Skip to main content

Visual Scaling

  • Chapter

Part of the book series: Handbook of Sensory Physiology ((1536,volume 7 / 4))

Abstract

“Scaling” refers to a family of procedures that attempt to give quantitative descriptions of perceptual attributes. The first part of this chapter discusses the three main families of scaling procedures : confusability scaling, direct estimation, and multidimensional scaling. Several applications of these procedures are described in the second part : scaling of brightness, hue and saturation, and color differences are discussed in some detail, and brief mention is made of work on space and form perception.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aczél, J.: Lectures on Functional Equations and Their Applications. New York: Academic Press 1966.

    Google Scholar 

  • Aiba, T. S., Stevens, S. S.: Relation of brightness to duration and luminance under light- and dark-adaptation. Vision Res. 4, 391–401 (1964).

    Article  PubMed  CAS  Google Scholar 

  • Beals, R., Krantz, D. H., Tversky, A.: Foundations of multidimensional scaling. Psychol. Rev. 75, 127–142 (1968).

    Article  PubMed  CAS  Google Scholar 

  • Bock, R. D., Jones, L. V.: The Measurement and Prediction of Judgment and Choice. San Francisco: Holden-Day 1968.

    Google Scholar 

  • Boynton, R. M., Gordon, J.: Bezold-Brücke hue shift measured by color-naming technique. J. opt. Soc. Amer. 55, 78–86 (1965).

    Article  Google Scholar 

  • Boynton, R. M., Ikeda, M., Stiles, W. S.: Interactions among chromatic mechanisms as inferred from positive and negative increment thresholds. Vision Res. 4, 87–117 (1964).

    Article  PubMed  CAS  Google Scholar 

  • Boynton, R. M., Kaiser, P. K.: Vision: the additivity law made to work for heterochromatic photometry with bipartite fields. Science 161, 366–368 (1968).

    Article  PubMed  CAS  Google Scholar 

  • Bradley, R. A.: Another interpretation of a model for paired comparisons. Psychometrika 30, 315–318 (1966).

    Article  Google Scholar 

  • Bradley, R. A., Terry, M. E.: Rank analysis of incomplete block designs. I. The method of paired comparisons. Biometrika 39, 324–345 (1952).

    Google Scholar 

  • Brown, D. R., Andrews, M. H.: Visual form discrimination: Multidimensional psycho-physics. Perc. Psychophys. 3, 401–406 (1968).

    Article  Google Scholar 

  • Brown, W. R. J., MacAdam, D. L.: Visual sensitivities to combined chromaticity and luminance differences. J. opt. Soc. Amer. 39, 808–834 (1949).

    Article  CAS  Google Scholar 

  • Coombs, C. H.: A Theory of Data. New York: Wiley 1964.

    Google Scholar 

  • Eisler, H.: On the problem of category scales in psychophysics. Scand. J. Psychol. 3, 81–87 (1962a).

    Article  Google Scholar 

  • Eisler, H.: Empirical test of a model relating magnitude and category scales. Scand. J. Psychol. 3, 88–96 (1962b).

    Article  Google Scholar 

  • Eisler, H.: Magnitude scales, category scales, and Fechnerian integration. Psychol. Rev. 70, 243–253 (1963a).

    Article  Google Scholar 

  • Eisler, H.: A general differential equation in psychophysics: Derivation and empirical test. Scand. J. Psychol. 4, 265–272 (1963b).

    Article  Google Scholar 

  • Eisler, H.: The connection between magnitude and discrimination scales and direct and indirect scaling methods. Psychometrika 30, 271–289 (1965).

    Article  PubMed  CAS  Google Scholar 

  • Ekman, G.: Dimensions of color vision. J. Psychol. 38, 467–474 (1954).

    Article  Google Scholar 

  • Ekman, G., Eisler, H., Künnapas, T.: Brightness scales for monochromatic light. Scand. J. Psychol. 1, 41–48 (1960).

    Article  Google Scholar 

  • Ekman, G., Junge, K.: Psychophysical relations in visual perception of length, area, and volume. Scand. J. Psychol. 2, 1–10 (1961).

    Article  Google Scholar 

  • Fagot, R. F., Stewart, M.: Tests of product and additive scaling axioms. Perc. Psychophys. 5, 117–123 (1969).

    Article  Google Scholar 

  • Falmagne, J.-C.: The generalized Fechner problem and discrimination. J. math. Psychol. 8, 22–43 (1971).

