Abstract

We evaluated a metric for predicting the discriminability of different digitized versions of alphanumeric characters. The metric is based on the assumption that there exists a visual filter such that discriminability is monotonic with the contrast energy in the visually filtered difference between stimuli. To test this hypothesis, we presented two same or different digital versions of a master character and asked subjects to indicate whether the characters were the same or different in a forced-choice procedure with feedback. The filtered contrast energy difference was calculated by convolving the difference between stimulus pairs with filters derived from published human contrast sensitivity functions, following an initial nonlinear transformation of stimulus intensity, and summing the squared result. For some types of stimulus difference, such as contrast quantization errors and Gaussian blurring, performance on discrimination tasks is monotonically related to the contrast energy of the filtered difference vector. The results are consistent with the hypothesis that there exists a single psychometric function that can predict the discriminability of different digitized versions of characters when displayed on various devices.

© 1990 Optical Society of America

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References

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  1. J. Kajiya, M. Ullner, “Filtering high quality text for display on raster scan devices,” Comput. Graphics 15, 7–15 (1981).
    [CrossRef]
  2. J. L. Mannos, D. J. Sakrison, “The effects of a visual fidelity criterion on the encoding of images,” IEEE Trans. Inf. Theory IT-20, 525–536 (1974).
    [CrossRef]
  3. S. Ohtsuka, M. Inoue, K. Watanabe, “Quality evaluation of pictures with multiple impairments based on visually weighted error,” SID Dig. 9, 428–431 (1988).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. T. N. Cornsweet, Visual Perception (Academic, New York, 1970).
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1990 (1)

J. M. A. Loomis, “Model of character recognition and legibility,” J. Exp. Psychol. Hum. Percept. Perform. 16, 106–120 (1990).
[CrossRef] [PubMed]

1989 (2)

N. P. Lyons, J. E. Farrell, “Linear systems analysis of CRT displays,” SID Dig. 10, 220–223 (1989).

A. B. Watson, A. E. Fitzhugh, “Modeling character legibility,” SID Dig. 10, 360–363 (1989).

1988 (2)

S. Ohtsuka, M. Inoue, K. Watanabe, “Quality evaluation of pictures with multiple impairments based on visually weighted error,” SID Dig. 9, 428–431 (1988).

K. R. K. Nielsen, B. A. Wandell, “Discrete analysis of spatial-sensitivity models,” J. Opt. Soc. Am. A 5, 743–755 (1988).
[CrossRef] [PubMed]

1985 (1)

1984 (1)

M. J. Gervais, L. O. Harvey, J. O. Roberts, “Identification confusions among letters of the alphabet,” J. Exp. Psychol. Hum. Percept. Perform. 10, 655–666 (1984).
[CrossRef] [PubMed]

1983 (1)

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

1981 (2)

J. Kajiya, M. Ullner, “Filtering high quality text for display on raster scan devices,” Comput. Graphics 15, 7–15 (1981).
[CrossRef]

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
[CrossRef] [PubMed]

1980 (1)

1978 (1)

N. Graham, J. G. Robson, J. Nachmias, “Grating summation of fovea and periphery,” Vision Res. 18, 815–825 (1978).
[CrossRef]

1974 (2)

J. L. Mannos, D. J. Sakrison, “The effects of a visual fidelity criterion on the encoding of images,” IEEE Trans. Inf. Theory IT-20, 525–536 (1974).
[CrossRef]

D. H. Kelly, “Spatial frequency selectivity in the retina,” Vision Res. 15, 665–672 (1974).
[CrossRef]

1968 (1)

F. W. Campbell, “The human eye as an optical filter,” Proc. IEEE 56, 1009–1014 (1968).
[CrossRef]

1957 (1)

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
[CrossRef] [PubMed]

1936 (1)

B. H. Crawford, “The dependence of pupil size upon external light under static and variable conditions,” Proc. R. Soc. London Ser. B 121, 373 (1936).
[CrossRef]

Barlow, H. B.

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

Campbell, F. W.

F. W. Campbell, “The human eye as an optical filter,” Proc. IEEE 56, 1009–1014 (1968).
[CrossRef]

Cornsweet, T. N.

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

Crawford, B. H.

B. H. Crawford, “The dependence of pupil size upon external light under static and variable conditions,” Proc. R. Soc. London Ser. B 121, 373 (1936).
[CrossRef]

Farrell, J. E.

N. P. Lyons, J. E. Farrell, “Linear systems analysis of CRT displays,” SID Dig. 10, 220–223 (1989).

Fitzhugh, A. E.

A. B. Watson, A. E. Fitzhugh, “Modeling character legibility,” SID Dig. 10, 360–363 (1989).

Foley, J. M.

Gervais, M. J.

M. J. Gervais, L. O. Harvey, J. O. Roberts, “Identification confusions among letters of the alphabet,” J. Exp. Psychol. Hum. Percept. Perform. 10, 655–666 (1984).
[CrossRef] [PubMed]

Graham, N.

