The basis of perceptual constancy and perceptual illusion R. H. Day A wide range of perceptual illusions, including many of size, orientation, and movement, can be explained in terms of the mechanisms which normally initiate and maintain perceptual constancy. Perceptual constancy is the relative stability of the apparent value of object properties (size, shape, orientation, movement, etc.) when the representation at the eye (retinal image) is variant with change in observer position, posture, and movement. These constancies are consequent on stimuli for object distance and observer posture and motion. When the retinal image is invariant and these stimuli are manipulated, perceptual illusions occur. That is, the mechanisms which normally preserve constancy can be invoked to cause illusions. able criticism, mainly on the grounds that they cannot cope with numerous specific geometrical illusions. Despite the inadequacies of earlier attempts, a general explanation of visual spatial illusions will be proposed here in terms of visual constancy, the tendency for apparent values of object properties such as their size, shape, and orientation to remain relatively stable despite considerable variation in their retinal projection, as the individual changes his position, bearing, and posture relative to the object. It will be suggested that the mechanisms which under normal conditions serve to initiate and maintain visual constancy of object size, orientation, and movement, to name three classes, under specified conditions also initiate visual illusions of these properties. Thus the problem of illusion reduces essentially to the problem of perceptual constancy. Indeed it can be argued that consistent failure to explain illusory phenomena either in psychophysiologic or neurophysiologic terms is due in large part to a failure to recognize their basis in perceptual constancy. The main justification for another attempt to explain perceptual illusion in terms of perceptual constancy is that previous attempts have hile the problem of perceptual illusion has not aroused quite the same degree of empirical or theoretical interest among neurophysiologists as among experimental psychologists there has nevertheless been a continuing concern with the neural correlates of illusory phenomena. Both Motokawa1 and Burns and Pritchard2 have recently attempted to establish the neural interactions associated with these distortions. However, the problem has proved extraordinarily intractable and the neural structures and processes associated with illusory effects remain quite obscure. Furthermore, it cannot be said that attempts to explain perceptual illusions at the behavioral level have so far met with much greater success, although efforts to do so have been more frequent and sustained and the body of data far more substantial. Recent explanations in terms of perceptual constancy by Gregory,3"5 Kristof,G and Tausch7 have been subjected to consider- From the Department of Psychology, Monash University, Clayton, Victoria 3168, Australia. Preparation of this paper was undertaken while the author was on sabbatical leave at the University of Exeter, United Kingdom. 525 Investigative Ophthalmology June 1972 526 Day 10 30 «O SO 73" IOO 10 cm 100 cm. s 3 10 25 cm. IS 1* // 21 SO IOO too +OO cm. s too «oo Equivalent Distance (cm) Fig. 1. Convergence and accommodation of the eyes gives rise to stimuli for distance which normally contribute to size constancy when the object image is variant with distance. Size illusions occur when convergence and accommodation are varied with object distance and object image invariant. For a fixed distance the degree of convergence-accommodation was optically adjusted to equivalence with that for greater and less distances (equivalent distance). For actual distances of 10, 25, 50, and 100 cm., apparent size corresponded with expectancies based on convergence-accommodation (diagonal lines). The horizontal lines represent expectancies for constant apparent size. (From Leibowitz, H., and Moore, D.: J. Opt. Soc. Am. 56: 1120, 1966.) been restricted to a small group of geometric illusions and have not taken into account illusions (and constancy) of orientation and motion involving body tilt and motion stimuli. It will be useful to make four introductory points. First, although visual illusions, which are defined as consistent discrepancies between the apparent and physical value of an object property, are usually associated with geometric diagrams, these represent only a small proportion of illusory phenomena. Second, there are numerous classes of illusion, each deriving from a particular class of perceptual constancy; the