The apparent length of a line as a function of its inclination

In the first of two experiments reported here, subjects adjusted the length of a variable line until it appeared to be as long as a standard line. There were two sizes of standard line, 3 and 6 inches, and each was shown vertically for some trials and horizontally for others. The variable line was presented in each of the 10° positions from 0° (horizontal), through 90° (vertical), to 170°. The principal results of the first experiment are:

(1) Vertical lines look longer than horizontal lines of the same length, but lines tilted 20°-30° to the left of vertical look longer than lines in any other orientation. The results are asymmetrical, because lines tilted to the right of vertical do not look as long as those tilted to the left of vertical.

(2) The variability of the settings increases as the angle increases between the standard and variable lines.

(3) When they are expressed in percentage terms, the data obtained with the 3-and 6-inch standards are virtually identical, i.e. the data for the 3-inch standard can be made to match those for the 6-inch standard simply by doubling the former.

(4) There are enormous differences among subjects in the patterns of settings made at the various angles. A few subjects apparently experienced no illusory effects since they adjusted the variable line to about the same physical length irrespective of its orientation. Other subjects showed exaggerated overestimations of the variable line for vertical and near-vertical positions.

In the first experiment, the variable line was always to the left of the standard, and it was natural to assume that this position effect had somehow produced the asymmetry noted in paragraph 1 above. This hypothesis was tested in the second experiment which alternatively showed the variable line above, below, to the right of, and to the left of the standard line. The results of this experiment generally confirm the data of the first experiment in showing that lines tilted 20°-30° to the left of vertical look longer than lines tilted to any other position. In addition, the second experiment shows that this asymmetry in the results is not a function of the relative positions of the variable and standard lines. In general, however, overestimations of length are smaller when the two lines are one above the other, greater when the two lines are side by side.     

Apparent combined length of two-line and four-line sets

Recent studies, using single-line stimuli, show apparent length to be a power function, with exponent 1.0, of objective or physical length. If apparent lengths are additive, then, given the 1.0 exponent, two lines should appear to S to have the same total length as the single line they would form if physically joined. When S adjusted the length of one line to match the combined length of two other lines, however, he generally made the variable line much longer than the actual combined length of the two lines. Dividing the total length equally between the two lines, so that each had 50%, represents the greatest departure from a single line, yet the largest overestimation occurred when one of the two lines had 65% to 75% of the total length. The overestimation was greater when the lines were spaced farther apart, suggesting that the amount of area occupied by the lines affected apparent combined length.     

Orientation,length and exposure duration in the identification of line segments

Summary Single line segments titled with 0, 45, 90, and 135 degrees orientation were briefly exposed as stimuli and the subjects had to identify the orientation of a presented line segment. The length of the lines and the exposure duration were varied. The multicomponent theory (Rumelhart, 1970, 1971) was applied to the observed frequencies of a correct response and of some incorrect responses given to a stimulus with a particular orientation, length, and exposure duration. Within the framework of this theory several hypotheses concerning the effects of orientation, length and exposure duration in identification were tested. The main results are: (1) The rate of component detection was higher for the horizontal and vertical orientations than for the two oblique orientations. (2) The number of components in a line segment quite accurately followed a linear function of the line's physical length, and the negatively valued additive constant in this function could not be neglected. (3) The information in the visual information store decayed more rapidly after longer exposure durations and more slowly after shorter exposure durations. These findings are discussed in relation to other research on the subject.     

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.     

Test of the effect of attention on judged length of a line

Studies to assess experimentally whether attention affects the judged length of a line have produced discordant results. This paper reports the results of a test designed to avoid factors that were not controlled in previous studies. Stimuli were either two vertical lines or two horizontal lines of equal physical length presented briefly on opposite sides of a fixation cross. Subjects were asked to direct their attention to one line when the arm of the cross pointing to the line changed in luminance. This arm was used either as a precue or as a postcue. Subjects judged lines to be longer when a precue preceded the line than when a postcue followed the line.     

