Structural factors of size contrast in the Ebbinghaus illusion

WALTER H. EHRENSTEIN; JIRO HAMADA

doi:10.4992/psycholres1954.37.158

エビングハウス錯視における大きさ対比の構造的要因

WALTER H. EHRENSTEIN, 濱田治良

著者情報

ジャーナルフリー

1995 年 37 巻 3 号 p. 158-169

DOI https://doi.org/10.4992/psycholres1954.37.158

詳細

発行日: 1995/10/25 受付日: 1994/08/08 J-STAGE公開日: 2009/02/24 受理日: 1994/09/03 早期公開日: - 改訂日: -
訂正情報
訂正日: 2009/02/24 訂正理由: - 訂正箇所: 論文抄録訂正内容: Wrong : Size contrast was studied in the Ebbinghaus illusion with inducing circles (ICs) that were either larger or smaller than the central test circle (TC). Four ICs formed either squares or diamonds; or in a mixed-size condition four large ICs alternated with four small ICs. Figures were presented on printed cards and studied as a function of IC-TC distance, or displayed on a computer screen at various angles of orientation. A separate circle, presented left or right of an Ebbinghaus figure and varying in size, served for simultaneous comparision. A general overestimation was found for figures presented right from the comparison circle. Size contrast diminished with increasing IC-TC distance for small ICs, but increased for large ICs. Square arrays had stronger inducing effects than diamonds with small ICs, but weaker with large ICs; the mixed-size condition resulted in a small underestimation. Furthermore, size contrast depended systematically on the angle of IC-array orientation. The Ebbinghaus illusion thus obeys structural factors in a rather peculiar way, suggesting the necessity of a compound model of size contrast.
Right : Size contrast was studied in the Ebbinghaus illusion with inducing circles (ICs) that were either larger or smaller than the central test circle (TC). Four ICs formed either squares or diamonds; or in a mixed-size condition four large ICs alternated with four small ICs. Figures were presented on printed cards and studied as a function of IC-TC distance, or displayed on a computer screen at various angles of orientation. A separate circle, presented left or right of an Ebbinghaus figure and varying in size, served for simultaneous comparision. A general overestimation was found for figures presented right from the comparison circle. Size contrast diminished with increasing IC-TC distance for small ICs, hut increased for large ICs. Square arrays had stronger inducing effects than diamonds with small ICs, but weaker with large ICs; the mixed-size condition resulted in a small underestimation. Furthermore, size contrast depended systematically on the angle of ICarray orientation, The Ebhinghaus illusion thus obeys structural factors in a rather peculiar way, suggesting the necessity of a compound model of size contrast.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Institut füt Arbeitsphysiologie
2) 徳島大学

