Abstract

After a short survey of some other metrics of perceived image quality, the square-root integral (SQRI) is described. In this metric a fixed mathematical expression for the contrast sensitivity of the eye is used. With the SQRI method the effect of various display parameters, such as resolution, addressability, contrast, luminance, display size, and viewing distance, on subjective image quality can be taken into account. Experimental data of subjective image quality, measured by various authors, are compared with calculated SQRI values. From the comparison it appears that the calculated SQRI values show a good linear correlation with perceived subjective image quality not only at variation of resolution but also at simultaneous variation of other display parameters.

© 1990 Optical Society of America

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  1. E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photog. Sci. Eng. 16, 221–230 (1972).
  2. H. L. Snyder, “Modulation transfer function area as a measure of image quality,” presented at the Visual Search Symposium of the Committee on Vision, National Academy of Sciences, Washington, D.C., 1970.
  3. A. van Meeteren, “Visual aspects of image intensification,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1973).
  4. G. C. Higgins, “Image quality criteria,” J. Appl. Photogr. Eng. 3, 53–60 (1977).
  5. H. L. Task, A. R. Pinkus, J. P. Hornseth, “A comparison of several television display image quality measures,” Proc. Soc. Inf. Displ. 19, 113–119 (1978).
  6. C. R. Carlson, R. W. Cohen, “A simple psycho-physical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).
  7. R. J. Beaton, “Quantitative models of image quality,” presented at the Human Factors Society 27th Annual Meeting, 1983.
  8. P. G. J. Barten, “The SQRI method: a new method for the evaluation of visible resolution on a display,” Proc. Soc. Inf. Displ. 28, 253–262 (1987).
  9. P. G. J. Barten, “Evaluation of CRT displays with the SQRI method,” Proc. Soc. Inf. Displ. 30, 9–14 (1989).
  10. P. G. J. Barten, “The effects of picture size and definition on perceived image quality,” IEEE Trans. Electron. Dev. 36, 1865–1869 (1989).
    [CrossRef]
  11. P. G. J. Barten, “The square root integral (SQRI): a new metric to describe the effect of various display parameters on perceived image quality,” in Human Vision, Visual Processing, and Digital Display, B. E. Rogowitz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1077, 73–82 (1989).
    [CrossRef]
  12. C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Rev. 43, 675–683 (1982).
  13. F. L. van Nes, “Experimental studies in spatiotemporal contrast transfer by the human eye,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1968).
  14. J. H. D. M. Westerink, J. A. J. Roufs, “A local basis for perceptually relevant resolution measures,” Soc. Inf. Display Digest 19, 360–363 (1988).
  15. S. H. Baker, M. E. Carpenter, “Correlation of spot characteristics with perceived image quality,” IEEE Trans. Commun. Electron. 35, 319–324 (1989).
  16. E. van der Zee, M. H. W. A. Boesten, “The influence of luminance and size on the image quality of complex scenes,” in IPO Annual Progress Report (Institute for Perception Research, Eindhoven, The Netherlands, 1980), pp. 69–75.
  17. J. H. D. M. Westerink, J. A. J. Roufs, “Subjective image quality as a function of viewing distance, resolution and picture size,” SMPTE J. 98, 113–119 (1989).
    [CrossRef]
  18. T. Hatada, H. Sakata, H. Kusaka, “Psychophysical analysis of the ‘sensation of reality’ induced by a visual wide-field display,” SMPTE J. 95, 560–569 (1980).
    [CrossRef]
  19. T. Mitsuhashi, “Scanning specifications and picture quality,” in “High-definition television,” NHK Tech. Monograph (Japan Broadcasting Corporation, Tokyo, 1982), pp. 21–32.
  20. L. C. Jesty, “The relation between picture size, viewing distance and picture quality,” Proc. Inst. Electr. Eng. Part B 105, 425–439 (1958).