Grouping with and without attention

The effects of perceptual grouping on a line discrimination task were investigated using Moore and Egeth's (1997) paradigm. Observers judged which of two lines, presented one above the other over a matrix of spots, was longer. On some trials, larger spots at both ends of the lines formed arrowheads, thereby making possible the Müller-Lyer illusion. When observers attended only to the lines, they were not aware of the arrowheads. Yet their line judgment performance showed that they had succumbed to the illusion. When the observers' attention was directed to the arrowheads but they nevertheless failed to discern the arrowheads' orientation, their line judgments were still influenced by the illusion.     

Differential effects of stimulus context on perceived length: Implications for the horizontal-vertical illusion

Six experiments examined orientation-specific effects of stimulus context on the visual perception of horizontal and vertical lengths: Using a paired-comparison method, Experiments 1–5 showed that the probability of judging a given vertical line to be longer than a given horizontal line was relatively great when the stimulus set comprised relatively long horizontals and short verticals, and relatively small when the stimulus set comprised short horizontals with long verticals. To the extent that stimulus context exerts orientation-specific effects on perceived length, it thereby modulates the degree to which verticals appear longer than physically equivalent horizontals: the horizontal—vertical illusion (HVI). Under various contextual conditions, the HVI was as small as 3% (horizontals had to be 3% greater than verticals to be perceived as equally long) and as great as 15%, equaling about 12% in a “neutral” context. In Experiment 6, subjects judged the absolute physical length of each stimulus, and the results indicated that stimulus context acted largely by decreasing perceived lengths. The results are consistent with the hypothesis that differential effects of context reflect a process of stimulus-specific perceptual attenuation.     

Selective attention modulates implicit learning

The effect of selective attention on implicit learning was tested in four experiments using the "contextual cueing" paradigm (Chun & Jiang, 1998, 1999). Observers performed visual search through items presented in an attended colour (e.g., red) and an ignored colour (e.g., green). When the spatial configuration of items in the attended colour was invariant and was consistently paired with a target location, visual search was facilitated, showing contextual cueing (Experiments 1, 3, and 4). In contrast, repeating and pairing the configuration of the ignored items with the target location resulted in no contextual cueing (Experiments 2 and 4). We conclude that implicit learning is robust only when relevant, predictive information is selectively attended.     

Culture and change blindness

Research on perception and cognition suggests that whereas East Asians view the world holistically, attending to the entire field and relations among objects, Westerners view the world analytically, focusing on the attributes of salient objects. These propositions were examined in the change-blindness paradigm. Research in that paradigm finds American participants to be more sensitive to changes in focal objects than to changes in the periphery or context. We anticipated that this would be less true for East Asians and that they would be more sensitive to context changes than would Americans. We presented participants with still photos and with animated vignettes having changes in focal object information and contextual information. Compared to Americans, East Asians were more sensitive to contextual changes than to focal object changes. These results suggest that there can be cultural variation in what may seem to be basic perceptual processes.     

Voluntary visual attention and phenomenal line length

In 1956, Fraisse, et al. reported subjects judged that lines were longer when voluntary attention was focused on the lines than when attention was distracted from the lines. In the many attempts to repeat these results, none has ascertained whether attention on reported line length was a phenomenal effect. In the present study, 46 subjects were shown as stimuli pairs of horizontal or vertical briefly flashed lines with a fixation cross placed equidistant between the lines but far from each one. A change in color of one arm of the cross was used as a cue to focus subjects' voluntary attention on one line. Analysis showed attention increased the judged length of attended lines. Since this effect of attention also occurred when subjects were absolutely certain they saw the stimulus lines differed in length, this effect indicates that attention increased the phenomenal length of the attended lines. This lengthening was quite small: it involved a maximum mean increase of about .15 in the probability of the comparative response that the attended line was longer. This effect occurred in the horizontal dimension and was almost absent in the vertical dimension. In agreement with data indicating that flashed lines expand phenomenally by activating motion detectors and that focused attention makes neural motion responses increase in amplitude, the present results suggest that focused attention makes attended lines look longer because it makes these lines expand phenomenally more rapidly.     

