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Visual Perception of Real arid Represented Objects arid Events JULIAN HOCHBERG INTRODUCTION Experimental psychology started with the study of how we perceive pictures and of the conditions under which one object is an effective sur- rogate for another (that is, the two objects elicit the same effect). Such study has served the purposes of other disciplines as well, and remains inherently interdisciplinary. Prior to 1850 the problem was primarily pursued by artists and philos- ophers, and the conceptual tools were essentially those of physics and geometry. In the classical period, roughly from 1850 to 1950, the primary theoretical concerns were those of neurophysiologists and psychologists. Major applications-in visual prosthesis (e.g., optometry and ophthal- mology), the visual media (e.g., photography, print, and eventually tele- vision), and the interface between human and machine currently called human factors motivated much of the research that provided a rich base of technical data. The present period of tremendous ferment started around 1950. The problems of perception continue to engage all the disciplines already men- tioned; in addition, computer science is now a major presence in the field, providing tools and motivation in several distinct but closely related ways: as a source of techniques for research, theory testing, and modeling; as a source of analogies and metaphors; as an overlapping enterprise, seeking to devise machines that will "perceive" in the same way that people do; and in the context of learning how to generate and display computer images that humans can readily and accurately comprehend. 249

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250 JULIAN HOCHBERG THE PRE-1850s: ARTISTS, PHILOSOPHERS, AND PHYSICISTS Artists have known for centuries that one way to produce a picture is to make a surrogate object that (ideally) offers the eye the same pattern of light as that offered by the scene itself. The most famous example of this is Leonardo's window (Figure 1A): By tracing the outlines of objects on a plane of glass interposed between his eye and the scene, the artist discovers the characteristics of a two-dimensional projection of a three-dimensional scene. Of course, the method could be used to provide pictures of existing (B) FIGURE 1 Surrogates and their preparation. A: One of the optical aids that artists have used for centuries (surer) to help in preparing a surrogate that provides the eye with much of the same stimulus information as the object or scene being represented. B: By studying the tracings made of scenes viewed through a glass pane Leonardo advised that artists could learn the characteristic two-dimensional projections of three- dimensional layouts and could then construct pictures of imagined scenes.

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VISUAL PERCEPTION OF REAL AND REPRESENTED OBJECTS AND EVENTS 251 scenes with no need for the artist to learn anything: the scene could be traced directly on the glass (Figure 1B) or with the growth of technology- by photographic or video media. Some traditional features that result from projecting normal three-di- mensional scenes on two dimensions appear in Figure 2: these include linear perspective, familiar size, relative size, and interposition. Note that even a perfect picture produced in this way is inherently ambiguous, in that both the flat surrogate and the very different three-dimensional layout it repre- sents offer the same light to the eye. This is the aspect of pictures that made them, and visual perception, of interest to the philosophers the epistemological issue of how we can know what is true. Philosophical concerns aside, the ambiguity is inherent as a matter of simple mathematics, and provides both the opportunity for pictorial communication and a tool for psychological and physiological inquiry. The artist who learns to use signs of depth, as in Figure 2, can produce surrogates of scenes that do not and perhaps could not exist virtual scenes of grottos, unicorns, and biblical and extraterrestrial events. Indeed, we shall see that in Me interest of visual comprehensibility it is necessary to depart from pure projection, and most pictures are therefore to some extent surrogates of virtual rather Man actual scenes. Today computers provide an increasing proportion of Me still and moving pictures that humans confront. For Hem to do so programmers must learn how to project ~ree-dimensional layouts in two-dimensional arrays and to generate the play of light and shade by which different surface textures are FIGURE 2 The major pictorial (monocular) depth cues: the tracing of the scene in Figure 1B. ~ Linear Perspective: paral- 3 ~ 19px 8 , let lines ~8, 7-9, etc., ~ ~ TIC >\ converge in the picture f ' l. / 5 plane. Interposition: the / / nearer object4 occludes I ~ / part of the farther object Em\/ / 4 5. Relative Size: the trac- / ~ ~ /C ~ sing of boy 1 Is larger / )\ / \ than that of boy 2. Tex- ~ /~ / 7 ture-Density Gradient: the evenly spaced bars on the field 6-7-8-9 project an image whose density increases with distance. Familiar Size: if man 3 is known to be larger than boy 1, and they are the same size in the picture plane, then the man must be proportionally farther away in the represented scene. Tracings on the picture plane