geometric illusions are drawn from more than one of these classes. Third, although there are different classes of visual constancy (and derived illusions) the general principles in terms of which they are explained are essentially the same for all classes. Finally, in recent years there has been dramatic success in isolating cells specifically tuned to single object features such as movement, orientation, contour, and color. It can be argued (and this is the point of the paper) that the next level of complexity are analyzers which respond to the constancy of object size, shape, orientation of movement despite retinal image changes. These analyzers may well be those responsible for illusions when they are invoked under conditions which will be generally described below. The visual constancies As the organism changes its position relative to environmental objects either by locomotion or postural change the projection of the object at the eye, i.e., the retinal image, undergoes change. Such changes occur with variation in the observer's distance, orientation, angular bearing, and movement relative to the object. However, even though the image changes at the eye are often large as, for example, when the observer moves to a great distance or changes posture through 90 degrees, the apparent values of object properties remain remarkably stable. Apparent size with distance variant is relatively very stable, as is apparent shape with change in bearing, apparent orientation with change in lateral body tilt, and apparent stationariness with movement of the head and eyes. This relative stability of apparent size, shape, orientation, and movement (including in the limit stationariness) are instances of visual constancy. The biological significance of these constancies is obvious; the observer sees object properties in terms of their physical characteristics Volume 11 Number 6 Perceptual constancy and illusion 527 Fig. 2. Examples of size illusions due to the manipulation of projected stimuli for distance such as perspective, texture, and elevation. rather than of their varying representation at the eye. Such a perceptual achievement has obvious biological utility. In order to show how illusory phenomena derive from the mechanisms controlling perceptual constancy it is convient to consider first the case of size constancy if for the only reason that it is the best known and most intensively studied. Visual size constancy and illusion As the observer recedes from an object (or vice versa) the retinal image of the latter diminishes but its apparent size is relatively constant. Therefore information for distance must be involved in the maintenance of constant apparent size. That this is so was made clear in the classic experiments of Holway and Borings in which distance stimuli were progressively reduced. Since then data from three separate experiments9"11 have shown that when distance stimuli are entirely eliminated an object's apparent size decreases as a linear function of observer-object-distance, i.e., apparent size follows the "law of the visual angle." "Cues" or stimuli for distance fall into five classes: (1) retinal disparity (or binocular parallax; (2) muscular stimuli (convergence and accommodation); (3) monocular parallax; (4) atmospheric stimuli (aerial perspective and the Tyndall ef- fect); and (5) projected stimuli (perspective, texture, overlay, elevation in field, element and interspace size, and element and interspace frequency. Normally all or most of these stimuli for distance are present and visual size constancy is perfect. However, although size constancy falls off as distance stimuli are systematically reduced (e.g., when binocular parallax is eliminated by using one eye and monocular parallax by holding the head stationary8) some degree of constancy obtains, i.e., apparent size does not follow the law of the visual angle, as observer-object distance increases. The principle of visual size constancy can be simply stated: With retinal image size variant consequent upon change in observer-objectdistance apparent size is relatively invariant when distance stimuli are present. Even in a picture some degree of size constancy obtains when perspective, texture, and elevation stimuli for distance are present.12 It follows from this principle that when the retinal image is invariant and the stimuli for distance are manipulated, apparent size will also vary. That is, when the distance stimuli which normally preserve size constancy are varied with the image fixed an illusion of object size must occur. Three examples will serve to make this point clear. First, Gogel, Wist, and Harker13 systematically varied retinal