1989 (4)

P. G. J. Barten, “Evaluation of CRT displays with the SQRI method,” Proc. Soc. Inf. Displ. 30, 9–14 (1989).

P. G. J. Barten, “The effects of picture size and definition on perceived image quality,” IEEE Trans. Electron. Dev. 36, 1865–1869 (1989).
[CrossRef]

S. H. Baker, M. E. Carpenter, “Correlation of spot characteristics with perceived image quality,” IEEE Trans. Commun. Electron. 35, 319–324 (1989).

J. H. D. M. Westerink, J. A. J. Roufs, “Subjective image quality as a function of viewing distance, resolution and picture size,” SMPTE J. 98, 113–119 (1989).
[CrossRef]

1988 (1)

J. H. D. M. Westerink, J. A. J. Roufs, “A local basis for perceptually relevant resolution measures,” Soc. Inf. Display Digest 19, 360–363 (1988).

1987 (1)

P. G. J. Barten, “The SQRI method: a new method for the evaluation of visible resolution on a display,” Proc. Soc. Inf. Displ. 28, 253–262 (1987).

1982 (1)

C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Rev. 43, 675–683 (1982).

1980 (2)

C. R. Carlson, R. W. Cohen, “A simple psycho-physical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).

T. Hatada, H. Sakata, H. Kusaka, “Psychophysical analysis of the ‘sensation of reality’ induced by a visual wide-field display,” SMPTE J. 95, 560–569 (1980).
[CrossRef]

1978 (1)

H. L. Task, A. R. Pinkus, J. P. Hornseth, “A comparison of several television display image quality measures,” Proc. Soc. Inf. Displ. 19, 113–119 (1978).

1977 (1)

G. C. Higgins, “Image quality criteria,” J. Appl. Photogr. Eng. 3, 53–60 (1977).

1972 (1)

E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photog. Sci. Eng. 16, 221–230 (1972).

1958 (1)

L. C. Jesty, “The relation between picture size, viewing distance and picture quality,” Proc. Inst. Electr. Eng. Part B 105, 425–439 (1958).

Baker, S. H.

S. H. Baker, M. E. Carpenter, “Correlation of spot characteristics with perceived image quality,” IEEE Trans. Commun. Electron. 35, 319–324 (1989).

Barten, P. G. J.

P. G. J. Barten, “Evaluation of CRT displays with the SQRI method,” Proc. Soc. Inf. Displ. 30, 9–14 (1989).

P. G. J. Barten, “The effects of picture size and definition on perceived image quality,” IEEE Trans. Electron. Dev. 36, 1865–1869 (1989).
[CrossRef]

P. G. J. Barten, “The SQRI method: a new method for the evaluation of visible resolution on a display,” Proc. Soc. Inf. Displ. 28, 253–262 (1987).

P. G. J. Barten, “The square root integral (SQRI): a new metric to describe the effect of various display parameters on perceived image quality,” in Human Vision, Visual Processing, and Digital Display, B. E. Rogowitz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1077, 73–82 (1989).
[CrossRef]

Beaton, R. J.

R. J. Beaton, “Quantitative models of image quality,” presented at the Human Factors Society 27th Annual Meeting, 1983.

Boesten, M. H. W. A.

E. van der Zee, M. H. W. A. Boesten, “The influence of luminance and size on the image quality of complex scenes,” in IPO Annual Progress Report (Institute for Perception Research, Eindhoven, The Netherlands, 1980), pp. 69–75.

Carlson, C. R.

C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Rev. 43, 675–683 (1982).

C. R. Carlson, R. W. Cohen, “A simple psycho-physical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).

Carpenter, M. E.

S. H. Baker, M. E. Carpenter, “Correlation of spot characteristics with perceived image quality,” IEEE Trans. Commun. Electron. 35, 319–324 (1989).

Cohen, R. W.

C. R. Carlson, R. W. Cohen, “A simple psycho-physical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).

Cupery, K. N.

E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photog. Sci. Eng. 16, 221–230 (1972).

Granger, E. M.

E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photog. Sci. Eng. 16, 221–230 (1972).

Hatada, T.

