Abstract
This research assessed the relative contribution of 3-D virtual structure that generated the stimulus drawings (scene-based and picture-based theories) and 2-D structure of the drawings (object-based theories). Virtual structures were right-angle convex and concave corners in front of and behind the picture plane, respectively. Virtual corner size was manipulated directly (Experiment 1) and indirectly by manipulating drawing station point distance (Experiments 2 and 3), corner depth (Experiment 4), and corner distance from the picture plane (Experiments 5 and 6). Experiments 2 and 4 held the size of the projected corner edge (interior target line) constant, causing virtual corner size to vary, whereas Experiments 3, 4, 5, and 6 held size of the virtual corners constant, causing size of the projected corner edge or interior target line to vary. Subjects reproduced the length of the projected corner edge (interior target line). The illusions (difference between reproduced size of the projected corner edge and T-junction control) were generally well fit by the weighted sum of virtual corner size and size of the projected corner edge, but the projected distance between boundary line terminations (intertip distance) appeared as an additional contributing factor in Experiments 5 and 6. The implications of this methodological approach are discussed for theories of the illusions.
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References
American Psychological Association (1992). Ethical principles of psychologists and code of conduct. American Psychologist, 47, 1597–1611.
Barrow, H. G., & Tenenbaum, J. M. (1981). Interpreting line drawings as three-dimensional surfaces. Artificial Intelligence, 17, 75–116.
Biederman, I. (1987). Recognition by components: A theory of human image understanding. Psychological Review, 94, 115–147.
Biederman, I. (1995). Visual object recognition. In S. M. Kosslyn & D. N. Osherson (Eds.), Visual cognition: An invitation to cognitive science (2nd ed., Vol. 2, pp. 121–165). Cambridge, MA: MIT Press.
Biederman, I., & Cooper, E. E. (1992). Size invariance in visual object priming. Journal of Experimental Psychology: Human Perception & Performance, 18, 121–133.
Biederman, I., & Gerhardstein, P. C. (1993). Recognizing depth-rotated objects: Evidence and conditions for three-dimensional viewpoint invariance. Journal of Experimental Psychology: Human Perception & Performance, 19, 1162–1182.
Binet, A. (1895). La mesure des illusions visuelles chez les enfants. Revue Philosophique, 40, 11–25.
Binford, T. O. (1981). Inferring surfaces from images. Artificial Intelligence, 17, 205–244.
Christie, P. (1975). Asymmetry in the Müller-Lyer illusion: Artifact or genuine effect? Perception, 4, 453–457.
Clowes, M. (1971). On seeing things. Artificial Intelligence, 2, 79–116.
Cohen, J., MacWhinney, B., Flatt, H., & Provost, J. (1993). Psy-Scope: An interactive graphic system for designing and controlling experiments in the psychology laboratory using Macintosh computers. Behavior Research Methods, Instruments, & Computers, 25, 257–271.
Coren, S., & Girgus, J. S. (1978a). Seeing is deceiving: The psychology of visual illusions. Hillsdale, NJ: Erlbaum.
Coren, S., & Girgus, J. S. (1978b). Visual illusions. In R. Held, H. Lei-bowitz, & H. L. Teuber (Eds.), Handbook of sensory psychology (Vol. 8, pp. 549–568). Berlin: Springer.
Day, R. H. (1972). Visual spatial illusions: A general explanation. Science, 175, 1335–1340.
Day, R. H., & Dickinson, R. G. (1976). Apparent lengths of the arms of the acute and obtuse angles, and the components of the Müller-Lyer illusion. Australian Journal of Psychology, 28, 137–148.
DeLucia, P. R., & Hochberg, J. (1991). Geometrical illusions in solid objects under ordinary viewing conditions. Perception & Psychophysics, 50, 547–554.
Erlebacher, A., & Sekuler, R. (1974). Perceived length depends on exposure duration: Straight lines and Müller-Lyer stimuli. Journal of Experimental Psychology, 103, 724–728.
Farber, J., & Rosinski, R. R. (1978). Geometric transformations of pictured space. Perception, 7, 269–282.