訂正後 :
1) Institute für Arbeitsphysiologie
2) 徳島大学

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : Appele, S. 1972 Perception and discrimination as a function of stimulus orientation: The “oblique effect” in man and animals. Psychological Bulletin, 78, 266-278.
Bradshaw, J. L., & Nettleton, N. C. 1983 Human cerebral asymmetry. Englewood Cliffs, N. J.: Prentice-Hall.
Bredenkamp, J. 1984 Theoretische und experimentelle Analysen dreier Wahmehmungstäuschungen. Zeitschrift für Psychologie, 192, 47-61.
Clem, R. K., & Pollack, R. H. 1975 Illusion magnitude as a function of visual field exposure. Perception & Psychophysics. 17, 450-454.
Coren, S., & Girgus, J. 1978 Seeing is deceiving: The psychology of visual illusions. Hilisdale, N. J.: Erlbaum.
Ebbinghaus, H. 1908 Grundzüge der Psychologie. Vol. II, Part 1. Leipzig: Veit.
Edgar, G. K., & Smith, A. T. 1990 Hemifield differences in perceived spatial frequency. Perception, 19, 759-766.
Ehrenstein, W. H. 1977 Geometry in visual space-some method-dependent (arti) facts. Perception, 6, 657-660.
Fisher. G. H., & Lucas, A. 1969 Illusions in concrete situations: I. Introduction and demonstrations. Ergonomics, 12, 11-24.
Gazzaniga, M. S., Bogen, J. E., & Sperry, R. W. 1965 Observations on visual perception after disconnection of the cerebral hemispheres. Brain, 88, 221-236.
Girgus, J. S., Coren, S., & Agdern, M. 1972 The interrelationship between the Ebbinghaus and Delboeuf illusions. Journal of Experimental Psychology, 95, 453-455.
Goto, T. 1987 Experimental study on the size illusion of contrastive circles (4): Effects of the combination of stimulus conditions and of the repeated observations on the magnitude of Ebbinghaus illusion. Journal of the Faculty of Letters: Nagoya University (Philosophy), 33, 53-76. (In Japanese with English summary)
Goto, T., & Ohya, K. 1989 Experimental study on the conditions of stimulus presentation in the size illusion of contrastive circles. Journal of the Faculty of Letters: Nagoya University (Philosophy), 35, 37-59. (In Japanese with English summary)
Guilford. J. P. 1954 Psychometric methods. New York: McGraw-Hill.
Hamada, J. 1991 Asymmetries in the perception of lightness and darkness. Trends in Biological Cybernetics, 2, 93-105.
Heinemann, E. G. 1972 Simultaneous brightness induction. In D. Jameson & L. M. Hurvich (Eds.), Handbook of sensory physiology. Vol. IV. Berlin-New York: Springer-Verlag. Pp. 146-169.
Kanizsa, G. 1979 Organization in vision: Essays on Gestalt perception. New York: Praeger.
Kitterle, F. 1989 Cerebral laterality. Theory and research. Hillsdale, N. J.: Erlbaum.
Kundt, A. 1863 Untersuchungen über Augenmaβ und optische Täuschungen. Poggendorffs Annalen, 120, 118-158.
Kuroda, K., & Noguchi, K. 1984 Similarity grouping effects in the size-assimilation and size-contrast illusions. Proceedings of the 48th Annual Convention of Japanese Psychological Association, 168.
Mach, E. 1861 Üher das Sehen von Lagen and Winkeln durch die Bewegung des Auges. Sitzungsberichte der mathematisch-naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften (Wien), 43, 215-224.
Mach, E. 1959 The analysis of sensations. New York: Dover Publications.
Massaro, D. W., & Anderson, N. H. 1971 Judgmental model of the Ebbinghaus circles illusion. Journal of Experimental Psychology, 89, 147-151.
Morinaga, S., 1959 Über die Raumwahrnehmung in Hinsicht auf die optischen Täuschungen. Proceedings of the 15th International Congress of Psychology. Amsterdam: North-Holland. Pp. 273-274.
Morinaga, S., & Noguchi, K. 1966 An attempt to unify the size-assimilation and size-contrast illusions. Psychologische Forschung, 29, 161-168.
Obonai, T. 1930 Experimentelle Untersuchung überdas periodische Phänomen der Abweichung. Japanese Journal of Psychology, 5, 11-13.
Obonai, T. 1954 Induction effect in estimates of extent. Journal of Experimental Psychology, 47, 57-60.
Obonai, T. 1977 Perception, learning and thinking: Psychophysiological induction theory. Tokyo: Hokuseido Press
Ono, H. 1967 Difference threshold for stimulus length under simultaneous and nonsimultaneous viewing conditions. Perception & Psychophysics, 2, 201-207.
Oyama, T. 1960 Japanese studies on the so-called geometrical-optical illusions. Psychologia, 3, 7-20.
Sarris, V. 1986 Hermann Ebbinghaus' law of relative size-contrast in optico-geometric distortions: Rediscovery and reformulation. In F. Klix & H. Hagendorf (Eds.), Human memory and cognitive capabilittes. Mechanisms and performance. Amsterdam: North-Holland-Elsevier. Pp. 139-151.
Schiller, P., & Wiener, M. 1962 Binocular and stereoscopic viewing of geometric illusions. Perceptiual and Motor Skills, 15, 39-47.
Schumann, F. 1900 Beiträge zur Analyse der Gesichtswahrnehmungen II: Zur Schätzung räumlicher GröBen. Zeitschrift für Psychologie und Physiologie der Sinnesorgane, 24, 1-33.
Smith, R. 1738 A compleat system of opticks (2 Vols.) Cambridge: C. Crownfield.
Stevens, H. C. 1908 Pecularities of peripheral vision. Psychological Review. 15, 69-93.
Taya, R., & Ohashi, Y. 1992 The reversed MüllerLyer illusion and figure-ground organization theory. Perception, 21, 611-626.
Thurstone. L. L. 1944 A factorial study of perception. Chicago: University of Chicago Press.
Titchener, E. B. 1901 Experimental psychology: A manual of laboratory practice. New York: Macmillan.
Wade, N. 1982 The art and science of visual illusions. London: Routlege & Kegan Paul.
Wundt, W. 1898 Die geometrisch-optischen Täuschungen. Leipzig: Teubner.
Zigler, E. 1960 Size estimates of circles as a function of adjacent circles. Perceptual and Motor Skills, 11, 47-53.