T. Hatada, H. Sakata, H. Kusaka, “Psychophysical analysis of the ‘sensation of reality’ induced by a visual wide-field display,” SMPTE J. 95, 560–569 (1980).
[CrossRef]

Higgins, G. C.

G. C. Higgins, “Image quality criteria,” J. Appl. Photogr. Eng. 3, 53–60 (1977).

Hornseth, J. P.

H. L. Task, A. R. Pinkus, J. P. Hornseth, “A comparison of several television display image quality measures,” Proc. Soc. Inf. Displ. 19, 113–119 (1978).

Jesty, L. C.

L. C. Jesty, “The relation between picture size, viewing distance and picture quality,” Proc. Inst. Electr. Eng. Part B 105, 425–439 (1958).

Kusaka, H.

T. Hatada, H. Sakata, H. Kusaka, “Psychophysical analysis of the ‘sensation of reality’ induced by a visual wide-field display,” SMPTE J. 95, 560–569 (1980).
[CrossRef]

Mitsuhashi, T.

T. Mitsuhashi, “Scanning specifications and picture quality,” in “High-definition television,” NHK Tech. Monograph (Japan Broadcasting Corporation, Tokyo, 1982), pp. 21–32.

Pinkus, A. R.

H. L. Task, A. R. Pinkus, J. P. Hornseth, “A comparison of several television display image quality measures,” Proc. Soc. Inf. Displ. 19, 113–119 (1978).

Roufs, J. A. J.

J. H. D. M. Westerink, J. A. J. Roufs, “Subjective image quality as a function of viewing distance, resolution and picture size,” SMPTE J. 98, 113–119 (1989).
[CrossRef]

J. H. D. M. Westerink, J. A. J. Roufs, “A local basis for perceptually relevant resolution measures,” Soc. Inf. Display Digest 19, 360–363 (1988).

Sakata, H.

T. Hatada, H. Sakata, H. Kusaka, “Psychophysical analysis of the ‘sensation of reality’ induced by a visual wide-field display,” SMPTE J. 95, 560–569 (1980).
[CrossRef]

Snyder, H. L.

H. L. Snyder, “Modulation transfer function area as a measure of image quality,” presented at the Visual Search Symposium of the Committee on Vision, National Academy of Sciences, Washington, D.C., 1970.

Task, H. L.

H. L. Task, A. R. Pinkus, J. P. Hornseth, “A comparison of several television display image quality measures,” Proc. Soc. Inf. Displ. 19, 113–119 (1978).

van der Zee, E.

E. van der Zee, M. H. W. A. Boesten, “The influence of luminance and size on the image quality of complex scenes,” in IPO Annual Progress Report (Institute for Perception Research, Eindhoven, The Netherlands, 1980), pp. 69–75.

van Meeteren, A.

A. van Meeteren, “Visual aspects of image intensification,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1973).

van Nes, F. L.

F. L. van Nes, “Experimental studies in spatiotemporal contrast transfer by the human eye,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1968).

Westerink, J. H. D. M.

J. H. D. M. Westerink, J. A. J. Roufs, “Subjective image quality as a function of viewing distance, resolution and picture size,” SMPTE J. 98, 113–119 (1989).
[CrossRef]

J. H. D. M. Westerink, J. A. J. Roufs, “A local basis for perceptually relevant resolution measures,” Soc. Inf. Display Digest 19, 360–363 (1988).

IEEE Trans. Commun. Electron. (1)

S. H. Baker, M. E. Carpenter, “Correlation of spot characteristics with perceived image quality,” IEEE Trans. Commun. Electron. 35, 319–324 (1989).

IEEE Trans. Electron. Dev. (1)

P. G. J. Barten, “The effects of picture size and definition on perceived image quality,” IEEE Trans. Electron. Dev. 36, 1865–1869 (1989).
[CrossRef]

J. Appl. Photogr. Eng. (1)

G. C. Higgins, “Image quality criteria,” J. Appl. Photogr. Eng. 3, 53–60 (1977).

Photog. Sci. Eng. (1)

E. M. Granger, K. N. Cupery, “An optical merit function (SQF), which correlates with subjective image judgments,” Photog. Sci. Eng. 16, 221–230 (1972).