    Article  Google Scholar 

  • Galanter, E., Messick, S.: The relation between category and magnitude scales of loudness. Psychol. Rev. 68, 363–372 (1961).

    Article  PubMed  CAS  Google Scholar 

  • Gilinsky, S.: Perceived size and distance in visual space. Psychol. Rev. 58, 460–482 (1951).

    Article  PubMed  CAS  Google Scholar 

  • Guth, S. L., Donley, N.J., Marrocco, R. T.: On luminance additivity and related topics. Vision Res. 9, 537–575 (1969).

    Article  PubMed  CAS  Google Scholar 

  • Helm, C. E.: A successive intervals analysis of color differences. Office of Naval Research Technical Report (Contract Nonr 1858–15), Princeton University 1960.

    Google Scholar 

  • Helm, C. E.: Multidimensional ratio scaling of perceived color relations. J. opt. Soc. Amer. 54, 256–262 (1964).

    Article  CAS  Google Scholar 

  • Helm, C. E. , Messick, S., Tucker, L. R.: Psychological models for relating discrimination and magnitude estimation scales. Psychol. Rev. 68, 167–177 (1961).

    Article  PubMed  CAS  Google Scholar 

  • Helson, H.: Adaptation-Level Theory. New York: Harper & Row 1964.

    Google Scholar 

  • Hurvich, L. M., Jameson, D.: A psychophysical study of white. I. Neutral adaptation. J. opt. Soc. Amer. 41, 521–527 (1951).

    Article  CAS  Google Scholar 

  • Indow, T., Kanazawa, K.: Multidimensional mapping of Munsell colors varying in hue, chroma, and value. J. exp. Psychol. 59, 330–336 (1960).

    Article  PubMed  CAS  Google Scholar 

  • Indow, T., Stevens, S. S.: Scaling of saturation and hue. Perc. Psychophys. 1, 253–271 (1966).

    Article  Google Scholar 

  • Indow, T., Uchizono, T.: Multidimensional mapping of Munsell colors varying in hue and chroma. J. exp. Psychol. 59, 321–329 (1960).

    Article  PubMed  CAS  Google Scholar 

  • Jameson, D.: Brightness scales and their interpretation. In: International Colour Meeting Stockholm 1969, pp. 377–385. Göttingen: Musterschmidt 1970.

    Google Scholar 

  • Jameson, D., Hurvich, L. M.: Perceived color and its dependence on focal, surrounding, and preceding stimulus variables. J. opt. Soc. Amer. 49, 890–898 (1959).

    Article  CAS  Google Scholar 

  • Jameson, D., Hurvich, L. M.: Theory of brightness and color contrast in human vision. Vision Res. 4, 135–154 (1964).

    Article  PubMed  CAS  Google Scholar 

  • Judd, D. B., Wyszecki, G.: Color in Business, Science, and Industry. New York: Wiley 1963.

    Google Scholar 

  • Krantz, D. H.: The scaling of small and large color differences. Ph. D. thesis, University of Pennsylvania. Ann Arbor: University Microfilms 1964.

    Google Scholar 

  • Krantz, D. H.: Rational distance functions for multidimensional scaling. J. math. Psychol. 4, 226–245 (1967a).

    Article  Google Scholar 

  • Krantz, D. H.: Small-step and large-step color differences for monochromatic stimuli of constant brightness. J. opt. Soc. Amer. 57, 1304–1316 (1967b).

    Article  CAS  Google Scholar 

  • Krantz, D. H.: Integration of just-noticeable differences. J. math. Psychol. 8, 591–599 (1971).

    Article  Google Scholar 

  • Krantz, D. H.: A theory of magnitude estimation and cross-modality matching. J. math. Psychol. 9, in press (1972).

    Google Scholar 

  • Kristof, W.: A foundation of interval scale measurement. Educational Testing Service Research Bulletin RB 67–22, Princeton, 1967.

    Google Scholar 

  • Kruskal, J. B.: Nonmetric multidimensional scaling: A numerical method. Psychometrika 29, 115–129 (1964).

    Article  Google Scholar 

  • Künnapas, T.: Measurements of subjective length in the vertical-horizontal illusion. Acta Psychologica 14, 371–374 (1958).

    Article  Google Scholar 

  • Künnapas, T.: Scales for subjective distance. Scand. J. Psychol. 1, 187–192 (1960).

    Article  Google Scholar 

  • Künnapas, T.: Visual perception of capital letters: Multidimensional ratio scaling and multidimensional similarity. Scand. J. Psychol. 7, 189–196 (1966).