Freeman, H. (1986). Computer graphics. In K. R. Boff, L. Kaufman, & J. P. Thomas (Eds.), Handbook of perception and human performance: Vol. 1. Sensory processes and perception (pp 3.1–3.42). New York: Wiley.
Gauld, A. (1975). A note on inappropriate constancy-scaling and the Müller-Lyer illusion. British Journal of Psychology, 66, 307–309.
Gibson, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton Mifflin.
Gillam, B. (1978). A constancy-scaling theory of the Müller-Lyer illusion. In J. P. Sutcliffe (Ed.), Conceptual analysis and method in psychology: Essays in honour of W. M. O’Neil (pp 57–70). Sydney: Sydney University Press.
Gillam, B. (1980). Geometrical illusions. Scientific American, 242, 102–111.
Gillam, B. (1998). Illusions at century’s end. In J. Hochberg (Ed.), Perception and cognition at century’s end (pp. 95–136). New York: Academic Press.
Girgus, J. S., & Coren, S. (1982). Assimilation and contrast illusions: Differences in plasticity. Perception & Psychophysics, 32, 555–561.
Gregory, R. L. (1963). Distortion of visual space as inappropriate constancy scaling. Nature, 199, 678–680.
Gregory, R. L. (1965). Reply to Humphrey and Morgan. Nature, 206, 745–746.
Gregory, R. L. (1967). Comments on the inappropriate constancy scaling theory of the illusions and its implications. Quarterly Journal of Experimental Psychology, 19, 219–223.
Gregory, R. L. (1968). Perceptual illusions and brain models. Proceedings of the Royal Society B, 171, 279–296.
Gregory, R. L. (1974). Concepts and mechanisms of perception. London: Duckworth.
Gregory, R. L., & Harris, J. P. (1975). Illusion-destruction by appropriate scaling. Perception, 4, 203–220.
Haesen, W. (1974). An examination of R. L. Gregory’s inappropriate constancy scaling theory of geometrical optical illusions. Psychologica Belgica, 14, 239–259.
Heymans, G. (1896). Quantitative Untersuchungen über das “optische Paradoxen.” Zeitschrift für Psychologie, 9, 221–225.
Humphrey, N. K., & Morgan, M. J. (1965). Constancy and the geometric illusions. Nature, 206, 744–745.
Ittelson, W. H. (1996). Visual perception of markings. Psychonomic Bulletin & Review, 3, 171–187.
Jordan, K., & English, P. W. (1989). Simultaneous sampling and length contrast. Perception & Psychophysics, 46, 546–554.
Jordan, K., & Haleblian, J. (1988). Orientation specificity of length assimilation and contrast. Perception & Psychophysics, 43, 446–456.
Jordan, K., & Schiano, D. J. (1986). Serial processing and the parallel lines illusion: Length contrast through relative spatial separation of contours. Perception & Psychophysics, 40, 384–390.
Jordan, K., & Uhlarik, J. (1985). Assimilation and contrast of perceived length depend on temporal factors. Perception & Psychophysics, 37, 447–454.
Jordan, K., & Uhlarik, J. (1986). Length contrast in the Müller-Lyer figure: Functional equivalence of temporal and spatial separation. Perception & Psychophysics, 39, 267–274.
Kubovy, M. (1986). The psychology of perspective and Renaissance art. Cambridge: Cambridge University Press.
Malik, J. (1987). Interpreting line drawings of curved objects. International Journal of Computer Vision, 1, 73–103.
Marr, D. (1982). Vision: A computational investigation in the human representation and processing of visual information. San Francisco: Freeman.
Morgan, M. J., Hole, G. J., & Glennerster, A. (1990). Biases and sensitivities in geometrical illusions. Vision Research, 30, 1793–1810.
Mountjoy, P. T. (1966). New illusory effect of the Müller-Lyer figure. Journal of Experimental Psychology, 71, 119–123.
Müller-Lyer, F. C. (1981). Optical illusions (R. H. Day & H. Knuth, Trans.). Perception, 10, 131–136. (Original work published in German in 1889)
Perkins, D. N. (1972). Visual discrimination between rectangular and nonrectangular parallelepipeds. Perception & Psychophysics, 12, 396–400.
