Area-matching strategies used by young children

Across three studies, conditions were varied under which children aged 4–5 years matched the area of a rectangle with a given width (or height) to that of a square. In the first study, subjects observed the rectangle being changed in height from trial to trial and had access to their immediately preceding response. Under these conditions, rectangle width (the dimension under subject control) was a linear decreasing function of rectangle height. This function was interpreted as evidence for a hypothetical addition/subtraction strategy for maintaining equality in area between the comparison rectangle and the standard square. As a test of this hypothesis, in a second experiment the subjects were denied access to their immediately previous response, and in a third study they were also unable to observe the rectangle as it was altered by the experimenter between trials. The purpose of these changes was to remove the information necessary for readily implementing an addition/subtraction strategy. In both studies, area matches seemed to be based on a side-matching strategy, such that subjects matched one dimension of the rectangle to one side of the standard square. It was suggested that young children use different cues or strategies with different variants of the matching task because they do not possess a fixed, specific concept of area.     

Spatio-temporal interaction and brightness judgments in sequentially presented,partially overlapping rectangles

Ss made magnitude estimates of brightness to three areas within a display consisting of two sequentially presented partially overlapping rectangles of light. The three areas were the singly stimulated region of the rectangle presented first (the trailing flank), the doubly stimulated overlap region, and the singly stimulated region of the rectangle presented second (the leading flank). The stimuli were presented in right-left or left-right order with stimulus onset asynchronies (SOAs) of 0, 25, 50, 75, 100, and 125 msec. A further condition was flank width. The results indicated that the apparent brightness of the overlap region decreased with increasing SOA. The leading flank was judged to increase in apparent brightness, while the trailing flank remained constant.     

Extent,multiplying, and proportionality rules in children's judgments of area

The study examined children's use of multiplying and proportionality rules in judgments of area. In two experiments children judged the area of rectangles. Seven-year-olds used linear extent as an index of area. Eight- and nine-year-olds replaced the extent rule with the height × width rule. In a third experiment 8-through 11-year-olds were presented with a rectangle and a horizontal line representing the width of a second rectangle. Children were asked to indicate the height that would make the second rectangle equal in area to the first. The correct response was proportional to the product of the ratio of the widths of the two rectangles and the height of the first rectangle. Graphical and statistical analyses indicated that children applied the ratio rule to these judgments. The implications for Piaget's theory of cognitive development were discussed.     

The Müller-Lyer contrast illusion: A computational approach

When a temporal delay is interposed between the contextual elements (wings) and the focal element (central axis) of the Müller-Lyer figures, the usual assimilation illusion changes to an illusion of contrast; that is, judged axis length is contrasted away from rather than assimilated toward the context provided by parallel extents between wings. Presentation time for the preceding contextual wings on the order of 1 sec or more was needed to produce contrast effects in judgments of the following focal axis (Experiment 3) and, given sufficient presentation time, these contrast effects were largely unaffected by the length of the temporal delay between contextual and focal elements, appearing equally strong for delays between 0 and 2 sec (Experiments 1 and 2). These results are consistent with a representational basis for these contrast effects that is high-level and long-lived. The Müller-Lyer contrast illusion may reflect the inadvertent error arising from basing judgments about particular objects on information about attribute differences among objects. Such judgmental errors may be the natural consequence of constrained computations that make explicit information required for certain common tasks, but at the expense of obscuring information required for less common tasks.     

Structural aspects of visual similarity

The hypothesis that visual representations for lines and/or points are independent structural units was tested using similarity judgment and speeded discrimination for pairs of six-segment letter-like figures. The stimuli were constructed such that each of two comparison figures had five segments in common with a standard figure. One figure was similar to the standard in its higher order structure (connectedness and closedness properties), whereas the other differed. The results show that the figures with similar higher order structure were systematically judged more similar to the standard than the figures with different structure. The former were also more difficult to discriminate from standards than the latter, as indicated by both time and error measurements. These effects were less pronounced in sequential than in simultaneous comparisons.     

Do bantams (Gallus gallus domesticus) amodally complete partly occluded lines? An analysis of line classification performance

Humans perceive a line touching an edge of a large rectangle longer than the reality. Kanizsa (1979) has suggested that this illusion occurs because we perceive that the line is partly "hidden" behind the rectangle and automatically completes it. We tested whether bantams (Gallus gallus domesticus) would experience this perceptual phenomenon using a line classification task on the touch monitor, which was used in our previous study with rhesus monkeys and pigeons (Fujita, 2001). We trained three bantams to classify six lengths of black target lines into two categories, "short" or "long," ignoring a gray rectangle (Experiment 1) or a gray area (i.e., a left or a right half of the monitor was filled with gray; Experiment 2) located at the same distance (8 pixels) from the target line. In the test, the gap between the line and the gray rectangle (or area) sometimes changed (0, 4, or 8 pixels; we labeled these stimuli as G0, G4, and G8 respectively). Both of the two successfully trained bantams showed an illusion for G0, but the direction of illusion was reversed; that is, they judged the line in G0 to be "shorter" than that in G4 and G8. Further analyses proved that neither the gaps between the target line and the gray rectangle nor the total widths of the stimuli could account for the bantams' responses. These results suggest that bantams do not complete the "occluded" portion even when identification of its shape is not required.     

Time course of amodal completion revealed by a shape discrimination task

We measured the extent of amodal completion as a function of stimulus duration over the range of 15–210 msec, for both moving and stationary stimuli. Completion was assessed using a performancebased measure: a shape discrimination task that is easy if the stimulus is amodally completed and difficult if it is not. Specifically, participants judged whether an upright rectangle was longer horizontally or vertically, when the rectangle was unoccluded, occluded at its corners by four negative-contrast squares, or occluded at its corners by four zero-contrast squares. In the zero-contrast condition, amodal completion did not occur because there were no occlusion cues; in the unoccluded condition, the entire figure was present. Thus, comparing performance in the negative-contrast condition to these two extremes provided a quantitative measure of amodal completion. This measure revealed a rapid but measurable time course for amodal completion. Moving and stationary stimuli took the same amount of time to be completed (≈ 75 msec), but moving stimuli had slightly stronger completion at long durations.     

Subjective assessments of firmness: The use of a rating scale

An experiment was carried out to investigate the extent to which an absolute standard for firmness could be held independently of variations occurring within the samples being judged.

Although the method gave good results as a whole, it was found that, when correlating the ratings to the objective measurements, the absolute standards were not held independently of the average firmness of the groups being judged. In practice, if a certain sample was judged, within a “soft” series of samples, it would be rated as being firmer than when it was judged among “firm” samples. Certain differences in the effects of these changes were related to the nature of the subjects' previous experience.

When the results were considered on a relative comparison basis, it was found that a much lower threshold was achieved than had previously been obtained with judgments for springs using paired comparison methods. There were certain trends in the levels of discrimination with time. These trends are discussed.

The strength of grip of the subjects bore some relation to their initial rating values, but apparently was not related to their level of discrimination. Subjects who were able to exert a more constant pressure throughout the test did not seem to be any better at discriminating than were others.

Ratings made for a single sample two months after the main experiment were very similar to those previously given for the same sample.     

The haptic Müller-Lyer illusion in sighted and blind people

We examined the effect of visual experience on the haptic Müller-Lyer illusion. Subjects made size estimates of raised lines by using a sliding haptic ruler. Independent groups of blind-folded-sighted, late-blind, congenitally blind, and low-vision subjects judged the sizes of wings-in and wings-out stimuli, plain lines, and lines with short vertical ends. An illusion was found, since the wings-in stimuli were judged as shorter than the wings-out patterns and all of the other stimuli. Subjects generally underestimated the lengths of lines. In a second experiment we found a nonsignificant difference between length judgments of raised lines as opposed to smooth wooden dowels. The strength of the haptic illusion depends upon the angles of the wings, with a much stronger illusion for more acute angles. The effect of visual status was nonsignificant, suggesting that spatial distortion in the haptic Müller-Lyer illusion does not depend upon visual imagery or visual experience.     

The effect of context on visual representational momentum

Effects of background context on representational momentum -were examined in six experiments. In each experiment, three orientations of a target rectangle undergoing implied rotation (i.e., the inducing stimuli) were presented, and subjects judged whether the orientation of a fourth rectangle (i.e., the probe) was the same as or different from that of the third inducing stimulus. Target rectangles were enclosed within a larger square frame context during induction (i.e., presentation of the inducing stimuli), judgment (i.e., presentation of the probe), or both induction and judgment. If context during induction moved in the same direction as the inducing stimuli or if context during judgment was rotated slightly forward from the orientation of the final inducing stimulus, representational momentum was increased. If context during induction moved in the direction opposite to the inducing stimuli or if context during judgment was rotated slightly backward from the orientation of the final inducing stimulus, representational momentum was decreased or reversed. If context was present during both induction and judgment, direction of representational momentum was biased toward the context at judgment Implications of context for accounts of representational momentum are discussed, and a tentative model is proposed.     

A large rectangle delays the perception of a separate small rectangle

Deciding whether two objects, rather than one, are present takes longer for large-small and small-large pairs of rectangles than for large-large and small-small pairs of rectangles. This large-small slowdown was eliminated when the large rectangle was slightly modified, when the large and small rectangles were contiguous, or when the task was to identify the large rectangle. However, it did occur when the task was to identify the small rectangle. These results suggest that the large rectangle delayed the perception of the small rectangle. Codes for features did not cause this delay. Instead, the evidence indicates that each rectangle evoked its own superordinate code, and that the large-rectangle superordinate code produced the gestalt of a large rectangle and also inhibited the small-rectangle superordinate code, thereby delaying the perception of the gestalt of a small rectangle. Thus, superordinate codes may also be the direct cause of other gestalts and their associated perceptual outcomes.     

Framing effects and the reversed Müller-Lyer illusion.

The enclosure hypothesis of the reversed Müller-Lyer illusion was examined in three experiments. In Experiment 1, the ingoing- and outgoing-wings forms of the illusion were measured separately, as a function of the size of the gap between the ends of the shaft and the apices of the wings. In Experiments 2 and 3, the effects of a square frame and of complete and amputated versions of a rectangle on the perceived length of an enclosed horizontal line were examined. For all non-Müller-Lyer illusion figures, an inverted U-shaped function describes the relationship between illusion magnitude and the length of the test line. The peak overestimation of the test line's length was obtained when the ratio of total figure length to test line length was about 3:2. Taken together, the results of the three experiments suggest that the reversed Müller-Lyer illusion can be explained within current theoretical frameworks, such as assimilation theory, without recourse to a special factor of enclosure.     

表象建构的面积评估

通过视觉或触觉给被试呈现完整的三角形,或呈现构成一个三角形所必要而又充分的一组部件以在表象上形成一个三角形,并评估其大小。结果发现,被试在表象中利用部件建构起来的三角形面积的增长,与实际知觉的三角形一样,均遵从幂函数定律,且幂函数指数均小于１,显示出表象与知觉的机能等价。     

The effects of location,orientation, and cumulation of boxes in the Baldwin illusion

Three experiments were conducted on variants of the Baldwin illusion. Experiment 1 showed that placing a box on each side of the standard line produced a larger illusion than placing both boxes on the same side of the line. These results failed to support the assimilation theory proposed by Brigell, Uhlarik, and Goldhorn (1977). In Experiment 2, the side of a rectangular box was varied when that side was either parallel or perpendicular to the standard line. The parallel rectangle produced a function that was similar to the one found with the classical Baldwin figure, but the perpendicular boxes produced a monotonically decreasing function with a reversal of illusion evident at the large sizes. The latter function did not support any version of the assimilation theory. The findings of Experiment 3 replicated previous findings that showed that cumulating contours as box size increased had no effect on the illusion. These findings explain two longstanding puzzles about the Müller-Lyer illusion: why a multifinned form is not the sum of its single-finned parts and why the shrinkage form produces a smaller effect than does the expansion form.     

Are thresholds reduced by illusions? An attempt at replication

Three experiments are reported, which are attempts to replicate the finding of Ross and Gregory (1964) that difference thresholds for weights can be lowered by means of the size-weight illusion. Three different procedures were used, the first one (experiment I) being designed to show whether or not changes in a subject's judgement criterion could account for apparent changes in sensitivity. The second method (Experiment II) was a replication of Ross and Gregory's first procedure, in which the standard weight was judged before the comparison. In Experiments I and II a larger illusion was induced than in the original studies, but in Experiment III both the weights and container sizes were practically identical to those used by Ross and Gregory. The procedure was also the same as their most successful procedure (number 3) in which standard and comparison were judged simultaneously. The findings were uniformly negative: there was no evidence of criterion shift when the size-weight illusion was induced nor did we find the lowering of threshold previously reported.     

Perceptions of depth elicited by occluded and shearing motions of random dots

A computer-controlled display of random dots was used to study perceptions of depth. In this display, a field of stationary random dots surrounded a rectangular area in which random dots moved with uniform velocity in a single direction. The boundaries of this rectangle did not move. When dot motion was perpendicular to the longer boundary of the rectangle (occluded motion), the rectangle seemed to be behind the stationary background surround. Motion parallel to the longer boundary of the rectangle (shearing motion) made it appear in front of the surround. The relative lengths of the sides of the rectangle determined which effect predominated. Thus, for motion perpendicular to the long axis of the rectangle the occlusion predominated and naive subjects reported that the central area seemed farther away than the surround. For shearing motion parallel to the long axis, the subjects reported that the rectangle was closer than the surround and the strength of both effects also depended on the length-to-width ratio of the rectangle. If there was occluded motion along the long axis, as the length-to-width ratio increased so did the likelihood that subjects would report seeing the rectangle behind the surround. Conversely, with shearing motion along the long axis, increasing the length-to-width ratio increased the likelihood that the rectangle would appear unambiguously in front of the surround. Some subjects integrated the two cues with the resulting perception being a rotating cylinder. The occlusion effect was stronger than the shearing effect.(ABSTRACT TRUNCATED AT 250 WORDS)     

Mental measurement of line length: the role of the standard

Reaction times were examined for magnitude estimates of line length. In the first two experiments, reaction times increased linearly with judged length. This result is consistent with the hypothesis the judgments are made by laying off a mental image of the standard along the line to be judged. The slope of the function relating judged length to reaction time was not affected by the length of the standard line, suggesting that the rate at which the image of the standard is laid off is not a function of the length of the standard. Reaction time also increased linearly with judged length when subjects judged line length when the standard of 1 in. was suggested but not provided as well as when no standard was suggested. The hypothesized laying-off process was compared to other cognitive manipulations, such as mental rotation and size scaling. Equivalence of judgments based on the representation of the standard in perceptual memory and in imagination is discussed.     

Selective attention and asymmetry in the Müller-Lyer illusion

Two experiments reexamined the effect of selective spatial attention on the magnitudes of the wings- in and wings-out forms of the Müller-Lyer (M-L) illusion and a version of the illusion in which the two forms are superimposed to produce a figure (XX) flanked at both ends by an X. For the XX figure, ignoring the outer wings produced significant underestimation of shaft length, whereas ignoring the inner wings had no significant effect. For the M-L figures, ignoring the wings was more effective in attenuating the magnitude of the wings-out than of the wings-in illusion. The results are discussed with reference to space-based approaches to visual attention and to claims that attentional modulation of illusion magnitudes implicates high-level or cognitive factors in the formation of the M-L illusion.     

A Mueller-Lyer illusion induced by selective attention

Subjects estimated the length of a horizontal line which was flanked by oblique angles pointing both inside and outside (this figure would be created by superimposing the wings-in and wings-out figures of the Mueller-Lyer illusion). Ignoring the outside wings resulted in an underestimation of the line length of comparable magnitude to that obtained for the wings-in Mueller-Lyer figure. Ignoring the inside wings caused an overestimation of the line length only when the inner and outer wings were of non-corresponding orientations. These results emphasize the role of cognitive factors in the Mueller-Lyer illusion.     

Speed constancy and the perception of distance

The distance-calibration hypothesis states that retinal velocity is scaled by using distance cues, and judged velocity remains unchanged when distance is changed. The relational hypothesis states that judged velocity depends on retinal velocities, and is proportional to judged distance. These hypotheses were compared in three experiments where the movements of the standard stimulus and the comparison stimulus were manipulated by the ratio of the angular velocity of the comparison stimulus to the angular velocity of the standard stimulus. The presentation conditions of the standard stimulus and the comparison stimulus, and the colour cues of the two stimuli were also manipulated in order to change the strength of the cues available to the observers. The results indicate that judged velocities and the relationship of judged distance and velocity depend on the strength of the cues. When cues are strong, the distance-calibration hypothesis adequately explains speed constancy. When cues are weak, judged velocity and the relationship between judged distance and velocity are consistent with the prediction of the relational hypothesis. The perceived speed of a stimulus depends not only on the physical speed of the stimulus but also on non-motion cues, some of which are distance cues involved in depth perception.