Abstract
The geometry of perceived space (phenomenal geometry) is specified in terms of three basic factors: the perception of direction, the perception of distance or depth, and the perception of the observer’s own position or motion. The apparent spatial locations of stimulus points resulting from these three factors thereupon determine the derived perceptions of size, orientation, shape, and motion. Phenomenal geometry is expected to apply to both veridical and illusory perceptions. It is applied here to explain a number of representative illusions, including the illusory rotation of an inverted mask (Gregory, 1970), a trapezoidal window (Ames, 1952), and any single or multiple point stimuli in which errors in one or more of the three basic factors are present. It is concluded from phenomenal geometry that the size-distance and motion-distance invariance hypotheses are special cases of the head motion paradigm, and that proposed explanations in terms of compensation, expectation, or logical processes often are unnecessary for predicting responses to single or multiple stimuli involving head or stimulus motion. Two hypotheses are identified in applying phenomenal geometry. It is assumed that the perceptual localization of stimulus points determines the same derived perceptions, regardless of the source of perceptual information supporting the localizations. This assumption of cue equivalence or cue substitution provides considerable parsimony to the geometry. Also, it is assumed that the perceptions specified by the geometry are internally consistent. Departures from this internal consistency, such as those which occur in the size-distance paradox, are considered to often reflect the intrusion of nonperceptual (cognitive) processes into the responses. Some theoretical implications of this analysis of phenomenal geometry are discussed.
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References
Ames, A., JR (1952) The rotating trapezoid (Cont) Explanation of visual phenomena In F. P. Kilpatrick (Ed.),Human behavior from the transactional point of view (pp. 75–86). Washington, DC: Office of Naval Research, Department of the Navy.
Biersdorf, W. R. (1966) Convergence and apparent distance as correlates of size judgments at near distances.Journal of General Psychology,75, 249–262.
Boring, E. G. (1946) The perception of objects.American Journal of Physics,14, 99–107
Cutting, J. E. (1988) Affine distortions of pictorial space Some predictions for Goldstein (1987) that La Gournerie (1859) might have made.Journal of Experimental Psychology Human Perception & Performance,14, 305–311
Coltheart, M. (1968) Size information as a factor in visual judgments of absolute distance under reduced conditions Unpublished doctoral dissertation, University of Sydney, Sydney, Australia
Day, R. H., &Parks, T. E. (1989) To exorcize a ghost from the perceptual machine. In M. Hershenson (Ed),The moon illusion (pp 343–350) Hillsdale, NJ. Erlbaum
Deregowski, J. B. (1980)Illusions, patterns, and pictures. A cross-cultural perspective. New York. Academic Press
Duncan, F. S. (1975) Kinetic art On my psychokinematic objects.Leonardo8, 97–101
Ellis, S. R., Smith, S., &McGreevy, M. W. (1987). Distortions of perceived visual directions out of pictures.Perception & Psychophysics,42, 535–544
Epstein, W., &Babler, T. (1989) Perception of slant-in-depth is automatic.Perception & Psychophysics,45, 31–33
Epstein, W., Broota, K. D. (1986) Automatic and attentional components in perception of size-at-a-distance.Perception & Psychophysics,40, 256–262
Epstein, W., &Landauer, A. A. (1969) Size and distance judgments under reduced conditions of viewing.Perception & Psychophysics,6, 269–272
Epstein, W., &Loviits, B. E. (1985) Automatic and attentional components in perception of shape-at-a-slant.Journal of Experimental Psychology Human Perception & Performance,11, 335–366
Foley, J. M. (1965). Visual space: A scale of perceived visual direction.Proceedings of the 73rd Annual Convention of the American Psychological Association,1, 49–50
Foley, J. M. (1968) Depth, size and distance in stereoscopic vision.Perception & Psychophysics,3, 265–274
Foley, J. M. (1972) The size-distance relation and intrinsic geometry of visual space: Implications for processing.Vision Research,12, 323–332.