    Article  PubMed  Google Scholar 

  • Le Grand, Y.: Light, Colour, and Vision. (2nd. Ed.) London: Chapman and Hall 1968.

    Google Scholar 

  • Levine, M. V.: Transformations that render curves parallel. J. math. Psychol. 7, 410–443 (1970).

    Article  Google Scholar 

  • Luce, R. D.: Individual Choice Behavior. New York: Wiley 1959.

    Google Scholar 

  • Luce, R. D., Edwards, W.: The derivation of subjective scales from just noticeable differences. Psychol. Rev. 65, 222–237 (1958).

    Article  PubMed  CAS  Google Scholar 

  • Luce, R. D., Galanter, E.: Discrimination. In: Handbook of Mathematical Psychology, Vol. 1. Luce, R. D., Bush, R. R., Galanter, E. (Eds.): New York: Wiley 1963a.

    Google Scholar 

  • Luce, R. D., Galanter, E.: Psychophysical scaling. In: Handbook of Mathematical Psychology, Vol. 1. Luce, R.D., Bush, R. R., Galanter, E. (Eds.) New York: Wiley 1963b.

    Google Scholar 

  • Luce, R. D., Mo, S.S.: Magnitude estimation of heaviness and loudness by individual subjects: A test of a probabilistic response theory. Brit. J. math. stat. Psychol. 18, 159–174 (1965).

    Article  Google Scholar 

  • MacAdam, D. L.: Specification of small chromaticity differences. J. opt. Soc. Amer. 33, 18–26 (1943).

    Article  Google Scholar 

  • Messick, S. J.: An empirical evaluation of multidimensional successive intervals. Psychometrika 21, 367–376 (1956).

    Article  Google Scholar 

  • Micro, H. C., Fischer, W.: The metric of multidimensional psychological space as a function of differential attention to subjective attributes. J. math. Psychol. 7, 118–143 (1970).

    Article  Google Scholar 

  • Micro, H. C., Fischer, W.: Munsell Book of Color. Baltimore: Munsell Color Co. 1929.

    Google Scholar 

  • Munsell, A. H.: Atlas of the Munsell Color System. Boston: 1915.

    Google Scholar 

  • Newhall, S. M.: The ratio method in the review of the Munsell colors. Amer. J. Psychol. 52, 394–405 (1939).

    Article  Google Scholar 

  • Newhall, S. M.: Preliminary report of the O. S. A. subcommittee on the spacing of the Munsell colors. J. opt. Soc. Amer. 30, 617–645 (1940).

    Article  Google Scholar 

  • Newhall, S. M.: Nickerson, D., Judd, D. B.: Final report of the O. S. A. subcommittee on the spacing of the Munsell colors. J. opt. Soc. Amer. 33, 385–418 (1943).

    Article  Google Scholar 

  • Onley, J. W.: Light adaptation and the brightness of brief foveal stimuli. J. opt. Soc. Amer. 51, 667–673 (1961).

    Article  CAS  Google Scholar 

  • Panek, D. W., Stevens, S. S.: Saturation of red: a prothetic continuum. Perc. Psychophys. 1, 59–66 (1966).

    Article  Google Scholar 

  • Piéron, H.: Récherches sur la latence de perception des accroissements de luminosité. Ann. Psychol. (Paris) 37, 1–16 (1936).

    Google Scholar 

  • Plateau, J.: Über die Messung physischer Empfindungen und das Gesetz, welches die Stärke der Empfindung mit der Stärke der erregenden Ursache verknüpft. Ann. Physik 150, 465–475 (1873).

    Google Scholar 

  • Pottlton, E. C.: The new psychophysics : six models for magnitude estimation. Psychol. Bull. 69, 1–19 (1968).

    Article  Google Scholar 

  • Rasch, G.: Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen : Nielsen and Lydiche 1960.

    Google Scholar 

  • Rasch, G.: An item analysis which takes individual differences into account. Brit. J. math. stat. Psychol. 19, 49–57 (1966).

    Article  CAS  Google Scholar 

  • Richardson, M. W.: Multidimensional psychophysics. Psychol. Bull. 35, 659–660 (1938).

    Google Scholar 

  • Shepard, R. N.: The analysis of proximities: Multidimensional scaling with an unknown distance function. I. Psychometrika 27, 125–140 (1962a).

    Article  Google Scholar 

  • Shepard, R. N.: The analysis of proximities: Multidimensional scaling with an unknown distance function. II. Psychometrika 27, 219–246 (1962b).