Proc. Inst. Electr. Eng. Part B (1)

L. C. Jesty, “The relation between picture size, viewing distance and picture quality,” Proc. Inst. Electr. Eng. Part B 105, 425–439 (1958).

Proc. Soc. Inf. Displ. (4)

P. G. J. Barten, “The SQRI method: a new method for the evaluation of visible resolution on a display,” Proc. Soc. Inf. Displ. 28, 253–262 (1987).

P. G. J. Barten, “Evaluation of CRT displays with the SQRI method,” Proc. Soc. Inf. Displ. 30, 9–14 (1989).

H. L. Task, A. R. Pinkus, J. P. Hornseth, “A comparison of several television display image quality measures,” Proc. Soc. Inf. Displ. 19, 113–119 (1978).

C. R. Carlson, R. W. Cohen, “A simple psycho-physical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).

RCA Rev. (1)

C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Rev. 43, 675–683 (1982).

SMPTE J. (2)

J. H. D. M. Westerink, J. A. J. Roufs, “Subjective image quality as a function of viewing distance, resolution and picture size,” SMPTE J. 98, 113–119 (1989).
[CrossRef]

T. Hatada, H. Sakata, H. Kusaka, “Psychophysical analysis of the ‘sensation of reality’ induced by a visual wide-field display,” SMPTE J. 95, 560–569 (1980).
[CrossRef]

Soc. Inf. Display Digest (1)

J. H. D. M. Westerink, J. A. J. Roufs, “A local basis for perceptually relevant resolution measures,” Soc. Inf. Display Digest 19, 360–363 (1988).

Other (7)

T. Mitsuhashi, “Scanning specifications and picture quality,” in “High-definition television,” NHK Tech. Monograph (Japan Broadcasting Corporation, Tokyo, 1982), pp. 21–32.

E. van der Zee, M. H. W. A. Boesten, “The influence of luminance and size on the image quality of complex scenes,” in IPO Annual Progress Report (Institute for Perception Research, Eindhoven, The Netherlands, 1980), pp. 69–75.

F. L. van Nes, “Experimental studies in spatiotemporal contrast transfer by the human eye,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1968).

P. G. J. Barten, “The square root integral (SQRI): a new metric to describe the effect of various display parameters on perceived image quality,” in Human Vision, Visual Processing, and Digital Display, B. E. Rogowitz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1077, 73–82 (1989).
[CrossRef]

R. J. Beaton, “Quantitative models of image quality,” presented at the Human Factors Society 27th Annual Meeting, 1983.

H. L. Snyder, “Modulation transfer function area as a measure of image quality,” presented at the Visual Search Symposium of the Committee on Vision, National Academy of Sciences, Washington, D.C., 1970.

A. van Meeteren, “Visual aspects of image intensification,” Ph.D. dissertation (University of Utrecht, Utrecht, The Netherlands, 1973).

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Figures (16)

Fig. 1
Fig. 1

Example of the MTFA for a color-television picture observed from a viewing distance of six times the picture height. The hatched area is used as a measure of visual resolution quality. The dashed vertical line represents the bandwidth limit of the television signal.

Fig. 2
Fig. 2

Example of a discriminable-difference diagram of Carlson and Cohen6 for a noise-free picture with a display luminance of 35 mL = 350/π cd/m2. The total number of tick marks in the area below the MTF curves (indicated by A and B) is used as a measure of visual resolution quality.

Fig. 3
Fig. 3

Contrast sensitivity as a function of angular spatial frequency at various luminance levels, measured by van Meeteren.3 Viewing distance 4 m. Angular display size 17° × 11°. The solid curves have been calculated with Eq. (6).

Fig. 4
Fig. 4

Contrast sensitivity as a function of angular spatial frequency at various display sizes, measured by Carlson.12 Viewing distance 1.9 m. Display luminance 34 mL = 340/π cd/m2.

Fig. 5
Fig. 5

Contrast sensitivity as a function of angular spatial frequency, calculated with Eq. (6) for the conditions of Fig. 4.