Gibson, J. J. (1950)The perception of the visual worm Boston. Houghton Mifflin
Gibson, J. J. (1966).The senses considered as perceptual systems Boston: Houghton Mifflin.
Gillam, B. J. (1968), Perception of slant when perspective and stereopsis conflict: Experiments with amseikonic lenses.Journal of Experimental Psychology,78, 299–305.
Gogel, W. C. (1954). Perception of the relative position of objects as a function of other objects In the field.Journal of Experimental Psychology,47, 335–342
Gogel, W. C. (1965) Equidistance tendency and its consequences.Psychological Bulletin,64, 153–163
Gogel, W. C. (1969a). The effect of object familiarity on the perception of size and distance.Quarterly Journal of Experimental Psychology,21, 239–247
Gogel, W. C. (1969b) The sensing of retinal size.Vision Research,9, 1079–1094
Gogel, W. C. (1970). The adjacency principle and three dimensional visual illusions. In J C Baird (Ed), Human space perception: Proceedings of the Dartmouth Conference.Psychonomic Monograph Supplement,3(13, Whole No 45), 153–169
Gogel, W. C. (1971). A validity of the size-distance invariance hypothesis with cue reduction.Perception & Psychophysics,9, 92–94
Gogel, W. C. (1976) An indirect method of measuring perceived distance fiom familiar size.Perception & Psychophysics,20, 419–429
Gogel, W. C. (1977) An indirect measure of perceived distance from oculomotor cues.Perception & Psychophysics,21, 3–11
Gogel, W. C. (1979a) The common occurrence of errors of perceived Distance.Perception & Psychophysics,25, 2–11
Gogel, W. C. (1979b) Induced motion as a function of the speed of the inducing objects, measured by means of two methods.Perception,8, 255–262
Gogel, W. C. (1980) The sensing of retinal motion.Perception & Psychophysics,28, 155–163.
Gogel, W. C. (1981a) Perceived depth is a necessary factor in apparent motion concomitant with head motion A reply to Shebilske and Proffitt.Perception & Psychophysics,29, 173–177
Gogel, W. C. (1981b) The role of suggested size In distance responsesPerception & Psychophysics,30, 149–155
Gogel, W. C. (1982). Analysis of the perception of motion concomitant with a lateral motion of the head.Perception & Psychophysics,32, 241–250
Gogel, W. C. (1983) An illusory motion of a stationary target during head motion is unaffected by paradoxical retinal motion. A reply to Shebilske and Proffitt (1983).Perception & Psychophysics,34, 482–487
Gogel, W. C. (1984) The role of perceptual interrelations in figural synthesis. In P. Dodwell & T. Caelh (Eds),Figural synthesis (pp 31–82) Hillsdale, NJ: Erlbaum
Gogel, W. C., &Dasilva, J A. (1987a) Familiar size and the theory of off-sized perceptions.Perception & Psychophysics,41, 318–328
Gogel, W. C., &Dasilva, J A (1987b) A two-process theory of the response to size and distance.Perception & Psychophysics,41, 220–238.
Gogel, W. C., & Eby, D. W. (1990)The perception of visual angle in optical change. Unpublished manuscript
Gogel, W. C., &Harkeb, G. S. (1955) The effectiveness of size cues to relative distance as a function of lateral visual separation.Journal of Experimental Psychology,50, 309–315
Gogel, W. C., Loomis, J. M., Newman, N. J., &Sharkey, T. J. (1985) Agreement between indirect measures of perceived distance.Perception & Psychophysics,37, 17–27,
Gogel, W. C., &Mershon, D. H. (1977) Local autonomy in visual space Scandinavian.Journal of Psychology,18, 237–250
Gogel, W. C., &Newton, R. E. (1969) Perception of off-sized objects.Perception & Psychophysics,5, 7–9
Gogel, W. C., &Sharkey, T. J. (1989) Measuring attention using induced motion.Perception,18, 303–320
Gogel, W. C., &Sturm, R. D. (1971) Directional separation and the size cue to distance.Psychologische Forschung,35, 57–80.