N. Graham, J. G. Robson, J. Nachmias, “Grating summation of fovea and periphery,” Vision Res. 18, 815–825 (1978).
[CrossRef]

Harvey, L. O.

M. J. Gervais, L. O. Harvey, J. O. Roberts, “Identification confusions among letters of the alphabet,” J. Exp. Psychol. Hum. Percept. Perform. 10, 655–666 (1984).
[CrossRef] [PubMed]

Inoue, M.

S. Ohtsuka, M. Inoue, K. Watanabe, “Quality evaluation of pictures with multiple impairments based on visually weighted error,” SID Dig. 9, 428–431 (1988).

Kajiya, J.

J. Kajiya, M. Ullner, “Filtering high quality text for display on raster scan devices,” Comput. Graphics 15, 7–15 (1981).
[CrossRef]

Kelly, D. H.

D. H. Kelly, “Spatial frequency selectivity in the retina,” Vision Res. 15, 665–672 (1974).
[CrossRef]

Klein, S. A.

Legge, G. E.

Levi, D. M.

Loomis, J. M. A.

J. M. A. Loomis, “Model of character recognition and legibility,” J. Exp. Psychol. Hum. Percept. Perform. 16, 106–120 (1990).
[CrossRef] [PubMed]

Lyons, N. P.

N. P. Lyons, J. E. Farrell, “Linear systems analysis of CRT displays,” SID Dig. 10, 220–223 (1989).

Mannos, J. L.

J. L. Mannos, D. J. Sakrison, “The effects of a visual fidelity criterion on the encoding of images,” IEEE Trans. Inf. Theory IT-20, 525–536 (1974).
[CrossRef]

Nachmias, J.

N. Graham, J. G. Robson, J. Nachmias, “Grating summation of fovea and periphery,” Vision Res. 18, 815–825 (1978).
[CrossRef]

Nielsen, K. R. K.

Ohtsuka, S.

S. Ohtsuka, M. Inoue, K. Watanabe, “Quality evaluation of pictures with multiple impairments based on visually weighted error,” SID Dig. 9, 428–431 (1988).

Roberts, J. O.

M. J. Gervais, L. O. Harvey, J. O. Roberts, “Identification confusions among letters of the alphabet,” J. Exp. Psychol. Hum. Percept. Perform. 10, 655–666 (1984).
[CrossRef] [PubMed]

Robson, J. G.

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

N. Graham, J. G. Robson, J. Nachmias, “Grating summation of fovea and periphery,” Vision Res. 18, 815–825 (1978).
[CrossRef]

Sakrison, D. J.

J. L. Mannos, D. J. Sakrison, “The effects of a visual fidelity criterion on the encoding of images,” IEEE Trans. Inf. Theory IT-20, 525–536 (1974).
[CrossRef]

Stevens, S. S.

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
[CrossRef] [PubMed]

Ullner, M.

J. Kajiya, M. Ullner, “Filtering high quality text for display on raster scan devices,” Comput. Graphics 15, 7–15 (1981).
[CrossRef]

Wandell, B. A.

Watanabe, K.

S. Ohtsuka, M. Inoue, K. Watanabe, “Quality evaluation of pictures with multiple impairments based on visually weighted error,” SID Dig. 9, 428–431 (1988).

Watson, A. B.

A. B. Watson, A. E. Fitzhugh, “Modeling character legibility,” SID Dig. 10, 360–363 (1989).

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

Westheimer, G.

The intersample distances were small (0.5 arcmin) relative to the width of the optical point-spread functions [see G. Westheimer, “The eye as an optical instrument,” in Handbook of Perception and Human Performance, 1: Sensory Processes and Perception, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 4.1–4.20]. The intensity of any sample point that falls within the area of the optical point-spread function will decrease with the square of the distance between the imaging surface (i.e., retina) and the stimulus (i.e., display).

Comput. Graphics (1)

J. Kajiya, M. Ullner, “Filtering high quality text for display on raster scan devices,” Comput. Graphics 15, 7–15 (1981).
[CrossRef]

IEEE Trans. Inf. Theory (1)

J. L. Mannos, D. J. Sakrison, “The effects of a visual fidelity criterion on the encoding of images,” IEEE Trans. Inf. Theory IT-20, 525–536 (1974).
[CrossRef]

J. Exp. Psychol. Hum. Percept. Perform. (2)

M. J. Gervais, L. O. Harvey, J. O. Roberts, “Identification confusions among letters of the alphabet,” J. Exp. Psychol. Hum. Percept. Perform. 10, 655–666 (1984).
[CrossRef] [PubMed]

J. M. A. Loomis, “Model of character recognition and legibility,” J. Exp. Psychol. Hum. Percept. Perform. 16, 106–120 (1990).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nature (London) (1)