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252 JULIAN HOCHBERG perceived (Figure 31. The study of such rules-traditionally called depth cues (Woodworth, 1938) and lately called "ecological optics" (Gibson, 1979) is fundamentally a branch of physics, but one that must be pursued with the psychological and neurophysiological limitations and contributions of the human viewer firmly in mind. Surrogates are therefore more than means of pictorial communication: they tell us about the limits of the information that the sense organ can pick up and about how the brain organizes that information. Perhaps the earliest major instance of that point was in Newton's (1672) famous experiment in visual sensation, showing that an appropriate mix of three narrow wave- lengths of light bands of color taken out of the spectrum, such as red, green, and blue can serve as a surrogate for any and all colors in the spectrum, and thus match any scene (Figure 41. This is not a fact about photic energy the light itself remains unchanged by the mixture. It is instead a strong clue about our sensory nervous systems, and it provided the background for the classical theory of perception and the nervous system, which we consider next. PSYCHOLOGY AND PHYSIOLOGY FROM 1850-1950 Given the facts of color mixture, the most parsimonious model of visual perception was the Young-Helmholtz theory (Helmholtz, 18661: that color perception is mediated by three kinds of specialized receptor neurons, the cones, each responsive to most of the spectrum, but each with a different sensitivity function. The three types were thought to be most sensitive to light that looks red, green, and blue, respectively, and their response to FIGURE 3 Computer-drawn image. A picture programmed directly from blueprints of a building, using a polygon facet approach with a simple lighting model that simulates direct sun and diffuse sky illumination. Paul Roberts, Computer Vision Lab, Columbia University.

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VISUAL PERCEPTION OF REAL AND REPRESENTED OBJECTS AND EVENTS 253 ,~,, A 650 ~ -__ 580 530 D I 460 _ _ I E _650 B 1 650 ~ 580 1 53o 460 1 RED C ORANGE YELLOW GREEN BLUE V IOLET ' 460 - - \ A I (_) ' ~ I \ O ~ ~ 9, ~ ~ > _ ~O G CC Z ~ ~ o Z o ~ 100 50 460 530 6s0 -VV 400 500 600 700 H FIGURE 4 Color surrogates. To the visual system G. a suitable mixture F of just Tree wavelengths selected by slits E from the visible spectrum D can, in principle, be a surrogate for any hue C, that is, any set of wavelengths in the spectrum. According to the traditional Young-Helrnholtz theory, the physiological explanation involves three types of retinal cone cells with the Tree sensitivity functions shown in H. From these we can see, for example, that a mix of equally effective intensities at 650 and 530 is indistinguishable from 580 and could serve as a surrogate for the latter. photic energy was thought to underlie the experience of those colors. The retina was envisioned as a mosaic of independent triads of the three cones (Figure 5), and the light provided to the eye by any scene was thought to be analyzed into the point-responses of the three component colors. The research most directly relevant to this theory was the attempt to map the sensitivity of each type of cone to the wavelengths of the visible spectrum and to map the spatial resolution of the retinal mosaic what detail the eye could be expected to resolve. Such information as the limits of resolution and the bases and specification of colors provided the first goals for what has become visual science and its applications, which now run from the prescription of spectacles to the design of television characteristics. It was also the foundation of the classical view of the perceptual process in general, diagrammed in Figure 6: at left, the object in the world, with its physical properties of distance, size, shape, reflectance (surface color). These do not affect the sense organs directly, of course, but only by means of the light they reflect to the sensitive cells. All things that cause the cells to respond in some specific way elicit the same sensory experience: the light coming from the object itself, the light produced by some surrogate of that object, the effects of mechanical or