Gogel, W. C., &Tietz, J. D. (1973) Absolute motion parallax and the specific distance tendency.Perception & Psychophysica,13, 284–292.
Gogel, W. C., &Tietz, J. D. (1974). The effect of perceived distance on perceived movement.Perception & Psychophysics,16, 70–78
Gogel, W. C., &Tietz, J. D. (1977) Eye fixation and attention as modifiers of perceived distance.Perceptual & Motor Skills,45, 343–362
Gogel, W. C., &Tietz, J. D. (1979). A comparison of oculomotor and motion parallax cues of egocentric distance.Vision Research,19, 1161–1170
Gogel, W. C., & Tietz, J. D. (1990)Limitations of the role of cognitive factors in the perception of orientation in depth. Unpublished manuscript
Goldstein, E. B. (1979). Rotation of objects in pictures viewed at an angle: Evidence for different properties of two types of pictorial spaceJournal of Experimental Psychology. Human Perception & Performance,8, 78–87
Goldstein, E. B (1987). Spatial layout, orientation relative to the observer, and perceived projection in pictures viewed at an angle.Journal of Experimental Psychology: Human Perception & Performance,13, 256–266.
Goldstein, E. B. (1988) Geometry or not geometry? Perceived orientation and spatial layout in pictures viewed at an angle.Journal of Experimental Psychology: Human Perception & Performance,14, 312–314
Gregory, R. L (1968, November).Visual illusions. Scientific American, pp. 66–76.
Gregory, R. L. (1970).The intelligent eye. New York: McGraw-Hill.
Hay, J. C. (1968). Visual adaptation to an altered correlation between eye movement and hand movement.Science,160, 429–430.
Hay, J. C., &Goldsmith, W. M. (1973). Space-time adaptation of visual position constancy.Journal of Experimental Psychology,99, 1–9
Heinemann, E. G., Tulving, E., &Nachmias, J (1959). The effect of oculomotor adjustments on apparent size.American Journal of Psychology,72, 32–45.
Holway, A. H., &Boring, E. G. (1941) Determinants of apparent visual size with distance variant.American Journal of Psychology,54, 21–37.
Ittelson, W. H. (1952).The Ames demonstrations in perception (pp. 21–25). Princeton, NJ: Princeton University Press.
Komoda, M. K., &Ono, H. (1974). Oculomotor adjustments and size distance perception.Perception & Psychophysics,15, 353–360.
Landauer, A. A., &Epstein, W. (1969). Does retinal size have a unique correlate in perceived size?.Perception & Psychophysics,6, 273–275.
Leibowitz, H. W. (1971). Sensory, learned, and cognitive mechanisms of size perception.Annals of the New York Academy of Sciences,188, 47–62.
Leubowitz, H., &Moore, D. (1966) Role of changesen accommodation and convergence in the perception of size.Journal of the Optical Society of America,56, 1120–1123.
Leibowitz, H. W., Shiina, K., &Hennessy, R. T. (1972). Oculomotor adjustments and size constancy.Perception & Psychophysics,12, 497–500.
Mack, A. (1978). Three modes of visual perception. In H. L Pick, Jr., & E. Saltzman (Eds.).Modes of percerving and processing information (pp. 171–186). Hillsdale, NJ: Erlbaum.
McCready, D. W., Jr. (1965). Size-distance perception and accommodation-convergence micropsia: A critique.Vision Research,5, 189–206.
McCready, D. (1985). On size, distance, and visual angle perceptionPerception & Psychophysics,37, 323–334.
McCready, D. (1986). Moon illusions redescribed.Perception & Psychophysics,39, 64–72.
MacCracken, P. J., Gogel, W. C., &Blum, G. S (1980). Effects of posthypnotic suggestion on perceived egocentric distance.Perception,9, 561–568.