disparity with 528 Investigative Ophthalmology June 1972 Day 1-0 G gravitational force I -414 G resultant force \ gravitoinertial vertical 10 G centrifugal force ' L h centrifugal centre post t \ 10 G gravitational (contact) force 1-414 G resultant (contact) force Fig. 3. The human centrifuge. Vestibular stimuli for observer orientation relative to the gravitational axis and for observer motion can be manipulated by centrifugation at constant angular velocity and by acceleration, respectively. image size fixed. This was achieved by effectively varying the interpupillary distance with object distance (152.4 cm.) invariant. For the three interpupillary bases of 12.4 (double), 6.5 (normal), and 3.2 (half), the apparent size of a 30.5 cm. object was 28.5, 31.9, and 40.0 cm., respectively. Second, Leibowitz and Moore14 varied convergence-accommodation taking care to preserve their normal relationship and obtained matches to a standard object at observation distances of 10, 25, 50, 100, or 400 cm. At each of these distances accommodation was adjusted to 0.25, 0.50, 1.00, 2.00, and 3.00 diopters with convergence in normal correspondence. Apparent size varied with convergence-accommodation following a linear function up to about 1 m. as shown in Fig. 1. Third, if the retinal image of an object is invariant and projected stimuli such as those of perspective, texture, and elevation are varied, the apparent size of the object undergoes change. This change in apparent size is the well known Ponzo illusion of which some examples are shown in Fig. 2. The point to be made is that when the retinal image varies with distance apparent size is relatively constant when some or all classes of distance stimuli are present. This is size constancy. When, however, the image does not vary, but distance stimuli do, changes occur in apparent size. These are size illusions. That is, the principle governing size constancy can be invoked to cause a size illusion. Geometric size illusions The projected stimuli for distance, stimuli which derive essentially from the projection of a three-dimensional space on to the two-dimensional retinal surface, are more frequent and subtle than is usually realized. In addition to the well-known Volume 11 Number 6 stimuli such as perspective, texture, overlay, and elevation, the size and frequency of elements other than the focal object and the size and frequency of interspaces between them vary with distance and provide information for distance. The trees on the near side of a lake are bigger and fewer per unit visual angle than the smaller and more frequent trees on the far side, as indeed are the interspaces between them. Many geometric optical illusions involve such distance stimuli.15 Of two objects one is usually located in the context of larger and less frequent elements or spaces consonant with nearness and the other in the context of smaller and more frequent elements corresponding to greater distance. The former object is judged smaller than the latter. The Oppel-Kundt, Delboeuf, and Miiller-Lyer illusions are examples of size illusions in which the retinal image of an object, usually a line or simple figure, is invariant but projected stimuli for distance are varied. It should be noted, however, that as had been pointed out elsewhere15 the Miiller-Lyer illusion as it is classically sbown represents two separate effects. The "short" version with "inboard" elements is probably a different illusion than the "long" version with "outboard" elements. Evidence for this difference has been adduced by Erlebacher and Sekuler.10 Visual orientation constancy and illusion When the observer's head is tilted laterally as posture is changed, the retinal orientation of the object's image relative to the normally vertical meridian of the eye changes. When the observer is recumbent this change is nearly 90 degrees. However, under conditions of normal illumination and when only the object itself is visible in a dark room, its apparent tilt is relatively stable, a phenomena called visual orientation constancy.17 In normal illumination the bar remains perceptually invariant even for large lateral body tilts.18 In darkness its apparent slant varies in Perceptual constancy and illusion 529 direction and magnitude as a function of tilt but is always less than retinal tilt. The complete function is referred to as the Aubert-Miiller effect.17 Since apparent orientation is relatively stable with image orientation variant, it follows that information for body tilt must be involved in this perceptual outcome. That is, information for body tilt must be combined with that for retinal image orientation to preserve constancy. There are