Visual field size necessary for length comparison

Influence of visual field size upon acuity for comparing lengths of two lines was investigated. The visual field was effectively narrowed to any desired size by use of a TV display system. The TV screen presented a portion of the test stimulus, the position of which was controlled by the subject’s eye movement so that his fixation point always coincided with the center of the portion. The test stimulus was composed of two lines arranged horizontally, one of which had a length of 81 mm and the other a slightly different value. Sizes of the narrowed visual field were 20, 40, 70, 100, 150, and 340 mm wide. The comparison acuity dropped rapidly as the visual field was narrowed to and below 70 mm which was about the same extent as one of the two lines. The implication is that our excellent ability for length comparison is only possible when we can observe the whole line at one time.     

Unilateral neglect: the effect of competing stimuli on estimated line length

Normal subjects and patients with right hemisphere lesions with or without signs of left unilateral neglect judged the length of a horizontal line presented on the left or on the right side of space. In half of the trials, the line was presented with a centrally located square or diamond, and subjects had to identify the central stimulus before performing the judgment of length. The presence of the central stimulus improved accuracy of performance in controls and in patients without neglect; neglect patients, however, produced more overestimations of left-sided lines when these was presented with a central stimulus than when the lines occurred in isolation. This finding underlines the importance of attentional factors in length estimates performed by neglect patients in their neglected space.     

Evidence of different developmental trajectories for length estimation according to egocentric and allocentric viewpoints in children and adults

This study investigated the influence of egocentric and allocentric viewpoints on a comparison task of length estimation in children and adults. A total of 100 participants ranging in age from 5 years to adulthood were presented with virtual scenes representing a park landscape with two paths, one straight and one serpentine. Scenes were presented either from an egocentric or allocentric viewpoint. Results showed that when the two paths had the same length, participants always overestimated the length of the straight line for allocentric trials, whereas a development from a systematic overestimation in children to an underestimation of the straight line length in adults was found for egocentric trials. We discuss these findings in terms of the influences of both bias-inhibition processes and school acquisitions.     

Short-term memory in the pigeon: delayed-pair-comparison procedures and some results.

A discrete-trials, delayed-pair-comparison procedure was developed to study visual short-term memory for tilted lines. In four experiments, pigeons' responses on left or right keys were reinforced with food depending on whether a comparison stimulus was or was not the same as a standard stimulus presented earlier in the same trial. In Experimental I, recall was an increasing function of the exposure time of the to-be-remembered stimulus and was a decreasing function of the retention interval. In Experiment II, retroactive interference was investigated: recall was poorer after a retention interval during which was presented either a tilted line or contextual stimuli in the form of the illuminated experimental chamber. In Experiment III, a subject was required to engage, throughout the retention interval, in one or the other of two different behaviors, depending on which of two stimuli a subject was to remember. This mnemonic strategy vastly improved recall after 15- and 20-second retention intervals. In Experiment IV, the opposite end of the performance continuum was studied: by combining the effects of a larger stimulus set and the effects of what presumably was an increased memory load, performance was reduced to approximately chance levels after retention intervals shorter than 1 second.     

A matter of design: Priming context and person perception

A matter of considerable debate is whether people spontaneously use categorical knowledge (i.e., stereotypes) to guide their interactions with others. Despite initial evidence for the unconditional automaticity of category activation, recent research has identified a range of factors that moderate this process. Extending this line of inquiry, the current investigation explored the extent to which contextual influences—specifically the order in which priming stimuli are presented to participants—may modulate person categorization. Using a standard semantic-priming paradigm to index category and stereotype activation, participants were presented with priming stimuli that were either intermixed or blocked by sex. The results revealed that: (i) category and stereotype activation are moderated by the order in which priming stimuli are presented; and (ii) priming effects decrease monotonically as a function of category repetition. The theoretical implications of these findings are considered.     

Circle size and diameter tilt: A new look at integrality and separability

In six experiments using the speeded classification paradigm, we provide evidence that the ostensibly “separable” dimensions of size and orientation can produce patterns of either separability or asymmetric configurality, depending on the spatial arrangement of the stimuli. In all experiments, subjects classified large or small circles contairting a single line in one of two possible orientations. When the line touched the circle’s perimeter, thereby defining the diameter of the circle (Experiments 1–4), asymmetric configurality obtained: Variations in size interfered with classification by orientation, but variations in orientation did not interfere with classification by size, and redundancy gain was weak or absent. When the lines fell completely within (i.e., did not touch) the circles (Experiments 5 and 6), the results were consistent with separability: There was neither redundancy gain nor interference. Taken together, the results add to the growing body of evidence that classification of specific dimensional pairs as separable or integral may be less feasible than identifying the more general conditions that increase or decrease the psychological salience of dimensional structures and facilitate or interfere with selection of optimal processing strategies.     

Application of signal detection theory to perception of differences in line length

This paper is an attempt to specify the equinormal model for application to different tasks which are currently used in psychophysics (i.e. phenomenal report, detection, and 2AFC). The same set of stimuli (pairs of horizontal colinear lines) is presented in procedures which differ by the task, the probability of the signal, and the succession of the stimuli of the set. This approach leads to the specification of the sensorial and the decisional aspects of the model.The data indicate that (1) the sensitivity index d' to differences in line length is the same function of the physical stimulus independently of paradigm, as far as the same task is concerned. However, and according to the predictions, its value becomes larger by a factor of 2 in a two alternative forced choice task; (2) d' increases with stimulus exposure time; (3) latency of responses generally decreases with increasing d', and are dissimilar for correct and incorrect responses; (4) when the temporal succession of the stimuli is random the subject's criterion, x_c, is not chosen to optimize the percentage correct, which would require a dependance of criterion upon stimulus amplitude and prior probabilities.     

Does attention have different effects on line orientation and line arrangement discrimination?

Visual search and texture segregation studies have led to the inference that stimuli differing in the orientation of their component line segments can be distinguished without focal attention, whereas stimuli that differ only in the arrangement of line segments cannot. In most of this research, the locus of attention has not been explicitly manipulated. In the first experiment presented here, attention was directed to a relevant peripheral target by a cue presented near the target location or at the fovea. Effects of attention on orientation discrimination were assessed in a two-alternative forced-choice task with targets that were either: (1) lines that slanted obliquely to the right or left, or were horizontal or vertical, or (2) Y-like targets that had a short arm leading obliquely right or left of a vertical line. In some groups, a four-alternative forced-choice test with lines at 0°, 45°, 90°, and 135° orientations was used. Discrimination of these targets (i.e. targets that differ in the orientation of component line segments) was only minimally facilitated as the time between the onset of the valid cue and the onset of the target (cue-target stimulus onset asynchrony, SOA) was increased from 0 or 17 msec to 267 msec. In contrast, discrimination of targets that did not differ in the orientation of component line segments but differed in line arrangement (T-like characters), was greatly facilitated by longer cue-target SOAs. In Experiment 2, a cue misdirected attention on 20% of the trials. A decrement occurred on incorrectly cued trials in comparison to correctly cued trials for both types of stimuli used (lines and Ts). The results from these experiments suggest that discrimination of line orientation benefits less from focal attention than does discrimination of line arrangement, but that both discriminations suffer when attention must be disengaged from an irrelevant spatial location.     

Context effects in visual length perception: role of ocular,retinal, and spatial location

In three experiments, we examined the transfer of orientation-contingent context effects between the eyes and across portions of the retina with or without variation in external spatial location. Previous research had shown that vertical lines are judged long, relative to horizontal lines, when the stimulus set comprises relatively long horizontals and short verticals (Contextual Condition B), as compared with the reverse when the stimulus set comprises relatively short horizontals and long verticals (Contextual Condition A). Consequently, the contextual set of stimuli influences the magnitude of the horizontal-vertical illusion (HVI), decreasing its size under Contextual Condition A and increasing its size under Contextual Condition B. Experiment 1 showed that exposing one eye to different stimulus contexts modulated the size of the HVI at the exposed eye but had little or no effect at the other eye. Experiments 2 and 3 showed that the effect of the contextual sets generalized poorly across adjacent portions of the retina but transferred almost perfectly across different locations in external space when retinal location was constant. Thus, orientation-contingent context effects in visual length perception appear to be specific to the eye and to the region of the retina stimulated, suggesting that these effects reflect relatively early and local changes in sensitivity, rather than relatively late and general shifts in response criteria.