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254 JULIAN HOCHBERG FIGURE 5 The sensory mosaic. ~ > In the simplest view, the retina of '~ the eye contains a mosaic of light- Ad. X sensitive cells. The spacing of the ~.F . ~ mosaic determines what detail can ( ~\ be seen: e.g., to distinguish a "C" ' from an "O." at least one cell (x) \>~ ~ must go unstimulated. The visible ~ it, i~ = portionoftheelectromagneticra- ye ~3 _ TO BRAIN diation incident at each point in the ~ iit.~3~ ~ retina that is capable of full color ~ ~. vision is coded into the output of \_ each of three cones according to its ' sensitivity curve (Figure 4H). This is, of course, essentially the way in which video cameras analyze the light they receive from D.S. UL1 Lit - SIZE REFL. SPACE ETC. RETINAL MOSAIC, P.S. SENSATION PERCEPTION 0 0 0~ Cam a' L,A L',RGB CUES CUES Z ~ o o Co O SIZE ROYGBIV WB (REFL.) SPACE ETC. FIGURE 6 The classical theory (1850-1950~. The distal stimulus, D.S. (an object or layout of objects), with such physical properties as size, reflectance, position in space, etc., impinges on the sensory surface by way of the proximal stimulus pattern, P.S., consisting of regions that vary in their spatial extent (~) and spectral distribution [lu minance (L), wavelengths (A)~. Sensory responses to each region (sensations) were thought to vary correspondingly in brightness (L') and hue (the mix of Red, Green, and Blue) over some extent all. Because of the regularities of the world and its geometry, the proximal stimulation will generally contain patterns (e.g., the cues in Figure 2) that are characteristic of and therefore provide information about the distal properties. The perception of such properties (objects' sizes, surface reflectances, spatial location, etc.) were thought to derive from the underlying sensations by associative learning and by computational processes.

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VISUAL PERCEPTION OF REAL AND REPRESENTED OBJECTS AND EVENTS 255 electrical stimulation of the eye, etc. Insofar as different objects and events produce the same responses, information about the world is lost in this encoding process. This is what makes surrogates possible. And the fact that very different objects, and indeed different patterns of light, have the same effects on the nervous system provides a tool with which to study that system's structure and function. The visual system thus conceived is a mosaic of receptors (the retina) on which the eye's optical system projects a focused image of the light provided by the object. The receptors (the three types of cone, supplemented by rods, which do not differentiate color) analyze each small region of that image into points of red, green, and blue. This conception of the visual system has now been embodied in the television camera: Television, like the Helmholtzian visual system, reduces the countless objects and events of the world to the different combinations of a set of three colors in a spatial mosaic. It is important both for the Helmholtzian theory and for television as a medium that such a simple set will suffice. In both cases, all of the remaining properties of the objects that we perceive in the world their sizes, forms, and reflectances (i.e., surface colors), their distances and movements are lost in the encoding process and must be supplied by the viewer. The simplest theory about such nonsensory processes was inherited from centuries of philosophical analyses of perception: the theory that we have learned the perceptual properties of objects from our experiences with the world. It runs as follows: The sense organs analyze the world into~ndamental sensations. Those sensations are, in the case of vision, the sets of points that differ in hue (R. G. B in Figure 6, signifying red, green, and blue sensory experiences) and brightness (L') over some effective extent, D'. These packets of sensations normally come in characteristic patterns that are im- posed by the regularities of the physical world, patterns such as the depth cues in Figure 2. By learning these regularities and their meanings, we learn to perceive the physical world and its properties. The theory seems to be economical and elegant. The principles of learning appeared to be at hand. For almost two centuries (from Hobbes in 1651 to James Mill in 1829), the British empiricist philosophers had discussed how the "laws of association," offered in essence by Aristotle, could serve to build our perceptions and ideas about the objects and events of the world. And a plausible neurophysiological explanation of association readily of- fered itself in terms of increased readiness of nerve cells that had been repeatedly stimulated simultaneously to fire together. This outline of how we perceive objects and their pictures fitted nicely into a general theory of knowledge and of science, spanning from neuro