Ono, H., Muter, P., &Mitson, L. (1974). Size-distance paradox with accommodative micropsia.Perception & Psychophysics,15, 301–307.
Peterson, M. A., &Shyi, G. C.-W. (1988). The detection of real and apparent concomitant rotation in a three-dimensional cube: Implications for perceptual interactions.Perception & Psychophysics,44, 31–42.
Post, R. B., &Leibowitz, H. W. (1982). The effect of convergence on the vestibulo-ocular reflex and implications for perceived movement.Vision Research,22, 461–465.
Rock, I. (1977). In defense of unconscious inference. In W. Epstein (Ed.),Stability and constancy in visual perception: Mechanisms and processes (pp. 321–373). New York: Wiley.
Rock, I. (1983).The logic of perception Cambridge, MA. MIT Press.
Rock, I., Hill, A. L., &Fineman, M. (1968). Speed constancy as a function of size constancy.Perception & Psychophysics,4, 37–40.
Rock, I., &McDermott, W. (1964) The perception of visual angleActa Psychologica,22, 119–134.
Roelops, C. O. (1935) Optische Lokalisation.Archiv für Augenheilkunde,109, 395–415.
Schriver, W. (1925). Experimentelle Studien über stereoskopisches Sehen.Zeitschrift für Psychologie,96, 113–170
Sherilske, W. L., Proffitt, D. R. (1981). The priority of perceived distance for perceiving motion has not been demonstrated: Critical comments on Gogel’s “The sensing of retinal motion”.Perception & Psychophysics,29, 170–172.
Sherilske, W. L., &Proffitt, D. R. (1983) Paradoxical retinal motions during head movements. Apparent motion without equivalent apparent displacement.Perception & Psychophysics,34, 476–481.
Swanston, M. T., &Gogel, W. C. (1986). Perceived size and motion in depth from optical expansion.Perception & Psychophysics,39, 309–326.
Tietz, J. D., &Gogel, W. C. (1978). Adaptation to apparent concomitant motion in the absence of physical or retinal motion.Bulletin of the Psychonomic Society,12, 1–4.
Van Des Meer, H. C. (1979). Interrelation of the effects of binocular disparity and perspective cues on judgments of depth and height.Perception & Psychophysics,26, 481–488.
Von Holst, E., &Mittelstaedt, H. (1950). Das Reafferenz-Prinzip.Die Naturwissenschaften,20, 464–476.
Wallach, H. (1985, May). Perceiving a stable environment.Scientific American, pp. 118–124
Wallach, H. (1987). Perceiving a stable environment when one moves.Annual Review of Psychology,38, 1–27.
Wallach, H., Bacon, J., &Schulman, P. (1978). Adaptation in motion perception: Alteration of induced motion.Perception & Psychophysics,24, 509–514.
Wallach, H., &Floor, L. (1970). On the relation of adaptation to field displacement during head movements to the constancy of visual direction.Perception & Psychophysics,8, 95–98.
Wallach, H., &Frey, K. J. (1969). Adaptation in the constancy of visual direction measured by a one-trial method.Perception & Psychophysics,5, 249–252.
Wist, E. R., Diener, H. C., &Dichgans, J. (1976). Motion constancy dependent upon perceived distance and the spatial frequency of the stimulus pattern.Perception & Psychophysics,19, 485–491
Wist, E. R., Diener, H. C., Dichgans, J., &Brandt, Th. (1975) Perceived distance and the perceived speed of self-motion: Linear vs. angular velocity?.Perception & Psychophysics,17, 549–554.
Wist, E. R., Summons, E. (1976). Spatial and fixation conditions affecting the temporal course of changes in perceived relative distance.Psychological Research,39, 99–112.
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The preparation of this article was supported by Research Grant MH 39457 from the United States National Institute of Mental Health.
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Gogel, W.C. A theory of phenomenal geometry and its applications. Perception & Psychophysics 48, 105–123 (1990). https://doi.org/10.3758/BF03207077
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DOI: https://doi.org/10.3758/BF03207077