Right : Appele, S. 1972 Perception and discrimination as a function of stimulus orientation'. The “oblique effect” in man and animals. Psychological Bulletin, 78, 266-278.
Bradshaw, J. L., &Nettleton, N. C. 1983 Human cerebral asymmetry. Englewood Cliffs, N. J.: Prentice-Hall.
Bredenkamp, J. 1984 Theoretische and experimentelle Anaiysen dreier Wahmehmungstäuschungen. Zeitschrift für Psycholagie, 192, 47-61.
Clem, R. K., &Pollack, R. H. 1975 Illusion magnitude as a function of visual field exposure. Perception A Psychophysics, 17, 450-454.
Coren, S., &Girgus, J. 1978 Seeing is dcceiring: The psychology of visual illusions. Hillsdale, N. J.: Erlbaum.
Ebbinghaus, H. 1908 Grundzüge der Psychologi:. Vol.II, Part I. Leipzig: Veit.
Edgar, G. K., &Smith, A. T. 1990 Hemifield differences in perceived spatial frequency. Perception, 19, 759-766.
Ehrenstein, W. H. 1977 Geometry in visual space-some method-dependent lanti facts. Perception, 6, 657-660.
Fisher. G. H., &Lucas, A. 1969 Illusions in concrete situations: I. Introduction and demonstrations. Ergonomic's, 12, I 1-24.
Gazzaniga, M. S., Bogen, J. E. &Sperry, R. W. 1965 Observations on visual perception atter disconnection of the cerebral hemispheres. Brain, 88, 221-236.
Girgus, J. S., Coren, S., &Agdern, M. 1972 The interrelationship between the Ebbinghaus and Delhoeuf illusions. Journal of Experimental Psychology, 95, 453-455.
Goto, T. 1987 Experimental study on the size illusion of contrastive circles (4): Effects of the combination of stimulus conditions and of the repeated observations on the magnitude of Ebbinghaus illusion. Journal of the Faculty of Letters: University (Philosophy), 33, 53-76. In Japanese with English summary)
Goto, T. &Ohya, K. 1989 Experimental study on the conditions of stimulus presentation in the size illusion of contrastive circles. Journal of the Faculty of Letters: Nagoya University (Philosophy), 35, 37-59.(In Japanese with English summary)
Guilford, J. P. 1954 Psychometric methods. New York McGraw-Hill.
Hanaada, J. 1991 Asymmetries in the perception of lightness and darkness. Trends in Biological Cybernetics, 2.93-105.
Heinemann, E. G. 1972 Simultaneous brightness induction. In D. Jameson&L. M. Hurvich (Eds.), Handbook of sensory physiology. Vol.IV. Berlin-New York: Springer-Verlag. Pp.146-169.
Kanizsa, G. 1979 Organization in vision: Essays on Gestalt perception. New York: Praeger.
Kitterle, F. 1989 Cerebral laterality. Theory and research. Hillsdale, N. J.: Erlbaum.
Kundt, A. 1863 Untersuchungenüber Augenmaßand optische Täuschungen. Poggendorffs Annalen, 120, 118-158.
Kuroda, K., &Noguchi, K. 1984 Similarity grouping effects in the size-assimilation and size-contrast illusions. Proceedings of the 48th Annual Convention of Japanese Psychological Association, 168.
Mach, E. 1861Über das Sehen von Lagen und Winkeln durch die Bewcgung des Auges. Sitz, ungsberichte der mathematisclt-naturwissenschaftlichen Classy der Kaiserlichen Akademie der Wissenschaften (Wien), 43, 215-224.
Mach, E. 1959 The analysis of sensations. New York: Dover Publications.
Massaro, D. W., &Anderson, N. H. 1971 Judgmental model of the Ebbinghaus circles illusion. Journal of Experimental Psychology, 89, 147-151.
Morinaga, S., 1959Über die Raumwahrnehmung in Hinsicht auf die optischen Täuschungen. Proceedings of the 15th International Congress of Psychology. Amsterdam: North-Holland. Pp.273-274.
Morinaga, S., &Noguchi, K. 1966 An attempt to unify the size-assimilation and size-contrast illusions. Psychologische Forschun, g, 29, 161-168.
Obonai, T. 1930 Experimentelle Untersuchungüber das periodische Phänomen der Abweichung. Japanese Journal of Psychology, 5, 11-13.
Obonai, T. 1954 Induction effect in estimates of extent. Journal of Experimental Psychology, 47, 57-60.
Obonai, T. 1977 Perception, learning and thinking: P, sychophvsiological induction theory. Tokyo: Hokuseido Press