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256 JULIAN HOCHBERG physiology to sociology and political science. With respect to the last, for example, the view that all our ideas about the world derive from our experiences with it leads readily (but not ineluctably) to the belief that human intelligence and character are generally perfectible through educa- tion, and to the advocacy of egalitarianism and individualism over a wide range of social and political issues. Although formulated by Helmholtz only one academic generation after his teacher, Johannes Mueller (1838), first undertook the scientific analysis of experience, what I am calling the classical theory of perception thus had wide and deep connections with the mainstream of Western thought, and it remained the dominant theory in neurophysiology and psychology until the l950s. It was not without opposition, however. Some opposition was based on a cluster of purely psychological flaws. Although, for example, the theory tells us which different stimuli will act as mutual surrogates that is, which different objects will produce the same perceptual experience it does not tell us what that experience will be like. It does not predict the attributes of the experience itself, i.e., it tells us that light composed of a mixture of 650 nanometers (red) and 540 nanometers (green) is indistinguishable in appearance from light of 580 nanometers (nary) (yellow), but it gives us no basis for predicting how that appearance is similar to and different from other colors. As we will see, alternative theories, almost as old as the Helmholtzian one, offer much more in the way of accounting for appear- ance. Notable among these proposals based on phenomenology (the study of appearances as such) were the following: Hering (1878) argued that perceived colors comprise red-green, yellow-blue, and black-white oppo- nent systems; that connections between cells of the two retinas provide for an innate sense of depth; and that lateral inhibition between adjacent regions of the visual system make their appearances mutually dependent. Mach (1886) proposed (among other things) that such lateral connections provide networks that are sensitive to contours and not merely to incident energy. A related problem is illustrated in Figure 7. In most situations in the real world, the local stimulation that is projected to the eye is not by itself information about object properties. Even if the two gray target disks on the cube are of identical lightness or reflectance (R0, the luminance or photic energy each provides the eye is different ELI, L2) because the illu- mination falling on each is different (E~, E21. Again, even if the two vertical rods on the right are of the same physical size (S), the size of the retinal image each provides all, 02) differs because the rods lie at different distances ODE, D21. Nevertheless, we tend to perceive such object properties correctly, despite changing retinal stimulation. The classical theory held that this object constancy, as it is now known, is achieved when the viewer takes

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VISUAL PERCEPTION OF REAL AND REPRESENTED OBJECTS AND EVENTS 257 Ems ~ E2 Rt = L1/E1 = L2/E2 S= DxTan ~ FIGURE 7 Object constancy. Although both target disks on Me cube have the same reflectance (Rt), the luminances ELI, L2) differ to the eye because the illuminations (E~, E2) differ. Similarly, objects of the same size (S) provide images of different extent aft, 02) depending on Den distances ODE, Do. We tend to see objects' relatively permanent qualities, such as their reflectance and size, as constant even though the proximal stimulation they provide is in flux. In the classical theory we do this by learning to process visual information according to the formulae R(reflectance) = L(lum~nance)/E(illum~nation), and S(size) = D(distance) x tangent of D(visual extent). the conditions of seeing into account: in effect, by using the depth cues to perceive depths Do and D2, and then using the latter to infer the object sizes from the retinal sizes All, 02~; similarly, to use cues to perceive the illu- minations En and E2, and, using the latter, to infer the reflectances of the parts of the scene from their luminances. This explanation is now commonly called "unconscious inference." Its operation assumes that the viewer has learned the constraints in the physical world (e.g., that L= R x E, that S =kDtanD, etch. These constraints, once learned, provide a mental structure that mirrors the physical relationship between the attributes of the object and those of sensory stimulation, per- mitting the viewer to infer or compute the former from the latter. A general form of this explanation is that we perceive just that state of affairs in the world that would, under normal conditions, be most likely to produce the pattern of sensory responses we receive. The learning processes that might underlie such computations have never been formally and explicitly worked out. What we would now call "lookup tables" (for example, with grouped entries for S. 0, and D) would be compatible with theories about associative learning. Helmholtz and others often wrote, however, as though we learn to apply the rules that mirror those of the physical world; they did not say explicitly, however, how such abstract principles, as distinguished from lookup tables listing the elements of sense data, are learned.

