Summary
The concept of filled area, i.e. the impressionistic ensemble of parts of a stimulus field occupied by dots, is used to account for various kinds of numerosity illusions due to perceptual interaction between a number of dots and their spatial arrangement. A measure of filled area is derived from a model for the perceptual clustering of dots on the basis of relative proximity. It is shown that the quantified concept of filled area successfully predicts illusion data from earlier studies. Subsequently, a two-alternatives forced-choice numerosity experiment is reported, the data of which gave further evidence of the predictive power of the filled-area hypothesis. Our approach is discussed with respect to spatial features of dot stimuli that might be in rivalry with the filled-area factor in numerosity-estimation tasks.
Similar content being viewed by others
References
Bevan, W., & Turner, E. D. (1964). Assimilation and contrast in the estimation of number. Journal of Experimental Psychology, 67, 458–462.
Binet, A. (1890). La perception des longueurs et des nombres chez quelques petits enfants. Revue philosophique de la France et de l'étranger, 30, 68–81 (Engl. transl. see Pollack & Brenner 1969).
Birnbaum, M. H., & Veith, C. T. (1973). Judgemental illusions produced by contrast with expectancy. Perception & Psychophysics, 1, 149–152.
Flavell, J. H. (1963). Cognitive development. Englewood Cliffs: Prentice Hall.
Frith, C. D., & Frith, U. (1972). The solitaire illusion: an illusion of numerosity. Perception & Psychophysics, 11, 409–410.
Ginsburg, N. (1976). Effect of item arrangement on perceived numerosity: randomness vs regularity. Perceptual and Motor Skills, 43, 663–668.
Ginsburg, N. (1978). Perceived numerosity, item arrangement, and expectancy. American Journal of Psychology, 91, 267–273.
Ginsburg, N. (1978). The regular-random numerosity illusion: Rectangular patterns. Journal of General Psychology, 103, 211–216.
Hochberg, J., & McAllister, E. (1953). A quantitative approach to figural “goodness”. Journal of Experimental Psychology, 46, 361–364.
Koffka, K. (1935). Principles of Gestalt psychology. London: Routledge & Kegan Paul.
Krueger, L. (1972). Perceived numerosity. Perception & Psychophysics, 11, 5–9.
Marr, D. (1982). Vision. San Francisco: Freeman.
Metzger, W. (1953). Die Gesetze des Sehens. Frankfurt am Main: Kramer.
Van Oeffelen, M. P., & Vos, P. G. (1982). Configurational effects on the enumeration of dots: Counting by groups. Memory & Cognition, 10, 396–404.
Van Oeffelen, M. P., & Vos, P. G. (1983). An algorithm for pattern description on the level of relative proximity. Pattern Recognition, 16, 341–348.
Palmer, S. E. (1982). Symmetry, transformation, and the structure of perceptual system. In J. Beck (Ed.), Organisation and representation in perception. Hillsdale, NJ: Erlbaum.
Piaget, J. (1965). The child's conception of number. New York: Morton.
Piaget, J., & Inhelder, B. (1971). Mental imagery in the child. London: Routledge & Kegan Paul.
Pollack, R. H., & Brenner, M. W. (1969). The perception of lengths and numbers in some small children (Eng. trans. of Binet, 1890). In Pollack & Brenner (Eds.), The experimental psychology of Alfred Binet. New York: Springer.
Smith, J. P. (1969). The effect of figural shape on the perception of area. Perception & Psychophysics, 5, 49–52.
Smits, J. T., & Vos, P. G. (1986). A model of the perception of curves in dot figures: The role of local salience of virtual lines. Biological Cybernetics, 54, 407–416.
Taves, E. H. (1941). Two mechanisms for the perception of visual numerousness. Archives of Psychology, No. 265.
Wertheimer, M. (1923). Untersuchungen zur Lehre von der Gestalt, II. Psychologische Forschung, 4, 310–350.
Wright, W. E. (1977). Gravitational clustering. Pattern Recognition, 9, 155–166.
Zahn, C. T. (1971). Graph-theoretical methods for describing and detecting Gestalt clusters. IEEE Trans. Comput. C-20, 68–86.
Zusne, L. (1970). Visual perception of form. New York: Academic Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vos, P.G., van Oeffelen, M.P., Tibosch, H.J. et al. Interactions between area and numerosity. Psychol. Res 50, 148–154 (1988). https://doi.org/10.1007/BF00310175
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00310175