Ono, H. 1967 Difference threshold for stimulus length under simultaneous and nonsimultaneous viewing conditions. Perception&Psychophysics, 2, 201-207.
Oyama, T. 1960 Japanese studies on the so-called geometrical-optical illusions. Psychologia, 3, 7-20.
Sarris, V. 1986 Hermann Ebbinghaus' law of relative size-contrast in optico-geometric distortions: Rediscovery and reformulation. In F. Klix&H. Hagendorf (Eds.), Human memory and cognitive capabilities. Mechanisms and performance. Amsterdam: North-Holland-Elsevier. pp.139-151.
Schiller, P., &Wiener, M. 1962 Binocular and stereoscopic viewing of geometric illusions. Pereeprival and Motor Skills, 15, 39-47.
Schumann, F. 1900 Beiträge zur Analyse der Gesichtswahrnehmungen II: Zur Schätzung räumlicher Größen. Zeitschrift für Psychologie and Phssiulogie der Sinnesor Rune, 24, 1-33.
Smith, R. 1738 A comple system of opticks l7 Vols. Cambridge: C. Crowntield.
Stevens, H. C. 1908 Pecularities of peripheral Vision Psychological Review, 15. 69-93.
Taya. R. &Ohashi. Y. 1997 The reversed Müller-Lyer illusion and figure-ground organization theory. Perception. 21. 611-626.
Thurstone. L. L. 1944 A fuctorial study e, f. perception. Chicago: University of Chicago Press.
Titchener, E. B. 1901 Exterimental psychology: A manual af, laboratory practice. New York: Macmillan.
Wade, N. 1952 The art and science of visual illusions. London: Routlege&Kegan Paul.
Wundt, W. 1898 Die keometrisch-optischen Tausrhungen. Leipzig: Teubner.
Ligler, E. 1960 Size estimates of circles as a function if adjacent circles. Perceptual and Motor Skills, 11, 47-53.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 論文抄録訂正内容: Wrong : Size contrast was studied in the Ebbinghaus illusion with inducing circles (ICs) that were either larger or smaller than the central test circle (TC). Four ICs formed either squares or diamonds; or in a mixed-size condition four large ICs alternated with four small ICs. Figures were presented on printed cards and studied as a function of IC-TC distance, or displayed on a computer screen at various angles of orientation. A separate circle, presented left or right of an Ebbinghaus figure and varying in size, served for simultaneous comparision. A general overestimation was found for figures presented right from the comparison circle. Size contrast diminished with increasing IC-TC distance for small ICs, hut increased for large ICs. Square arrays had stronger inducing effects than diamonds with small ICs, but weaker with large ICs; the mixed-size condition resulted in a small underestimation. Furthermore, size contrast depended systematically on the angle of ICarray orientation, The Ebhinghaus illusion thus obeys structural factors in a rather peculiar way, suggesting the necessity of a compound model of size contrast.
Right : Size contrast was studied in the Ebbinghaus illusion with inducing circles (ICs) that were either larger or smaller than the central test circle (TC). Four ICs formed either squares or diamonds; or in a mixed-size condition four large ICs alternated with four small ICs. Figures were presented on printed cards and studied as a function of IC-TC distance, or displayed on a computer screen at various angles of orientation. A separate circle, presented left or right of an Ebbinghaus figure and varying in size, served for simultaneous comparision. A general overestimation was found for figures presented right from the comparison circle. Size contrast diminished with increasing IC-TC distance for small ICs, but increased for large ICs. Square arrays had stronger inducing effects than diamonds with small ICs, but weaker with large ICs: the mixed-size condition resulted in a small underestimation. Furthermore, size contrast depended systematically on the angle of IC-array orientation. The Ebbinghaus illusion thus obeys structural factors in a rather peculiar way, suggesting the necessity of a compound model of size contrast.