at least three classes of stimuli for body orientation: vestibular involving the utricular statocysts, visual involving the contours of the visual field, and kinesthetic.17 It is likely that interoceptive stimuli are also involved. It follows that if the observer is upright and the orientation of the retinal image is invariant while the stimuli for body orientation are manipulated either singly or together, an illusion or orientation must occur, e.g., an upright object will appear tilted. The vestibular stimulus for body tilt, i.e., gravity, can be independently manipulated in direction by rotating the observer at constant angular velocity in the darkened cabin of a human centrifuge as shown in Fig. 3. The resultant gravitoinertial force acting on the statocysts modifies information for body tilt so that a gravitationally vertical bar in an otherwise dark cabin is apparently tilted. This is the oculogravic illusion noted by Mach19 and investigated in detail by Graybiel.20'21 The normally near-vertical and near-horizontal contours of the natural and man-made environment which also serve as stimuli controlling lateral body tilt can be changed simply by tilting them while the observer himself remains upright. Even though the vestibular (gravitational) stimulus is present a considerable illusion of object orientation occurs.22' 23 The "tilting room" effect, the rodframe effect, and the tilted line illusion are visual orientation illusions which include many of the Zollner group. In general then, as is the case with size when distance stimuli are varied, apparent orientation, 530 Day which is normally constant as the body tilts, varies when the image is invariant and body orientation stimuli are manipulated. If kinesthetic and interoceptive stimuli could be similarly varied visual orientation illusions would also be expected to occur. Visual movement constancy and illusion When the image of a stationary object sweeps across the retina as the body and head move, the object remains apparently stationary. This constancy of position (and movement, if the object is moving) occurs even when the object alone is visible in an otherwise dark space.24 In a manner essentially similar to visual orientation constancy, visual movement and position constancy must depend on information for body motion and stationariness. This information is carried in large part by vestibular and visual stimuli such that when the image of a stationary object moves it remains perceptually stationary. If, however, the retinal representation of a stationary object is invariant and body movement stimuli changed, illusions of movement occur. The oculogyral illusion occurs when vestibular stimuli are manipulated by accelerating the observer in a human centrifuge thus activating semicircular canal receptors-5'2G (Fig. 3) and induced movement occurs when the usually stationary visual field itself is made to move.27'2S Mechanisms of visual constancy and illusion Visual constancy, a biologically important feature of space perception, refers to the relative stability of the apparent value of an object property as its retinal representation changes in various ways. Visual illusion, for long a curiosity of the psychological laboratory, refers to a consistent discrepancy between the apparent and physical values of an object property. The second derives from the first for a wide range of conditions and separate classes Investigative Ophthalmology June 1972 of constancy; if the stimuli which preserve constancy when the image is variant are independently manipulated when it is invariant, an illusion occurs. Such is the case with visual size, orientation, and movement. A central question is: Are there neural mechanisms which serve to maintain perceptual constancy and which when invoked under "inappropriate" conditions give rise to illusory effects? There is already a small body of data which suggests that such mechanisms do exist. These structures continue to respond in a stable manner even though the stimulus at the eye varies, and it can be concluded that input to the system includes that from sources additional to the visual representation of the object property itself. Wiersma29 has reported "space constant" fibers in the neural system of the crayfish Procamberus clarki such that when the animal is rotated about either its transverse or longitudinal axis so that the projection at the eye varies in orientation the space constant fibers continue to respond. Wiersma has suggested that positional information which preserves this stability of response might derive from the statocysts. More recently Horn and Hill30 have reported unchanging output from units in the visual