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pcrccpl (fast Speed)

pcrccpl (fast Speed)

In the framework we had been pursuing to explain other visual qualities, the flash-lag and related effects would be signatures of this same empirical strategy applied to the perception of object speed. To test this supposition, Wojtach and Sung asked whether the amount of lag subjects see over a range of speeds is accurately predicted by the relative frequency of occurrence of image sequences arising from 3-D object motion transformed by projection onto the retina (see Figure 12.1). The first step was to determine the relevant psychophysical function by having observers align a flash with the moving bar, varying the speed of the moving object over the full range that elicits a measurable flash-lag effect ( Figure 12.3C). To test whether this function accords with an empirical explanation of perceived speed, Sung repeatedly sampled the image sequences generated by objects moving in the simulated environment, tallying the frequency of occurrence of the different projected speeds generated by millions of possible sources moving in the simulated 3-D world (see Figure 12.2). In an empirical framework, the speeds that observers see should be given by the relative frequencies of occurrence of projected speeds on the retina, which in turn would have determined how observers see object motion. If the flash-lag effect is indeed a signature of visual motion processing on an empirical basis, the lag that observers report for different stimulus speeds should be accurately predicted by the relative ranks of different image speeds in perceptual space arising from this experience. As shown in Figure 12.4, the psychometric function in Figure 12.3C is closely matched by accumulated experience with the speeds on the retina that moving objects generate.

Figure 12.4 Empirical prediction of the flash-lag effect. The graph shows the perceived lag that observers report (see Figure 12.3C) plotted against the empirical rank (relative frequency of occurrence) of the projected image speeds that moving objects generate. The black diamonds are the empirically predicted lags; the dashed line indicates perfect correlation between the predicted lags and the amount of lag subjects report. (From Wojtach, et al., 2008. Copyright 2008 National Academy of Sciences, U.S.A.)

Empirical rank

This explanation of perceived speed is similar to the accounts given for lightness, brightness, color, and geometry. As in the subjective organization of

Empirical rank

This explanation of perceived speed is similar to the accounts given for lightness, brightness, color, and geometry. As in the subjective organization of these other perceptual qualities, contending with the inverse problem requires that the speeds we see be organized in perceptual space according to the frequency of occurrence of projected speeds on the retina (because this information permits successful behavior). Since the flash is not moving, it will always have a lower empirical rank than a moving stimulus (such as the moving bar in Figure 12.3) and therefore should appear to lag behind the position of the speed of any moving object projected on the retina. And because increases in image speed correspond to a higher relative rank in the perceptual space of speed (more sources will have generated image sequences that traverse the retina more slowly than the retinal speed of the stimulus in question), the magnitude of the flash-lag effect should increase as a function of image speed.

Despite this successful prediction, there are serious concerns with this approach to understanding the speeds we see. Foremost is the adequacy of a simulated environment in determining the frequency of occurrence of different image sequences, a necessary approach because of the inability of present technology to glean this information in nature. A variety of real-world factors—gravity, the bias toward horizontal movements arising from the surface of Earth, and many others—were not included in the simulation. However, these influences are less important in the determination of image speeds than might be imagined. The overwhelming influence of perspective, which the simulation captures quite well, renders the approach relatively immune from the effects of these omissions. Because object speeds projected on a plane produce image speeds that are always less than or equal to the speeds of objects in 3-D space (see Figure 12.1), the corresponding speeds on the retina are strongly biased by perspective toward slower values. This bias is readily apparent in statistical analyses of image speeds in movies, or simply from a priori calculations. As a result, perspective is the major determinant of the frequencies of occurrence of image speeds that humans experience. Another obvious concern is how seeing motion in this counterintuitive way could possibly explain complex visually guided actions, such as hitting a fastball or returning a tennis serve. Imagining that success in the face of such challenges arises empirically from past experience seems a stretch.