訂正日: 2009/02/24 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : Appele, S. 1972 Perception and discrimination as a function of stimulus orientation'. The “oblique effect” in man and animals. Psychological Bulletin, 78, 266-278.
Bradshaw, J. L., &Nettleton, N. C. 1983 Human cerebral asymmetry. Englewood Cliffs, N. J.: Prentice-Hall.
Bredenkamp, J. 1984 Theoretische and experimentelle Anaiysen dreier Wahmehmungstäuschungen. Zeitschrift für Psycholagie, 192, 47-61.
Clem, R. K., &Pollack, R. H. 1975 Illusion magnitude as a function of visual field exposure. Perception A Psychophysics, 17, 450-454.
Coren, S., &Girgus, J. 1978 Seeing is dcceiring: The psychology of visual illusions. Hillsdale, N. J.: Erlbaum.
Ebbinghaus, H. 1908 Grundzüge der Psychologi:. Vol.II, Part I. Leipzig: Veit.
Edgar, G. K., &Smith, A. T. 1990 Hemifield differences in perceived spatial frequency. Perception, 19, 759-766.
Ehrenstein, W. H. 1977 Geometry in visual space-some method-dependent lanti facts. Perception, 6, 657-660.
Fisher. G. H., &Lucas, A. 1969 Illusions in concrete situations: I. Introduction and demonstrations. Ergonomic's, 12, I 1-24.
Gazzaniga, M. S., Bogen, J. E. &Sperry, R. W. 1965 Observations on visual perception atter disconnection of the cerebral hemispheres. Brain, 88, 221-236.
Girgus, J. S., Coren, S., &Agdern, M. 1972 The interrelationship between the Ebbinghaus and Delhoeuf illusions. Journal of Experimental Psychology, 95, 453-455.
Goto, T. 1987 Experimental study on the size illusion of contrastive circles (4): Effects of the combination of stimulus conditions and of the repeated observations on the magnitude of Ebbinghaus illusion. Journal of the Faculty of Letters: University (Philosophy), 33, 53-76. In Japanese with English summary)
Goto, T. &Ohya, K. 1989 Experimental study on the conditions of stimulus presentation in the size illusion of contrastive circles. Journal of the Faculty of Letters: Nagoya University (Philosophy), 35, 37-59.(In Japanese with English summary)
Guilford, J. P. 1954 Psychometric methods. New York McGraw-Hill.
Hanaada, J. 1991 Asymmetries in the perception of lightness and darkness. Trends in Biological Cybernetics, 2.93-105.
Heinemann, E. G. 1972 Simultaneous brightness induction. In D. Jameson&L. M. Hurvich (Eds.), Handbook of sensory physiology. Vol.IV. Berlin-New York: Springer-Verlag. Pp.146-169.
Kanizsa, G. 1979 Organization in vision: Essays on Gestalt perception. New York: Praeger.
Kitterle, F. 1989 Cerebral laterality. Theory and research. Hillsdale, N. J.: Erlbaum.
Kundt, A. 1863 Untersuchungenüber Augenmaßand optische Täuschungen. Poggendorffs Annalen, 120, 118-158.
Kuroda, K., &Noguchi, K. 1984 Similarity grouping effects in the size-assimilation and size-contrast illusions. Proceedings of the 48th Annual Convention of Japanese Psychological Association, 168.