A. B. Watson, H. B. Barlow, J. G. Robson, “What does the eye see best?” Nature (London) 302, 419–422 (1983).
[CrossRef]

Proc. IEEE (1)

F. W. Campbell, “The human eye as an optical filter,” Proc. IEEE 56, 1009–1014 (1968).
[CrossRef]

Proc. R. Soc. London Ser. B (1)

B. H. Crawford, “The dependence of pupil size upon external light under static and variable conditions,” Proc. R. Soc. London Ser. B 121, 373 (1936).
[CrossRef]

Psychol. Rev. (1)

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
[CrossRef] [PubMed]

SID Dig. (3)

N. P. Lyons, J. E. Farrell, “Linear systems analysis of CRT displays,” SID Dig. 10, 220–223 (1989).

A. B. Watson, A. E. Fitzhugh, “Modeling character legibility,” SID Dig. 10, 360–363 (1989).

S. Ohtsuka, M. Inoue, K. Watanabe, “Quality evaluation of pictures with multiple impairments based on visually weighted error,” SID Dig. 9, 428–431 (1988).

Vision Res. (3)

D. H. Kelly, “Spatial frequency selectivity in the retina,” Vision Res. 15, 665–672 (1974).
[CrossRef]

N. Graham, J. G. Robson, J. Nachmias, “Grating summation of fovea and periphery,” Vision Res. 18, 815–825 (1978).
[CrossRef]

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–467 (1981).
[CrossRef] [PubMed]

Other (2)

The intersample distances were small (0.5 arcmin) relative to the width of the optical point-spread functions [see G. Westheimer, “The eye as an optical instrument,” in Handbook of Perception and Human Performance, 1: Sensory Processes and Perception, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 4.1–4.20]. The intensity of any sample point that falls within the area of the optical point-spread function will decrease with the square of the distance between the imaging surface (i.e., retina) and the stimulus (i.e., display).

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

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Figures (6)

Fig. 1
Fig. 1

Campbell’s data6 on contrast sensitivity together with the least-squares solution to Eq. (1) (see text).

Fig. 2
Fig. 2

Discrimination performance, estimated by d, for subjects AEF and JEF plotted as a function of the log CED metric for each character pair presented in Experiment One. Experimental conditions referred to as filters, Gaussian blur, and gray-level quantization are represented as diamonds, circles, and squares, respectively. Solid curves represent the best-fitting Weibull psychometric functions.

Fig. 3
Fig. 3

Discrimination performance, estimated by d, for subjects AEF and JEF plotted as a function of the log CED metric for each character pair presented in Experiment Two. The data are parameterized by character pair identity: diamonds, squares, and circles represent the O, &, and R characters, respectively. Solid curves represent the best-fitting Weibull psychometric functions.

Fig. 4
Fig. 4

(a) Amplitude of vertical spatial frequency components in the difference between two of the stimuli used in Experiments One and Two. The solid curve represents the contrast sensitivity function (see text) derived from Campbell’s6 measurements of human contrast sensitivity. (b) Vertical spatial frequency components in the difference between two of the stimuli used in Experiments Three. Again, the solid curve represents the contrast sensitivity function derived by Campbell.6

Fig. 5
Fig. 5

Discrimination performance, estimated by d, for subjects AEF and JEF plotted as a function of the log CED metric for character pairs presented in Experiment Three (diamonds) and in the gray-level quantization condition of Experiment 1 (squares).

Fig. 6
Fig. 6

Discrimination performance, estimated by d, for subjects AEF and JEF plotted as a function of the log CED metric for character pairs presented in Experiment One (squares), Experiment Two (diamonds), and Experiment Three (circles). The CED metric was calculated assuming an initial stage of nonlinear intensity transduction after character image intensity was corrected for the two different viewing distances. The solid curves represent the best-fitting Weibull psychometric functions.

Equations (13)

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C ( f ) = K ( b f ) a e b f ,
i = 1 n [ ( A i B i ) 2 ] 1 / 2 ,
I = ( 4 x W 2 + 2 x ) ( 4 y W 2 + 2 y ) ,
I = 1 / W 2 ,
I = cos ( π x 2 + y 2 W ) ,
I = exp { 2 [ 3 x 2 + y 2 W ] 2 } .
Y ( x ) = 1.0 K exp [ ( x α ) β ] ,
d = i = 0 N [ ( X i υ c ) p ( Y i υ c ) p ] 2 ,
d = ( 1 υ c ) 2 p i = 0 N ( X i p Y i p ) 2 .
s = log [ ( 1 υ c ) 2 p ] .
C ( f ) = K ( b f ) a e b f ,
ρ e ρ 16 π 4 ( 4 π 2 q 2 + 4 π 2 ) 5 / 2 ( 2 q 2 ) ,
K b ρ e b ρ ( K b 2 ) 2 ( q b ) 2 2 π [ 1 + ( q b ) 2 ] 5 / 2 .

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