Fig. 6
Fig. 6

Just-noticeable relative change in resolution bandwidth (u2u1)/u2 as function of the original resolution bandwidth u1, measured by Carlson and Cohen.6 Average display luminance 35 mL = 350/π cd/m2. The solid curve has been calculated with the SQRI model.

Fig. 7
Fig. 7

Calculated SQRI value of a projection television picture as a function of the spot size of the projection tube for an experiment of Baker and Carpenter.15 The average slope of the curve in the spot size range used in the experiment is 0.04 mm/jnd.

Fig. 8
Fig. 8

Measured data of the ratio Δ η / η as a function of the factor η by which the MTF is multiplied.9 Δη corresponds to a just-noticeable change of contrast. According to the SQRI model the ratio should be constant. The dashed curve represents a ratio proportional to 1 / η, as predicted by the MTFA model, and the dotted curve represents a ratio proportional to η, as predicted by the Carlson–Cohen model.

Fig. 9
Fig. 9

Linear regression between measured subjective image quality and calculated SQRI value for projected color-slide pictures with different luminances and sizes, measured by van der Zee and Boesten.16 Viewing distance 2.9 m. Correlation coefficient R = 0.993.

Fig. 10
Fig. 10

SQRI value as a function of luminance at three different display sizes for the subjective image-quality measurements of Fig. 9. The measured data have been linearly transformed to the SQRI scale with the aid of the regression equation. The solid curves have been calculated with the SQRI model.

Fig. 11
Fig. 11

Linear regression between measured subjective image quality and the calculated SQRI value for projected color-slide pictures with different resolutions and sizes, measured by Westerink and Roufs.17 Viewing distance 2.9 m. Average display luminance 30 cd/m2. Correlation coefficient R = 0.994.

Fig. 12
Fig. 12

SQRI value as a function of angular resolution for the subjective image-quality measurements of Fig. 11. The measured data have been linearly transformed to the SQRI scale with the aid of the regression equation. The solid curves have been calculated with the SQRI model.

Fig. 13
Fig. 13

Measured subjective image quality as a function of calculated SQRI value for similar measurements by Westerink and Roufs as given in Fig. 11 but carried out at three different viewing distances: 2.9, 3.9, and 5.4 m. Points of equal viewing distance are interconnected.

Fig. 14
Fig. 14

Linear regression between measured subjective image quality and calculated SQRI value for progressively scanned television pictures with different numbers of scan lines and observed at different viewing distances, measured by Mitsuhashi.19 Correlation coefficient R = 0.956.

Fig. 15
Fig. 15

SQRI value of progressively scanned television pictures as a function of viewing distance for the subjective image-quality measurements of Fig. 14. The viewing distance is expressed in units of picture height (45 cm). The measured data have been linearly transformed to the SQRI scale with the aid of the regression equation. The solid curves have been calculated with the SQRI model.

Fig. 16
Fig. 16

Linear regression between measured and calculated optimum viewing distance for projected color slide pictures with different resolutions and luminances, measured by Jesty.20 The optimum viewing distance is expressed in units of picture height. Correlation coefficient R = 0.984. The luminances are 5 fL (squares), 20 fL (circles), and 80 fL (triangles).

Equations (8)

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A = 0 u max [ M ( u ) M t ( u ) ] d u ,
M ( u max ) = M t ( u max ) .
I = 0 [ M ( u ) / M t ( u ) ] d u .
SQF = u 1 u 2 M ( u ) d ( ln u ) .
J = 1 ln 2 0 u max [ M ( u ) M t ( u ) ] 1 / 2 d u u ,
1 / M t ( u ) = a u exp ( b u ) [ 1 + c exp ( b u ) ] 1 / 2 ,
a = 540 ( 1 + 0.7 / L ) 0.2 1 + 12 w ( 1 + u / 3 ) 2 , b = 0.3 ( 1 + 100 / L ) 0.15 , c = 0.06 ,
η = L av L av + Δ L ,

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