Mach, E. 1861Über das Sehen von Lagen und Winkeln durch die Bewcgung des Auges. Sitz, ungsberichte der mathematisclt-naturwissenschaftlichen Classy der Kaiserlichen Akademie der Wissenschaften (Wien), 43, 215-224.
Mach, E. 1959 The analysis of sensations. New York: Dover Publications.
Massaro, D. W., &Anderson, N. H. 1971 Judgmental model of the Ebbinghaus circles illusion. Journal of Experimental Psychology, 89, 147-151.
Morinaga, S., 1959Über die Raumwahrnehmung in Hinsicht auf die optischen Täuschungen. Proceedings of the 15th International Congress of Psychology. Amsterdam: North-Holland. Pp.273-274.
Morinaga, S., &Noguchi, K. 1966 An attempt to unify the size-assimilation and size-contrast illusions. Psychologische Forschun, g, 29, 161-168.
Obonai, T. 1930 Experimentelle Untersuchungüber das periodische Phänomen der Abweichung. Japanese Journal of Psychology, 5, 11-13.
Obonai, T. 1954 Induction effect in estimates of extent. Journal of Experimental Psychology, 47, 57-60.
Obonai, T. 1977 Perception, learning and thinking: P, sychophvsiological induction theory. Tokyo: Hokuseido Press
Ono, H. 1967 Difference threshold for stimulus length under simultaneous and nonsimultaneous viewing conditions. Perception&Psychophysics, 2, 201-207.
Oyama, T. 1960 Japanese studies on the so-called geometrical-optical illusions. Psychologia, 3, 7-20.
Sarris, V. 1986 Hermann Ebbinghaus' law of relative size-contrast in optico-geometric distortions: Rediscovery and reformulation. In F. Klix&H. Hagendorf (Eds.), Human memory and cognitive capabilities. Mechanisms and performance. Amsterdam: North-Holland-Elsevier. pp.139-151.
Schiller, P., &Wiener, M. 1962 Binocular and stereoscopic viewing of geometric illusions. Pereeprival and Motor Skills, 15, 39-47.
Schumann, F. 1900 Beiträge zur Analyse der Gesichtswahrnehmungen II: Zur Schätzung räumlicher Größen. Zeitschrift für Psychologie and Phssiulogie der Sinnesor Rune, 24, 1-33.
Smith, R. 1738 A comple system of opticks l7 Vols. Cambridge: C. Crowntield.
Stevens, H. C. 1908 Pecularities of peripheral Vision Psychological Review, 15. 69-93.
Taya. R. &Ohashi. Y. 1997 The reversed Müller-Lyer illusion and figure-ground organization theory. Perception. 21. 611-626.
Thurstone. L. L. 1944 A fuctorial study e, f. perception. Chicago: University of Chicago Press.
Titchener, E. B. 1901 Exterimental psychology: A manual af, laboratory practice. New York: Macmillan.
Wade, N. 1952 The art and science of visual illusions. London: Routlege&Kegan Paul.
Wundt, W. 1898 Die keometrisch-optischen Tausrhungen. Leipzig: Teubner.
Ligler, E. 1960 Size estimates of circles as a function if adjacent circles. Perceptual and Motor Skills, 11, 47-53.