Putting these concerns aside for the moment, what about the other aspect of perceived motion—the directions of motion that we see? Can this further characteristic of motion be explained empirically? In exploring this question, another class of motion anomalies was especially useful, namely the changes in apparent direction that occur when moving objects are seen through an occluding frame (called an "aperture" in the jargon of the field). For example, when a rod oriented at 45° moving physically from left to right at a constant speed is viewed through a circular opening that obscures its ends, its perceived direction of movement changes from horizontal to downward at about 45° from the horizontal axis ( Figure 12.5). This change in direction occurs instantaneously when the frame is applied. Stranger still, the direction seen depends on the shape of the frame. For example, if the same oriented rod moving from left to right is seen through a vertically elongated rectangular frame (a vertical "slit"), the perceived direction of motion is nearly straight down. Psychologist Hans Wallach first studied these dramatic changes in perceived direction when he was a graduate student in Berlin some 70 years ago using rods moved by hand behind cardboard frames. These robust aperture effects demand some sort of explanation, and, as with the flash-leg effect, had been the subject of many studies and debates.

Figure 12.5 The effects of an occluding frame on the perceived direction of motion. The linear object in the aperture (the black line) is moving horizontally from left to right, as indicated by the yellow arrow. When viewed through the aperture, however, the rod or line is seen moving downward to the right (red arrow). (From Purves and Lotto, 2003)

Possi&se directum of rpo!i-5fi fer prsrt ;:f I nej in frame moving downwards

Actual direction of rnoîion

Possi&se directum of rpo!i-5fi fer prsrt ;:f I nej in frame moving downwards

Actual direction of rnoîion

Horizontally moving line

Circular aperture

Perched direction of motion (discrepancy of - 45)

Horizontally moving line

A good place to begin thinking about the effects of apertures in empirical terms is the frequency of occurrence of the projected directions of unoccluded lines that objects moving in 3-D space generate ( Figure 12.6A and 12.6B). Figure 12.6C shows the frequency of occurrence of fully visible lines moving in different directions on the image plane generated by moving objects. As expected, the movement of a projected line with a given length and orientation on the image plane occurs about equally in all possible directions. This uniform distribution of image directions in the absence of occlusion describes, to a first approximation, how humans have always experienced the retinal sequences that moving rods or lines generate when they are in full view.

Figure 12.6 The frequency of occurrence of lines moving in different directions projected onto an image plane (a proxy for the retina) in the absence of an occluding frame. A) Diagram of a simulated environment showing rods with different orientations in space moving in different directions, but all projecting in the same orientation. B) Enlargement of the image plane in (A); notice that the projected lines move in directions that are different from the movements of the objects in space. C) The jagged black circle indicates the distribution of the directions of movement of lines or rods such as those in (B) determined by sampling all the sequences generated by objects in the virtual environment projecting at an angle (45° in this example) on the image plane. The directions of movement are indicated around the perimeter of the graph; the distance from the center to any point on the jagged black line indicates the frequency of occurrence of image sequences moving in that direction. (After Sung, et al., 2009. Copyright 2009 National Academy of Sciences, U.S.A.)

Image plane

When a line moves behind an aperture, however, this uniform distribution of image directions changes. The different experience of projected directions that humans will always have experienced as a result of an occluding frame offers a way of examining whether the perceived directions elicited by different aperture shapes can be accounted for in wholly empirical terms. If the perceptual space for direction of motion is determined by past experience, then effects of any particular aperture should be predicted by the frequency of occurrence of the various directions generated by object motion projected through that frame.

The simplest effect to test in this way is the altered direction of motion induced by a circular aperture (Figures 12.5 and 12.7A). The frequency of occurrence of projected directions that humans will always have experienced in this circumstance can be approximated by systematically applying a circular template to the image plane of the virtual environment illustrated in Figure 12.6A and tallying the frequency of occurrence of the 2-D directions of the lines that generate image sequences within the aperture. Considering the perception of a line moving in some direction from left to right, only half the projected directions are possible (projected lines moving from right to left will never contribute to the pertinent distribution, whether looking through an aperture or not; see Figure 12.5). More important, the frequency of occurrence of lines that can move across a circular aperture with both ends occluded is strongly biased in favor of the direction orthogonal to the line ( Figure 12.7B; the geometrical reasons for this are explained in Figure 12.9). Therefore the mode of this distribution (red arrows in Figure 12.7B) is the direction humans will have experienced most often whenever moving rods or lines are seen through a circular aperture. In an empirical framework, this experience should predict the direction that observers report. The green arrows in Figure 12.7B are the directions that subjects saw in psychophysical testing. As is apparent, the predicted directions (the red arrows) closely match the directions actually seen.

Figure 12.7 Comparison of psychophysical results and empirical predictions of the perceived directions of moving lines in different orientations seen through a circular aperture. A) As in Figure 12.6, the orientation (0) of the line in the aperture is measured from the horizontal axis; the direction of movement is shown as a positive or negative deviation from the direction perpendicular to the moving line (0°). B) The ovoids described by the jagged black lines are the distributions of the projected directions constrained by a circular aperture for the orientations indicated. The green arrows show the perceived directions reported in psychophysical testing, and the red arrows show the directions predicted empirically. (After Sung, et al., 2009. Copyright 2009 National Academy of Sciences, U.S.A.)

Because the perceived direction of motion of a line traversing a circular aperture can be accounted for in several other ways, the close correspondence of the observed and predicted results in Figure 12.7 is not as impressive as it seems. More convincing would be how well this (or any other) approach explains the effects on perceived direction produced by other apertures. A case in point is oriented lines or rods traveling in a horizontal direction across a vertical slit; as mentioned earlier, the stimulus in Figure 12.8A generates an approximately vertical perception of movement. A more subtle effect is also apparent: As the orientation of the line becomes steeper, the perceived downward direction increasingly deviates from straight down ( Figure 12.8B). To test the merits of an empirical explanation in this case, Sung and Wojtach determined the frequency of occurrence of projected directions as a function of orientation using a vertical slit template applied millions of times to different locations across the image plane of the virtual environment. An empirical analysis again predicted the effects apparent in psychophysical testing (compare the directions of the red and green arrows in Figure 12.8). Similar success in other frames that generate peculiar effects on perceived direction (such as a triangular aperture) further buttressed the case that the directions of object motion seen are generated empirically.

The account so far begs the question of why the frequencies of occurrence of image sequences observed through differently shaped frames change in the ways they do. To understand the reasons for the empirically determined distributions in Figures 12.7 and 12.8, consider the biased directions of image sequences projected through a circular aperture. Figure 12.9A illustrates that for a line in any particular orientation on an image plane, there is a direction of motion (black arrow) that entails the minimum projected line length (the red line) that can fully occupy the aperture. A projected line traveling in any other direction (such as the blue line) must be longer if it is to fill the aperture; one end of any shorter line moving in that direction will fall inside the aperture boundary at some point, producing a different stimulus and a different perceived direction of motion. Because a line of any length includes all shorter lines, far more lines that satisfy the aperture are projected moving orthogonally to their orientation than lines moving in other directions. As a result, the distribution of directions that satisfies a circular aperture is strongly biased in the direction orthogonal to the orientation of any line, as indicated by the distributions (the jagged ovoids) in Figure 12.7B. These facts about projective geometry explain the major bias that a circular apertureproduces and therefore the way humans have always experienced image sequences of linear objects moving behind a frame of this sort.

Figure 12.8 Comparison of the psychophysical results and empirical predictions of the perceived directions of moving lines in different orientations seen through a vertical slit. A) The aperture. B) Distributions of the frequency of occurrence of the projected directions of moving lines in different orientations (jagged black ovals) when constrained by a vertical aperture. As in Figure 12.7, the green arrows are the results of psychophysical testing and the red arrows are the empirical predictions (the gray arrows indicate vertical). (After Sung, et al., 2009. Copyright 2009 National Academy of Sciences, U.S.A.)

Figure 12.8 Comparison of the psychophysical results and empirical predictions of the perceived directions of moving lines in different orientations seen through a vertical slit. A) The aperture. B) Distributions of the frequency of occurrence of the projected directions of moving lines in different orientations (jagged black ovals) when constrained by a vertical aperture. As in Figure 12.7, the green arrows are the results of psychophysical testing and the red arrows are the empirical predictions (the gray arrows indicate vertical). (After Sung, et al., 2009. Copyright 2009 National Academy of Sciences, U.S.A.)

Figure 12.9 Explanation of the biased generated by that the projection of lines onto an image plane such as the retina. Because a line of any given length includes all shorter lines, the occurrence of projections that fill a circular aperture generated by the red line moving in the direction indicated by the black arrow on the left will be always be more frequent than the projections generated by the blue line moving in any other direction, indicated by the black arrow on the right. As a result, the most frequently occurring projected direction when linear objects are seen through a circular aperture will always be the direction orthogonal to the orientation of the projected line (gray arrows), but not for other apertures (see Figure 12.8). (After Sung, et al., 2009. Copyright 2009 National Academy of Sciences, U.S.A.)

The upshot is that any aperture will produce a bias in the frequency of directions experienced that depends on the shape of the frame. But understanding the details for various apertures can be tricky. For example, perspective also requires that images of objects have dimensions that are equal to or smaller than the dimensions of physical objects that produce them. As a result, the oval-shaped distributions of the 2-D directions of lines translating in the apertures shown in Figures 12.7 and 12.8 are narrower toward the center of the graph than would be expected from the effect illustrated in Figure 12.9A

alone. For a circular aperture, this additional influence does not affect the mode of the distribution, which remains orthogonal to the moving line no matter how the line is oriented on the image plane. However, for a vertical slit aperture, this addtional bias causes the frequency of occurrence of the projected directions to change as a function of the orientation of the line in the image sequence (see Figure 12.8B). The reason is that although the minimum projected line length and distance traveled needed to satisfy a circular aperture are identical, they are not the same for a vertical slit aperture. As a result, the generation of more short lines and travel distances arising from perspective for a vertical slit varies as the orientation of the line in the slit changes, explaining the empirical biases apparent when moving lines in different orientations are projected through a vertical slit.

Taken together, these empirical explanations of flash-lag and aperture effects argue that human experience with retinal projections of moving objects determines the speeds and directions we actually see. This idea is hard to swallow, and quite different from other explanations proposed for these effects and for motion perception in general. With respect to the apparent speed of moving objects, two types of theories have been offered to explain the discrepancies between physical and perceptual speeds that are apparent in the flash-lag effect and related phenomena: A misperception of objects in time versus a misperception of objects in space. The misperception in time theory proposes that the visual system compensates for neuronal processing delays by adjustments in the apparent time at which an object is seen with respect to an instantaneous marker (the flash) by anticipating or predicting the processing delays (remember that action potentials are conducted relatively slowly along axons). In contrast, the spatial theory suggests that vision employs ongoing motion information to "postdict" the position of moving objects, thereby "pushing" the apparent position of an object to a point in its trajectory that will more closely accord with its physical location when a behavioral response occurs. However, both these proposals assume that the perceived discrepancies derive from an analysis of the features of image sequences on the retina. This interpretation ignores the fact that no direct analysis of 2-D speed can specify the 3-D speed that produced it (see Figure 12.1). As a result, seeing speeds in the way these theories propose could not successfully guide behavior directed toward objects moving in the real world.

Attempts to rationalize the perceived directions of moving objects projected through apertures have taken a different approach. The most popular explanation supposes that the visual system calculates the local velocity vector field in an image sequence. The gist of this idea is that the ambiguous direction of a moving line seen through an aperture is resolved by computations based on prior knowledge about how the speeds and directions of the line in the aperture are related to the 3-D world. This approach is partly empirical, but it fails to recognize or explain the directions observers actually see in a variety of different apertures (such as the subtle effects of vertical apertures; see Figure 12.8). This theory also lacks a biological rationale.

Finally, consider again how seeing speeds and directions on a wholly empirical basis could enable us to succeed in a demanding motor task such as hitting a ball. At first blush, it seems impossible that complex motor behaviors are made possible by trial-and-error experience instantiated in the inherited brain circuitry of the species and refined by the trial-and-error experience of individuals. This prejudice is no doubt one reason why people have regarded phenomena such as flash-lag and aperture effects as perceptual anomalies ("illusions") and not signatures of the historical way the visual system generates all motion percepts. But if one takes to heart the facts illustrated here, there is no clear alternative to this way of linking perceptions with successful actions. Although empirically determined speeds and directions can provide only an approximate guide to behavior, they will always tie necessarily uncertain image sequences to motor responses that have a good chance of succeeding. When the equally empirical but differently determined influences of other visual qualities (and the qualities associated with other sensory modalities) are taken into account, the motor responses we make have a reasonable chance of hitting a pitch or returning a serve, and an excellent chance of successfully handling more ordinary challenges. Indeed, perception of motion on an empirical basis works so well in guiding behavior it is hard to believe that the motions we see are not the motions of objects in the world.

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