 Picture

Tables Icon

Table II Predicted Threshold Parameters for pt = 0.95, N = 104

Tables Icon

Table III Line Pair Gratings

Equations (15)

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p c = 0 p G ( x ) A N ( x ) d x = 0 p G ( x ) [ 0 x p B ( y ) d y ] N d x ,
p B ( x ) = 1 P 0 M x ( M - 1 ) exp ( - x / P 0 ) Γ ( M )             for x > 0 ,
p G ( x ) = 1 P 0 M ( 1 + b ) M x ( M - 1 ) Γ ( M ) exp { - x / [ P 0 ( 1 + b ) ] }             for x > 0 ,
A N ( x ) = P [ largest of B i ( i = 1 , 2 , , N ) x ] .
A N a ( x ) = exp { - exp [ - a N ( x - x N ) ] } ,
F ( x N ) = 1 - ( 1 / N ) ,
a N = N f ( x N ) ,
p c = 0 p G ( x ) A N a ( x ) d x .
z p l ( N ) + ( 4 M - 1 ) 1 / 2 ( 1 + b ) 1 / 2 - ( 4 M - 1 ) 1 / 2 = z p t ,
p l = ( 0.95 ) 1 / N ,
M = L D 2 .
b D L constant ,
SSNR = 16 π 2 ( b / 2 ) 2 ( 1 + b / 2 ) 2 + ( b / 2 ) 2 2 D 1.5 L ( H V · 1.5 2 D ) 1 / 2 ,
= 16 π 2 ( b / 2 ) 2 ( 1 + b / 2 ) 2 + ( b / 2 ) 2 L ( H V · 2 D 1.5 ) 1 / 2 .
p ^ c = 1 - ½ exp [ - ( SSNR ) 0.25 ] + e ,

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