Right : Appele, S. 1972 Perception and discrimination as a function of stimulus orientation: The “oblique effect” in man and animals. Psychological Bulletin, 78, 266-278.
Bradshaw, J. L., & Nettleton, N. C. 1983 Human cerebral asymmetry. Englewood Cliffs, N. J.: Prentice-Hall.
Bredenkamp, J. 1984 Theoretische and experimentelle Analysen dreier Wahmehmungstäuschungen. Zeitschrift für Psychologie, 192, 47-61.
Clem, R. K., & Pollack, R. H. 1975 Illusion magnitude as a function of visual field exposure. Perception & Psychophysics, 17, 450-454.
Coren, S., & Girgus, J. 1978 Seeing is deceiving: The psychology of visual illusions. Hillsdale, N. J.: Erlbaum.
Ebbinghaus, H. 1908 Grundzüge der Psychologie. Vol.II, Part 1. Leipzig: Veit.
Edgar, G. K., & Smith, A. T. 1990 Hemifield differences in perceived spatial frequency. Perception. 19, 759-766.
Ehrenstein, W. H. 1977 Geometry in visual space-some method-dependent (arti) facts. Perception. 6, 657-660.
Fisher. G. H., & Lucas, A. 1969 Illusions in concrete situations: I. Introduction and demonstrations. Ergonomics, 12. 11-24.
Gazzaniga, M. S., Bogen, J. E. & Sperry, R. W. 1965 Observations on visual perception after disconnection of the cerebral hemispheres. Brain, 88, 221-236.
Girgus, J. S., Coren, S., & Agdern, M. 1972 The interrelationship between the Ebbinghaus and Delboeuf illusions. Journal of Experimental Psychology, 95, 453-455.
Goto, T. 1987 Experimental study on the size illusion of contrastive circles (4): Effects of the combination of stimulus conditions and of the repeated observations on the magnitude of Ebbinghaus illusion. Journal of the Faculty of Letters: Nagoya University (Philosophy), 33, 53-76.(In Japanese with English summary)
Goto, T.& Ohya, K. 1989 Experimental study on the conditions of stimulus presentation in the size illusion of contrastive circles. Journal of the Faculty of Letters: Nagoya University (Philosophy), 35, 37-59.(In Japanese with English summary)
Guilford, J. P. 1954 Psychometric methods. New York: McGraw-Hill.
Hamada, J. 1991 Asymmetries in the perception of lightness and darkness. Trends in Biological Cybernetics, 2. 93-105.
Heinemann, E. G. 1972 Simultaneous brightness induction. In D. Jameson & L. M. Hurvich (Eds.), Handbook of sensory physiology. Vol.IV. Berlin-New York: Springer-Verlag. Pp.146-169.
Kanizsa, G. 1979 Organization in vision: Essays on Gestalt perception. New York: Praeger.
Kitterle, F. 1989 Cerebral laterality. Theory and research. Hillsdale, N. J.: Erlbaum.
Kundt, A. 1863 Untersuchungen über Augenmaß und optische Täuschungen. Poggendorffs Annalen, 120, 118-158.
Kuroda, K., & Noguchi, K. 1984 Similarity grouping effects in the size-assimilation and size-contrast illusions. Proceedings of the 48th Annual Convention of Japanese Psychological Association, 168.
Mach, E. 1861 Über das Sehen von Lagen und Winkeln durch die Bewegung des Auges. Sitzungsberichte der mathematisch-naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften (Wien), 43, 215-224.
Mach, E. 1959 The analysis of sensations. New York: Dover Publications.
Massaro, D. W., &Anderson, N. H. 1971 Judgmental model of the Ebbinghaus circles illusion. Journal of Experimental Psychology, 89, 147-151.
Morinaga, S., 1959 Über die Raumwahrnehmung in Hinsicht auf die optischen Täuschungen. Proceedings of the 15th International Congress of Psychology. Amsterdam: North-Holland. Pp.273-274.