    Article  Google Scholar 

  • Sternberg, S.: Four theories of the effect of distance on apparent size. Psychonomic Society Meetings, 1966.

    Google Scholar 

  • Stevens, J. C., Mack, J. D., Stevens, S. S.: Growth of sensation on seven continua as measured by force of handgrip. J. exp. Psychol. 59, 60–67 (1960).

    Article  PubMed  CAS  Google Scholar 

  • Stevens, J. C., Stevens, S. S.: Brightness function: Effects of adaptation. J. opt. Soc. Amer. 53, 375–385 (1963).

    Article  CAS  Google Scholar 

  • Stevens, S. S.: On the psychophysical law. Psychol. Rev. 64, 153–181 (1957).

    Article  PubMed  CAS  Google Scholar 

  • Stevens, J. C.: Sic transit gloria varietatis ? (Review of L. L. Thurstone, The measurement of values.) Contemp. Psychol. 4, 388–389 (1959).

    Google Scholar 

  • Stevens, J. C.: To honor Fechner and repeal his law. Science 133, 80–86 (1961).

    Article  PubMed  CAS  Google Scholar 

  • Stevens, J. C.: Matching functions between loudness and ten other continua. Perc. Psychophys. 1, 5–8 (1966).

    Article  Google Scholar 

  • Stevens, J. C., Diamond, A. L.: Effect of the glare angle on the brightness function for a small target. Vision Res. 5, 649–659 (1965).

    Article  PubMed  CAS  Google Scholar 

  • Stevens, J. C., Guirao, M.: Subjective scaling of length and area and the matching of length to loudness and brightness. J. exp. Psychol. 66, 177–186 (1963).

    Article  PubMed  CAS  Google Scholar 

  • Teghtsoonian, M.: The judgment of size. Amer. J. Psychol. 78, 392–402 (1965).

    Article  PubMed  CAS  Google Scholar 

  • Teghtsoonian, M., Teghtsoonian, R.: Seen and felt length. Psychon. Sci. 3, 465–466 (1965).

    Google Scholar 

  • Teghtsoonian, R.: Range effects in psychophysical scaling and a revision of Stevens’ law. Amer. J. Psychol. 85, in press (1972).

    Google Scholar 

  • Thompson, W. A., Singh, J.: The use of limit theorems in paired comparison model building. Psychometrika 32, 255–264 (1967).

    Article  PubMed  Google Scholar 

  • Thurstone, L. L.: A law of comparative judgment. Psychol. Rev. 34, 273–286 (1927a).

    Article  Google Scholar 

  • Thurstone, L. L.: Psychophysical analysis. Amer. J. Psychol. 38, 368–389 (1927 b).

    Article  Google Scholar 

  • Torgerson, W. S.: A Theoretical and Empirical Investigation of Multidimensional Scaling. Ph. D. thesis, Princeton University 1951.

    Google Scholar 

  • Torgerson, W. S.: Theory and Method of Scaling. New York: Wiley 1958.

    Google Scholar 

  • Torgerson, W. S.: Distances and ratios in psychophysical scaling. Acta Psychologica 19, 201–205 (1961).

    Article  Google Scholar 

  • Tversky, A., Krantz, D. H.: The dimensional representation and the metric structure of similarity data. J. math. Psychol. 7, 572–596 (1970).

    Article  Google Scholar 

  • Tversky, A., Russo, J. E.: Substitutability and similarity in binary choices. J. math. Psychol. 6, 1–12 (1969).

    Article  Google Scholar 

  • Wilson, B. C.: An experimental examination of the spectral luminosity construct. Ph. D. thesis, New York University. Ann Arbor: University Microfilms 1964.

    Google Scholar 

  • Wright, H.: Precision of color differences derived from a multidimensional scaling experiment. J. opt. Soc. Amer. 55, 1650–1655 (1965).

    Article  Google Scholar 

  • Wyszecki, G., Stiles, W. S.: Color Science. New York: Wiley 1967.

    Google Scholar 

  • Yager, D., Taylor, E.: Experimental measures and theoretical account of hue scaling as a function of luminance. Perc. Psychophys. 7, 360–364 (1970).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1972 Springer-Verlag, Berlin · Heidelberg

About this chapter

Cite this chapter

Krantz, D.H. (1972). Visual Scaling. In: Jameson, D., Hurvich, L.M. (eds) Visual Psychophysics. Handbook of Sensory Physiology, vol 7 / 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88658-4_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-88658-4_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-88660-7

  • Online ISBN: 978-3-642-88658-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics