An empirical test of formal equivalence between Emmert's law and the size-distance invariance hypothesis

Emmert's law and the size-distance invariance hypothesis have been said to be formally equivalent, provided that Emmert's law means that the perceived size of an afterimage is proportional to the perceived distance of the projected surface of the afterimage. However, there have been very few studies that have attempted to verify this formal equivalence empirically. We measured both the perceived size and distance of afterimages and real objects with the same proximal size. Nineteen participants projected afterimages of 1 deg in visual angle on the wall located at distances of 1 to 23 meters from the participants. They also observed real objects, disc-shaped and made from a sheet of Styrofoam board, with the same proximal size as that of the afterimages, which were located at the same physical distances as those of the wall on which the afterimages were projected. Each participant reproduced the apparent sizes of the afterimages and real objects using the reproduction method and estimated the apparent distances using the magnitude estimation method. When the mean apparent sizes of the afterimages and real objects, represented as a function of apparent distance, were fitted to a linear function, the slopes for the afterimages and real objects did not differ significantly. These results are interpreted as evidence for the formal equivalence of Emmert's law and the size-distance invariance hypothesis.     

Binocular rivalry between single lines viewed as real images and afterimages

Binocular rivalry alternations between single lines oriented at 0 and 90 deg or 0 and 45 deg were measured. The lines were viewed as either real images or afterimages. The experiment was designed to determine whether or not a vertical (0 deg) line predominates for longer than a nonvertical line and to compare the temporal characteristics of rivalry between real images and afterimages. There were no systematic differences in predominance durations under any of the rivalry pairings or viewing conditions. The dominance periods for rivalry between afterimages were longer than those for real images. Frequency distributions of the dominance periods were all positively skewed, and the parameters of the fitted gamma distributions were similar in all cases. Tests of the sequential dependence of successive dominance periods indicated that they were independent for both real images and afterimages.     

Metameric intransitivity

There are two kinds of afterimages. In negative afterimages, looking at a blank field after staring at a colored figure gives a figure whose color is complementary to that of the original figure. Less well understood and studied is the phenomenon of induced positive afterimages, in which staring at a colored area surrounding a small white test patch produces an afterimage in which the hue of the surround is transferred into the previously white area. Using these differences between positive and negative afterimages and also simultaneous color contrast, which has an effect on a test patch different from either of the afterimage effects, we describe a new effect, metameric intransitivity, in which perceptually similar images can generate markedly different afterimages, whereas perceptually different images can generate indistinguishable afterimages. Supplemental figures depicting the stimuli, results, and method for generating the intransitive metamers in this study may be downloaded from http://app.psychonomic-journals.org/content/supplemental.     

Orientation and spatial frequency effects on linear afterimages: The retinal reference for selectivity — A supplementary report

Afterimages of gratings oriented vertically or at 45 deg relative to gravity were generated with the head upright or tilted so that the retinal meridian was inclined 45 deg. The duration of visibility of the whole afterimage was longer for the vertical grating when the head was upright and for the 45-deg grating when the head was tilted. It was concluded that this orientation selectivity of afterimages is dependent upon the orientation of the grating with respect to the retinal meridian rather than to the direction of gravity.     

Perceptual filling-in of negative coloured afterimages

Filling-in of brightness, colour, and texture refers to the perceptual spreading of surround features onto the target area. This phenomenon has been extensively investigated in real images. Here, we study colour spreading in afterimages of disk-ring patterns, using a variety of colour combinations. We show that colour filling-in and filling-out in afterimages follow rules different from those found for real images, suggesting that the brain treats afterimages as genuine 'stimuli'.     

Motion-induced blindness does not affect the formation of negative afterimages

Aftereffects induced by invisible stimuli constitute a powerful tool to investigate what type of neural information processing can occur in the absence of visual awareness. This approach has been successfully used to demonstrate that awareness of oriented gratings or translating stimuli is not necessary to obtain a robust orientation-specific or motion-specific aftereffect. We exploit motion-induced blindness (MIB, Bonneh, Cooperman, & Sagi, 2001) to investigate the related question of the influence of visual awareness on the formation of negative afterimages. Our results show that MIB does not affect the persistence and intensity of afterimages. Thus, there is no significant contribution to the formation of afterimages beyond the sites mediating MIB.     

Projected afterimages after manipulation of cognitive schemes in children.

Telling one group of subjects that afterimages are a physical reality largely independent of the observer and another group that afterimages are projected by the subject himself, it was predicted that the afterimages in these groups would differ. In all 10 pairs of nine-year-old children, matched with respect to cognitive maturity, the subject getting the former instruction reported more size-constant and/or positive afterimages than the subject getting the latter instruction.     

Orientation and spatial frequency effects on linear afterimages

Single lines and gratings oriented vertically or at 45 deg were observed as prolonged afterimages in two experiments. The duration of complete visibility exhibited consistent orientation selectivity for the gratings but not for single lines: vertical gratings were visible for longer than were 45-deg gratings. The results are discussed in relation to the hypothesized spatial frequency channels in the human visual system.     

Orientation effects on line afterimages

Lines of various orientations were viewed as prolonged afterimages in six experiments. The duration of unitary appearance was not influenced by line orientation for monocular afterimages, but there was a marginal effect for afterimages generated binocularly; vertical and horizontal lines tended to be visible for longer than did 45-deg lines. Measures of fragmentation frequency and the latency to the first disappearance did not vary reliably with orientation under any conditions. Binocular afterimages lasted longer than did monocular ones, but generally showed the same pattern of fragmentations. These results are compared with those from experiments using optical stabilization and steady fixation, in which orientation differences have been reported.     

Afterimages, binocular rivalry, and the temporal properties of dominance and suppression

When different contours are presented to the two eyes, an unstable percept, binocular rivalry, is the result. Parts of each set of contours may be seen but the two sets are not seen in the same place at the same time. The contours need not be physically present. Afterimages will produce binocular rivalry. Normal rivalry can be prevented if intermittent stimulation is used. Previous work has shown that orthogonal gratings, flashed for less than 150 ms and separated by more than 150 ms, will appear to fuse into a plaid or checkerboard pattern. In the present experiment this phenomenon is examined with afterimages used to produce rivalry. This abnormal 'fusion' is seen when negative afterimages are stroboscopically illuminated at less than 5 Hz. The results obtained with afterimages are predictable from the previous results obtained with stimuli external to the eye.     

The glare effect does not give rise to a longer-lasting afterimage

The glare effect is an illusion in which a region appears self-luminous when flanked by gradients that decrease in luminance with distance from the region (Zavagno, 1999 Perception 28 835-838). This region also appears brighter than a surface of the same luminance. We investigated, using the paradigm of afterimages, whether a low-level mechanism at the level of the retina or LGN could account for this apparent brighter sensation. We first replicated the result from the literature that brighter and longer-lasting physical stimuli generate longer-lasting afterimages. We then compared the glare-effect stimuli with their counterpart controls, and found that the glare-effect stimuli did not give rise to longer-lasting afterimages. This suggests that the apparent brighter sensation of the glare effect is not due to a retinal or LGN mechanism, but must have a cortical origin.     

Majority and minority influence using the afterimage paradigm: A replication with an unambiguous blue slide

This study re-examines the afterimage paradigm which claims to show that a minority produces a conversion in a task involving afterimage judgements (more private influence than public influence) as opposed to mere compliance produced by a majority. Subsequent failures to replicate this finding have suggested that the changes in the afterimages could be attributed to increased attention due to an ambiguous stimulus coupled with subject suspiciousness. This study attempted to replicate the original experiment but with an unambiguous stimulus in order to remove potential biases. The results showed shifts in afterimages consistent with the increased attention hypothesis for a minority and majority and these were unaffected by the level of suspiciousness reported by the subjects. Additional data shows that no shifts were found in a no-influence control condition showing that shifts were related to exposure to a deviant source and not to response repetition.     

The apparent shape of afterimages in the Ames room.

When observers project afterimages of circular patterns onto a surface slanting away from them the images are reported as being oval in shape. In this paper it is reported that this does not occur when similar afterimages are projected onto the slanting rear wall of an Ames room. Instead of appearing as ovals, the afterimages remain circular. It appears as though the actually-slanted rear wall of the room not only looks as if it is normal to the line of vision, but also that it functions as if it was in such an orientation as far as a projection surface for afterimages is concerned. While these results are consistent with Emmert's law and with traditional accounts of shape and size constancy, they raise once again the age-old issue of whether the 'image on the retina' constitutes an object of perception that can be described in terms of its shape or size.     

The effect of moving and static trans-scleral illumination of visual afterimages

The inside of the eye was illuminated by shining a small light through the upper eyelid and the sclera. After viewing a bright light flash, Ss closed their eyes and reported the duration of the afterimage under the following conditions: the light on and moving across the S’s eyelid (moving trans-scleral illumination), the light on but stationary (static trans-scleral illumination), and two corresponding control conditions in which the light was turned off (darkness). Results indicate that when the trans-scleral light is moving, afterimages are seen clearly for periods of approximately the same duration as those seen in complete darkness. However, when the trans-scleral illumination is stationary, the duration of the afterimages is significantly reduced. These results are compatible with other afterimage data that suggest that changes within the field after initial stimulation are needed to prolong afterimages.     

Afterimages: a tool for defining the neural correlate of visual consciousness

Our visual system not only mediates information about the visual environment but is capable of generating pictures of nonexistent worlds: afterimages, illusions, phosphenes, etc. We are "aware" of these pictures just as we are aware of the images of natural, physical objects. This raises the question: is the neural correlate of consciousness (NCC) of such images the same as that of images of physical objects? Images of natural objects have some properties in common with afterimages (e.g., stability of verticality) but there are also obvious differences (e.g., images maintain size constancy, whereas afterimages follow Emmert's Law: when seen while screens at different distances are observed, an afterimage looks larger, the greater the distance of the screen). The differences can be explained by differences in the retinal extent of images and afterimages, which favors the view that both have the same NCC. It seems reasonable to assume that before neural activity can produce awareness, all the computations necessary for a veridical representation of, e.g., an object, must be completed within the neural substrate and that information characteristic of a particular object must be available within the NCC. Given these assumptions, it can be shown that no retinotopic (in a strict sense) cortical areas can serve as the NCC, although some type of topographic representation is necessary. It seems also to be unlikely that neurons classified as cardinal cells alone can serve as NCC.     

The effect of orientation in binocular contour rivalry of real images and afterimages

Binocular rivalry was investigated using gratings of different orientations in three experiments. No consistent effects of orientation were found for predominance measures of rivalry between real images. Rivalrous afterimages, on the other hand, did exhibit orientation selectivity: vertical gratings were visible for longer than were 45-deg gratings. This effect was compared to the similar orientation selectivity found for monocular observation of grating afterimages. Comparisons of binocular rivalry between real images and afterimages were made in terms of the frequency distributions of the dominance periods.     

Emmert's law in the dark: active and passive proprioceptive effects on positive visual afterimages

The relationship between apparent size and apparent distance is given by Emmert's law, which states that a retinal image is proportional in size to the distance of the surface it is projected upon. This principle also applies to retinal afterimages in that they, too, will change in apparent size if distance cues suggest that the location of the object onto the retinal image has been altered. It has also been known for some time that non-retinal cues can produce quantitative and qualitative effects on an afterimage when it is viewed in the dark. In the present two studies, positive afterimages of an observer's hand, as well as objects held by that hand, were used as targets to investigate the effects on size-constancy scaling of moving the hand to and fro along the line of sight for different distances in the dark. Results show that, when observers focus on a held object, the changes in size predicted by Emmert's law occur in response to both active and passive proprioceptive or haptic cues. The most intriguing result consisted of the finding that, when only the hand is the target, there appears to be a limit to the decrease in apparent hand size. It appears that the visual system 'refuses' to size-scale the hand below a limit it accepts as representative or acceptable of 'its' hand.     

Types of attention matter for awareness: A study with color afterimages

It has been argued that attention and awareness might oppose each other given that attending to an adapting stimulus weakens its afterimage. We argue instead that the type of attention guided by spatial extent and perceptual levels is critical and might result in differences in awareness using afterimages. Participants performed a central task with small, large, local, or global letters and a blue square as an adapting stimulus in three experiments and indicated the onset and offset of the afterimage. We found that increases in the spatial spread of attention resulted in the decrease of afterimage duration. In terms of levels of processing, global processing produced larger afterimage durations with stimuli controlled for spatial extent. The results suggest that focused or distributed attention produce different effects on awareness, possibly through their differential interactions with polarity dependent and independent processes involved in the formation of color afterimages.     

Memory colors in afterimages: A bicentennial demonstration

Six observers adjusted a colorimeter to match afterimages that resembled either a red, white, and blue American flag or a simple striped pattern. They matched the afterimages of stripes in a flag pattern as redder than afterimages of the same stripes in a simple striped pattern. The results suggest that the apparent color of an afterimage depends on memory color.     

Subitizing and counting depend on different attentional mechanisms: Evidence from visual enumeration in afterimages

Two experiments showed that, when selective eye movements were disabled by the presentation of stimuli in the form of afterimages, increased inspection time and facilitative stimulus configurations failed to increase the subitizing limit of 4 objects. Afterimages of two to eight dots induced by a photographic flashgun were shown to 3 adult subjects. For more than 4 objects, enumeration errors occurred at a rate of 20%–30%. Enumeration was effectively perfect for 2–4 linearly configured dots, with occasional errors surprisingly occurring in that range when dots appeared in groups of up to 3 items. No errors occurred in nonafterimage control conditions. Enumeration errors were attributed to failures of individuating dots to be counted due to the deactivation of selective eye movements in afterimages. A third experiment supported this interpretation by disabling eye movements with briefly presented stimuli and producing results much like those of the afterimage conditions.