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258 JULIAN HOCHBERG The Helmholtzian idea that our perceptions of objects rest on compu- tational or inferential process was, like the classical theory's failure to predict appearances, roundly criticized over the years as being uneconom- ical, mentalistic, and unparsimonious. Gestalt theory, which had a signif- icant impact in psychology and art theory between the two world wars, was particularly vocal in this regard. But the criticisms of the classical theory did not amount to much until the end of World War II. Then the needs of new technology (flight training, radar and sonar displays, etc.), the devel- opment of new instrumentation (notably, direct amplifiers that made the measurement of very small bioelectrical tissue responses common and re- liable), and the effects of grants that made the research career a viable occupation, all combined to turn the tables. As we will see, Helmholtz was right about the three cones and in some sense about the existence of mental structure and computation. But most of the rest of what lay between those points was wrong, and most of the alternative proposals that had been made by the critics of that dominant approach, especially those of Hering and Mach, were quite remarkably vindicated within a period of a very few years, after having been largely ignored for many decades. THE 1950s AND AFTER: "DIRECT" SENSITIVITY TO OBJECT ATTRIBUTES The two main arguments on which the classical theory rested were, first, that it was the simplest answer to the problem of analyzing the world of sensory stimulation, and second, that it was in accord with neurophysio- logical observation. In the l950s both of these supports were withdrawn. Technically, as is widely recognized, the most important single advance in instrumentation was the microelectrode, which made it possible to record the activity of individual nerve cells in the visual system and brain of an essentially intact animal that is exposed to various sensory displays. It quickly became evident that most of the cells observed in this way respond not to individual points of local stimulus energy but to extended spatial and temporal patterns-to adjacent differences in intensity, specific features, and movements in one rather than another direction (Figure 81. They appear to do so by means of networks of lateral connections, which were very much what Hering and Mach had argued. In the 1950s lIurvich and Jameson (1957) offered sensitivity curves for the red-green and yellow-blue opponent process cells that Hering had pro- posed, using procedures based on colors' appearances and not just on their discriminabilities (Figure 9A). They "titrated" the response that each of these hypothetical red-green and blue-yellow opponent pairs makes to wavelengths throughout the spec

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VISU~ PERCEPTION OF REM AD REPRESENTED OBJECTS AD EVENTS 259 'it, - MICROELECTRODE '; 3 C 0 STI MU LUS + 3 + 2 -| ~ _ RESPONSE '/~` ~ STIMULUS +3 +2h +O 4 5 - RESPONSE FIGURE 8 Pattern-sensitive neural network. Microelectrode recordings from individ- ual cells in the visual system (Hartline, 1949; Hubel and Wiesel, 1962) reveal far more complex organization than the simple individual punctate analysis of Figures 5 and 6. For example, receptors in the retina 1 send both excitatory ~ +) and inhibitory (- ~ connections to more proximal cells 2; those connections are arranged in networks so that cells at level 2 are stimulated by light falling in a center region and inhibited by light falling in its surround. Other cells 3 still deeper in the system are so connected as to be more highly stimulated by a bar or edge falling on the line of 2 than by bars of other orientation 4. Cells farther in the nervous system are sensitive to a bar of specific orientation moving in a specific direction 5. trum by determining how much of each pure hue was needed to cancel all traces of its opponent. That is, how much pure red was needed to cancel the greenishness at each point between approximately 480 and 580 nm, thus indicating the strength of the response labeled G; how much pure green would cancel the reddishness of wavelengths above and below this region, thus indicating the strength of the response labeled R; etc. Wavelengths that appear as blue, green, yellow, orange, and red are shown at 1-5, respectively, and what they look like can be read off the graph. In explanation of these functions, Hurvich and Jameson (1974) proposed the following networks (see Figure 9B): Given three cones with the sen- sitivity functions they are now known to have (only approximately those of Figure 4H) and the network of excitatory connections (solid lines) and inhibitory connections (dotted lines) that is shown, each of the rightmost cells would serve as one or another of the yoked opponents by firing above or below their baseline activity. Informed by the opponent-process theory, microelectrode research iden- tified cells in the visual system of the goldfish (Svaetichin, 1956) and in the rhesus macaque (DeValois and Jacobs, 1968) that responded to wave- length in just these ways. Moreover, cells have been found that respond to lines and edges, at particular orientations, moving and stationary (Hubel and Wiesel, 1962),