cortex of the cat. When the head axis of the animal was tilted through 30 degrees, the meridian of maximum response remained more or less stable. In all, 57 units responding in this manner were studied. It is worth noting that in this experiment there was sometimes an "overshoot" of the axis when the animal was returned to the normal orientation suggesting a correlate for the visual orientation aftereffect reported recently.31 If the observer is tilted for about two minutes with closed eyes and then returned to the upright, a gravitationally vertical line of line in a dark room is apparently tilted in the opposite direction to body tilt. This finding, together with Horn and Hill's data, suggests that the aftereffect represents a breakdown of spatial constancy due to Volume 11 Number 6 adaptive processes. Of course, it has long been recognized that vestibular input affects activity in the visual system.32 A means for isolating those mechanisms associated with visual illusions follows from the suggestion that perceptual constancy and illusion are related. A neural unit which continues to respond in a uniform fashion to a variable stimulus at the eye, e.g., as the animal is tilted, would be expected to show a highly variable discharge pattern if the stimulus is invariant at the eye and the stabilizing stimulus changed. If, for example, the cat were subjected to a gravitoinertial force with the retinal image fixed, a change in the neural pattern correlated with the oculogravic illusion would be expected. Similarly, a unit which responds uniformly when the size of the stimulus changes would be expected to exhibit a different pattern with fixed image and manipulation of one or more of the distance stimuli described above (providing, of course, the other stimuli for distance are eliminated. To put the point succinctly: Where there exist units which normally respond with a constant excitation pattern to a variable stimuli ("constancy units"), it can be expected that the pattern will change when the stimuli are invariant and the stabilizing stimuli (e.g., distance, body orientation, body movement stimuli) are varied. Assistance in the preparation of this paper by the Department of Psychology, University of Exeter, is gratefully acknowledged. REFERENCES 1. Motokawa, K.: Physiology of color and pattern vision, New York, 1970, Springer-Verlag. 2. Burns, B. D., and Pritchard, R.: Geometrical illusions and the response of neurones in the cat's visual cortex to angle patterns, J. Physiol. 213: 599, 1971. 3. Gregory, R. L.: Distortion of visual space as inappropriate constancy scaling, Nature 199: 678, 1963. 4. Gregory, R. L.: Visual illusions, in Foss, B. M., editor: New horizons in psychology, Perceptual constancy and illusion 531 Harmondsworth, 1966, Penguin Books, Inc. 5. Gregory, R. L.: Eye and brain, London, 1966, Weidenfeld and Nicholson. 6. Kristof, W.: Ober die Einordnung geometrisch-optischer Tauschungen in die Gesetzin assigkeiten der visuellen Wahrnehmung, Arch. Gesamte Psychol. 113: 1, 1961. 7. Tausch, R.: Optische Tauschungen als artifizielle Effekte der Gestaltungs prozesse von Grossen und Formenkonstantz in der niiturlichen Raumwahrnehmung, Psychol. Forsch. 24: 299, 1954. 8. Holway, A. H., and Boring, E. G.: Determinants of apparent visual size with distance variant, Am. J. Psychol. 54: 21, 1941. 9. Hastorf, A. H., and Way, K. S.: Apparent size with and without distance cues, J. Gen. Psychol. 47: 181, 1952. 10. Lichen, W., and Lurie, S.: A new technique for the study of perceived size, Am. J. Psychol. 63: 280, 1950. 11. Over, R.: The effect of instructions or sizejudgments under reduced conditions, Am. J. Psychol. 73: 599, 1960. 12. Boring, E. G.: Size constancy in a picture, Am. J. Psychol. 77: 494, 1964. 13. Gogel, W. C., Wist, E. R., and Harker, G. S.: A test of the invariance of the ratio of perceived size to perceived distance, Am. J. Psychol. 76: 537, 1963. 14. Leibowitz, H., and Moore, D.: Role of changes in accommodation and convergence in the perception of size, J. Opt. Soc. Am. 56: 1120, 1966. 15. Day, R. H.: Visual spatial illusions: A general explanation, Science 75: 1335, 1972. 16. Erlebacher, A., and Sekuler, R.: Explanation of the Miiller-Lyer illusion: confusion theory examined, J. Exp. Psychol. 80: 462, 1969. 17. Day, R. H., and Wade, N. J.: Mechanisms involved in visual orientation constancy, Psychol. Bull. 71: 33, 1969. 18. Neal, E.: Visual localization of the vertical, Am. J. Psychol. 37: 287, 1926. 19. Mach, E.: Beitrage zur Analyse der Empinfindungen, Jena, 1886, Fischer. 20. Graybiel, A.: Oculogravic illusion, Arch. Opthalmol. 48: 605, 1952. 