Perkins, D. N. (1973). Compensating for distortion in viewing pictures obliquely. Perception & Psychophysics, 14, 13–18.
Piaget, J. (1969). The mechanisms of perception (G. N. Seagrim, Trans.). New York: Basic Books. (Original work published in French in 1961)
Pike, A. R., & Stacey, B. G. (1968). The perception of luminous Müller-Lyer figures and its implication for the misapplied constant theory. Life Sciences, 7, 355–362.
Pirenne, M. H. (1970). Optics, painting, and photography. Cambridge: Cambridge University Press.
Predebon, J. (1994). Illusion of length in acute—and obtuse-angle figures. Perceptual & Motor Skills, 78, 259–264.
Predebon, J. (2000). Length illusions in conventional and single-wing Müller-Lyer stimuli. Perception & Psychophysics, 62, 1086–1098.
Pressey, A. W. (1970). The assimilation theory applied to a modification of the Müller-Lyer illusion. Perception & Psychophysics, 8, 411–412.
Pressey, A. W. (1972). The assimilation theory of geometric illusions: An additional postulate. Perception & Psychophysics, 11, 28–30.
Pressey, A. W. (1974). Evidence for the role of attentive field in the perception of illusions. Quarterly Journal of Experimental Psychology, 26, 464–471.
Pressey, A. W., & Pressey, C. A. (1992). Attentive fields are related to focal and contextual features: A study of Müller-Lyer distortions. Perception & Psychophysics, 51, 423–436.
Redding, G. M., & Hawley, E. A. (1993). Length illusion in fractional Müller-Lyer stimuli: An object-perception approach. Perception, 22, 819–828.
Redding, G. M., Winson, G. D., & Temple, R. O. (1993). The Müller-Lyer contrast illusion: A computational approach. Perception & Psychophysics, 54, 527–534.
Restle, P., & Decker, J. (1977). Size of the Müller-Lyer illusion as a function of its dimensions: Theory and data. Perception & Psychophysics, 21, 489–503.
Rosinski, R. R., & Farber, J. (1980). Compensation for viewing point in the perception of pictured space. In M. A. Hagen (Ed.), The perception of pictures (Vol. 1, pp. 137–176). New York: Academic Press.
Sedgwick, H. A. (1980). The geometry of spatial layout in pictorial representation. In M. A. Hagen (Ed.), The perception of pictures (Vol. 1, pp. 33–90). New York: Academic Press.
Sekuler, R., & Erlebacher, A. (1971). The two illusions of Müller-Lyer: Confusion theory reexamined. American Journal of Psychology, 84, 477–486.
Shepard, R. N. (1981). Psychophysical complementarity. In M. Kubovy & J. Pomerantz (Eds.), Perceptual organization (pp. 279–341). Hillsdale, NJ: Erlbaum.
Shepard, R. N. (1990). Mind sights. New York: Freeman.
Stacey, B., & Pike, R. (1970). Apparent size, apparent depth, and the Müller-Lyer illusion. Perception & Psychophysics, 7, 125–128.
Sugihara, K. (1984). An algebraic approach to shape-from-image problems. Artificial Intelligence, 23, 59–95.
Waltz, D. (1975). Understanding line drawings of scenes with shadows. In P. H. Winston (Ed.), The psychology of computer vision (pp. 19–92). New York: McGraw-Hill.
Warren, R. M., & Bashford, J. A. (1977). Müller-Lyer illusions: Their origin in processes facilitating object recognition. Perception, 6, 615–626.
Yang, T., & Kubovy, M. (1999). Weakening the robustness of perspective: Evidence for a modified theory of compensation in picture perception. Perception & Psychophysics, 61, 456–467.
Yue, X., Vessel, E. A., & Biederman, I. (2007). The neural basis of scene preferences. NeuroReport, 18, 525–529.
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Redding, G.M., Vinson, D.W. Virtual and drawing structures for the Müller-Lyer illusions. Atten Percept Psychophys 72, 1350–1366 (2010). https://doi.org/10.3758/APP.72.5.1350
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DOI: https://doi.org/10.3758/APP.72.5.1350