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288 JULIAN HOCHBERG find ample evolutionary demands, imply that something that corresponds to motion through space occurs in the mind's eye of the viewer. The filmmaker or graphics programmer who cuts away from one event to an- other, and then returns to the first one, must make some assumptions about how well the viewer keeps track of any motion that is going on in the first event. The following research shows that discussing such mental motion is more than just a poetic metaphor. Shepard and his colleagues had shown in a wide range of experiments that the time subjects need to judge whether two objects are the same or different (Figure 21A) is proportional to the angle between them, as though one object were being mentally rotated at some constant rate to bring it to the same orientation as the other in making the comparison (Shepard and Cooper, 1982; Shepard and Metzler, 1971~. Using that paradigm, Cooper (1976) first determined each subject's characteristic "mental rotation" rate, co, and then, after having had subjects memorize the figures, displayed the comparison figure at some variable angle (~) and delayed after a starting signal by a variable interval (t). She found that if the product of It) x (t) = Gil, judgment times no longer increased with angle Ail: they were now inde- pendent of the angle between the two objects being compared (Figure 21B). The results are what one would expect if the object had in fact been rotated at angular velocity co x (t) between presentations i and ii, and if both objects had come to the same orientation by the time the comparison was called for. Given these findings, "mental rotation" seems more than a metaphor that summarizes the fact that judgment time is a function of angle (~) in Figure 21A. It implies a usable and consistent relationship between time and distance in a mental structure that cannot be attributed to physical stimulus information. A third and quite different paradigm, which appears in a recent technical report by Cooper (1984) on work in progress, may tell us something more general about the form in which perceived objects are manipulated and stored and may also eventually provide a tool with which to compare how well different methods of representation accord with the ways in which objects are perceived and remembered. Subjects had been given two or- thographic projections of an object (a and b in Figure 22) and were to judge whether a third orthographic projection (c) was of the same or of a different object. No isometric projections (e.g., c) of any objects were shown to the subjects at this time. Subsequently the subjects were shown a set of isometric projections (e.g., c, f), some of which represented the objects used in the previous tasks and some of which did not. Subjects tended to report that they had seen the former before, even though no isometric pictures at all had been shown. Although this research is still in progress, and various

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VISUAL PERCEPTION OF REAL AND REPRESENTED OBJECTS AND EVENTS 289 . i '1 is; I. _ .. ~ 11 1 B . E11- 1 ...1, 111 ~ ... . Ill,lV,, ~ . . . 1,11 i' i' a' ANG LE A . ~1 - ~' it, ,,' 1' A' t=0 cot= 0 FIGURE 21 Mental rotation. A: Given two objects at different orientations, the time that it takes to judge whether they are the same or different is a function of the angle between their orientations, whether in the picture plane i, ii or in depth iii, iv. It is as though the subject must rotate one object into the orientation of the other before the two can be compared (Shepard and Metzler, 1971~. B: If the two shapes to be compared i, ii are presented simultaneously (i.e., separated in time by an interval t = 0.0) their reaction time R.T. increases with angle, , between their orientations, as above. But if the comparison figure is presented after an interval t = /m, where ~ is the subject's characteristic rotation rate (obtained from the slope of the function at t = 0.0), then the R.T. does not increase with increasing angle ~ (Cooper, 1976~. This is just what one would mean by saying that the subjects had rotated the object before making the comparison.