21. Graybiel, A.: The importance of the otolith organs in man based on a specific test for utricular function, Ann. Otol. Rhin. Laryngol. 65: 470, 1956. 22. Asch, S. E., and Witkin, H. A.: Studies in space orientation. I. Perception of the upright with displaced visual fields, J. Exp. Psychol. 38: 325, 1948. 23. Austin, M., Singer, C., and Day, R. H.: Visual orientation illusion following judg- 532 Day 24. 25. 26. 27. 28. 29. 30. 31. 32. ments with a tilted visual field, Nature 221: 583, 1969. Wallach, H., and Kravitz, J. H.: The measurement of the constancy of visual direction and its adaptation, Psychonom. Sci. 2: 217, 1965. Graybiel, A., and Hupp, D. I.: The oculogyral illusion; a form of apparent motion which may be observed following stimulation of the semicircular canals, J. Aviat. Med. 17: 3, 1946. Craybiel, A.: The effect on vision produced by stimulation of the semicircular canals by linear acceleration, in White, C. S., and Benson, O. O., editors: Physics and medicine of the upper atmosphere, Mexico, 1952, University of Mexico Press. Duncker, K.: Induced motion, in Ellis, W. D., editor: A source book of Gestalt Psychology, New York, 1938, Harcourt Brace. Wallach, H.: Perception of motion, Sci. Am. 201: 56, 1959. Wiersma, C. A. G.: Integration in the visual pathway of Crustacea, Symp. Soc. Exp. Biol. 20: 151, 1966. Horn, G., and Hill, R. M.: Modification of receptive fields of cells in the visual cortex occurring spontaneously and associated with body tilt, Nature 221: 186, 1969. Day, R. H., and Wade, N. J.: Visual spatial aftereffect from prolonged head tilt, Science 154: 1201, 1966. Jung, R..- Neuronal integration in the visual cortex and its significance for visual information, in Rosenblith, W. A., editor: Sensory communication, New York, 1961, John Wiley & Sons, Inc. Discussion PETTIGREW: There have been a number of attempts including my own to confirm the Horn and Hill experiment but they have been unsuccessful. It is very difficult to keep the eyes from shifting under these circumstances. DAY: It is of course disappointing to learn that that is so. However, one mentions the experiment merely to emphasize the sort of experimental approach to perceptual constancy and, therefore, to illusion that is suggested by my argument. The lesson is: Look for the mechanism of constancy first and then you will have that of the illusion. Investigative Ophthalmology June 1972 :' I would like to make a pedagogic comment to neurophysiologists here. We have to appreciate two categories of perceptual constancies. One category occurs when the nervous system has information available about bodily changes, and every engineer knows if he wants to build a stabilized gun site platform on a tank that it is not difficult to do so since he has all the information available on position and by proper feedback it can be stabilized. On the other hand to make devices which would know now that a coin in different perspective is still a coin when, for example, it looks like an ellipse is a completely different and much more involved problem. It can be solved by some advanced ideas in mathematics, but it is several orders of magnitude more difficult. For example when we speak about size constancy, this again is a fantastically different thing if we consider Emmert's law and convergence movements which occur within about one meter where stereopsis is handy and helps you to get almost perfect size constancy from the problems involved in seeing someone begin to shrink as a train moves away. These points came out in your talk, but I would like to emphasize it for neurophysiologists who, whenever they listen to size constancy, should ask if it is type I (the simple one) or type II. Most optical illusions belong to the latter class and consequently are very controversial. DAY: I do not wish to make such an unequivocally clear distinction between constancies based on stimuli for observer posture and movement and those based on observer distance and bearing from the object. In both situations the same principle applies; stimuli which serve to preserve perceptual constancy of an object property can be manipulated to produce an illusion. To me it matters little that those stimuli activate proprioceptive or exteroceptive systems. BURKE : Is there any demonstration that an animal can have an illusion? DAY: Yes, there is good evidence that they do. MACKAY: Don't you think some illusions are due to the fact that we view a three-dimensional world in two-dimensional array and are not merely a problem of constancy? DAY: It is conceivable. I do not claim that all illusions derive from activating those mechanisms which normally maintain constancy, merely that there is a wide range of such effects.