Morinaga, S., & Noguchi, K. 1966 An attempt to unify the size-assimilation and size-contrast illusions. Psychologische Forschung, 29, 161-168.
Obonai, T. 1930 Experimentelle Untersuchung über das periodische Phänomen der Abweichung. Japanese Journal of Psychology, 5, 11-13.
Obonai, T. 1954 Induction effect in estimates of extent. Journal of Experimental Psychology, 47, 57-60.
Obonai, T. 1977 Perception, learning and thinking: Psychophysiological induction theory. Tokyo: Hokuseido Press
Ono, H. 1967 Difference threshold for stimulus length under simultaneous and nonsimultaneous viewing conditions. Perception & Psychophysics, 2, 201-207.
Oyama, T. 1960 Japanese studies on the so-called geometrical-optical illusions. Psychologia, 3, 7-20.
Sarris, V. 1986 Hermann Ebbinghaus' law of relative size-contrast in optico-geometric distortions: Rediscovery and reformulation. In F. Klix & H. Hagendorf (Eds.), Human memory and cognitive capabilities. Mechanisms and performance. Amsterdam: North-Holland-Elsevier. Pp.139-151.
Schiller, P., & Wiener, M. 1962 Binocular and stereoscopic viewing of geometric illusions. Percepriual and Motor Skills, 15, 39-47.
Schumann. F. 1900 Beiträge zur Analyse der Gesichtswahrnehmungen II: Zur Schätzung räumlicher Größen. Zeitschrift für Psychologie und Physiologie der Sinnesorgane, 24, 1-33.
Smith, R. 1738 A compleat system of opticks (2 Vols.) Cambridge: C. Crownfield.
Stevens, H. C. 1908 Pecularities of peripheral Vision_ Psychological Review. 15. 69-93.
Taya. R. & Ohashi. Y. 1992 The reversed Müller-Lyer illusion and figure-ground organization theory. Perception. 21. 611-626.
Thurstone. L. L. 1944 A factorial study of perception. Chicago: University of Chicago Press.
Titchener, E. B. 1901 Experimental psychology: A manual of laboratory practice. New York: Macmillan.
Wade. N. 1982 The art and science of visual illusions. London: Routlege & Kegan Paul.
Wundt, W. 1898 Die geometrisch-optischen Täuschungen. Leipzig: Teubner.
Zigler, E. 1960 Size estimates of circles as a function of adjacent circles. Perceptual and Motor Skills, 11, 47-53.

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Size contrast was studied in the Ebbinghaus illusion with inducing circles (ICs) that were either larger or smaller than the central test circle (TC). Four ICs formed either squares or diamonds; or in a mixed-size condition four large ICs alternated with four small ICs. Figures were presented on printed cards and studied as a function of IC-TC distance, or displayed on a computer screen at various angles of orientation. A separate circle, presented left or right of an Ebbinghaus figure and varying in size, served for simultaneous comparision. A general overestimation was found for figures presented right from the comparison circle. Size contrast diminished with increasing IC-TC distance for small ICs, but increased for large ICs. Square arrays had stronger inducing effects than diamonds with small ICs, but weaker with large ICs: the mixed-size condition resulted in a small underestimation. Furthermore, size contrast depended systematically on the angle of IC-array orientation. The Ebbinghaus illusion thus obeys structural factors in a rather peculiar way, suggesting the necessity of a compound model of size contrast.

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