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290 JULIAN HOCHBERG a EE] b d ~ f ~ ; \ \ \ _ ,-~ , a Cal ~3 e FIGURE 22 The structure of perceived objects orthographic and isometric projec- tions. Two different pictorial systems are shown here: Pictures a and b and pictures d and e are orthographic projections of objects whose respective isometric projections are c and I. Isometric projections are easier to grasp, at least for these objects. Cooper (1984) presents preliminary evidence that even when subjects have been presented only with orthographic projections of objects, they tend to report later that they have seen isometric projections of those objects. controls are needed, the preliminary results will, I feel certain, survive the necessary replication and controls: Orthographic and isometric projections can both specify the form of a three-dimensional object, but the isometric projections are in some sense closer to the way in which we extract and store the information-closer to the mental structure involved in perceiving and comparing the objects. Although I know of no research to the point, it hardly needs an experiment to discover that isometric pictures are more rapidly and accurately comprehended than orthographic ones. What ex- periments can do is give us a better understanding of why that is so, and of the sense in which the isometric picture is more like the structure that underlies our perception of the object. These three research procedures that I have described in connection with Figures 20 through 22 are interesting more as examples of a field of ex

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VISUAL PERCEPTION OF REAL AND REPRESENTED OBJECTS AND EVENTS 291 penmental and quantitative inquiry than as demonstrations that mental pro- cesses can be studied and are in that sense real; the latter is not a new conception. It has repeatedly come into and gone out of scientific fashion, and merely showing that mental structure "exists," in some sense, will not add much to its history. Fortunately, this time there are vested interests in obtaining and systematizing the knowledge, and technical facilities for doing so, that should keep research and theory centered on these problems of object perception and representation for some time to come. REFERENCES Ames, A. 1951 Visual perception and the rotating trapezoidal window. Psychological Monographs, No. 324. Attneave, F. 1954 Some informational aspects of visual perception. Psychological Review 61:183-193. 1959 Applications of Information Theory to Psychology. New York: Holt, Rinehart and Winston. Barlow, H., Blakemore, C., and Pettigrew, J. 1967 The neural mechanism of binocular depth discrimination. Journal of Physiology 193:327- 342. Bekesy, G., van 1960 Neural inhibitory units of eye and skin. Quantitative description of contrast phenomena. Journal of the Optical Society of America 50:1060-1070. Berry, R.N. 1948 Quantitative relations among vernier, real depth, and stereoscopic acuities. Journal of Experimental Psychology 38:708-721. Blakemore, C., and Campbell, F.W. 1969 On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images. Journal of Physiology 203:237-260. Braddick, O.J. 1980 Low-level and high-level processes in apparent motion. In H.C. Longuet-Higgins and N.S. Sutherland, eds., The Psychology of Vision. London: The Royal Society. Braddick, O.J., Campbell, F.W., and Atkinson, J. 1978 Channels in vision: basic aspects. In R. Held, H.W. Leibowitz, and H.L. Teuber, eds., Handbook of Sensory Physiology, Vol. 8. Heidelberg: Springer. Braunstein, M.L. 1976 1983 Depth Perception Through Motion. New York: Academic Press. Contrasts between human and machine vision: should technology recapitulate phy- logeny? In J. Beck, B. Hope, and A. Rosenfeld, eds., Human and Machine Vision. New York: Academic Press. BNnswik, E. 1956 Perception arid the Representative Design of Psychological Experiments, 2nd ed. Berkeley: University of California Press. Buffart, H., Leeuwenberg, E.L.J., and Restle, F. 1981 Coding theory of visual pattern completion. Journal of Experimental Psychology: Human Perception and Performance 7:241-274.

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Ago ~e, BE ~ ~s=, G. 19e Icky of ~=s~g ~ get of emend go tic apt as pl~s. WHIZ ~Z f~- e loll. Watt, A. 1911 On ~ ~c1 ~ son avert. Bh~k FIZZ ~^- ~S~- P~, 1. act, R.S. 1938 -~_Z ant. New Yak: Hok, ~ ~ West. @