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.     

The relational determination of length illusions and length aftereffects.

When two lines were presented simultaneously, in an illusion paradigm, the judged length of one of the lines (the focal line) assimilated toward the length of the contextual line. When the lines were presented sequentially, in an aftereffect paradigm, the apparent length of the focal line was displaced away from the length of a previously presented contextual line (i.e. contrast). The largest effects obtained at inverse contextual-to-focal length ratios: 1.67:1 for contextual lines longer than the focal line and 0.60:1 for contextual lines shorter than the focal line. Overestimation of focal length was larger than underestimation for both illusions and aftereffects despite the fact that identical stimuli produced effects in opposite directions in the two paradigms. Results were discussed in terms of a neural length-coding model and were related to visual size constancy.     

Procedure-specific estimates of structural and strategic factors in the Horizontal-Vertical illusion

The present study examined potential differences in structural and strategic factor estimates involved in the Horizontal-Vertical (HV) illusion. Performance on adjustment and production-task forms of the illusion was examined under the conditions of intertrial feedback, continued visual inspection, combined feedback and visual inspection, as well as control procedures. Estimates of structural and strategic factors were procedure-specific and, for each task, the correction of inaccurate strategic factors was significantly greater for the feedback than the visual-inspection and control groups. There were no significant additive effects when feedback was combined with visual inspection. The illusion results from an overestimation of the length of vertical lines, seems to be predominantly cognitive in nature, and exists in the absence of line bisection and a comparison line.     

Double fusion does not occur in Panum's limiting case: evidence from orientation disparity.

When two lines of different orientations are combined in regular stereograms, the orientation of the resulting line is different from those of the monocular lines. In this study we investigate the percept elicited by orientation disparity in Panum's limiting case. A variant of Panum's limiting case was designed to include orientation disparity. The single line in one half-image tilted leftwards. One of the double lines in the other half-image was parallel to the single line, while the other one tilted rightwards with obliquity one third that of the single line. In this stimulus configuration, if the single line in one half-image fuses with both lines in the other half-image at the same time, both of the two lines perceived after fusion should tilt leftwards. If double fusion does not happen, the two lines should tilt leftwards and rightwards respectively. The results of this study are in agreement with the latter prediction, which implies that double fusion does not occur in this variant of Panum's limiting case.     

Visual and visually mediated haptic illusions with Titchener’s ⊥

For a replication and expansion of a previous experiment of mine, 14 newly recruited participants provided haptic and verbal estimates of the lengths of the two lines that make up Titchener’s ⊥. The stimulus was presented at two different orientations (frontoparallel vs. horizontal) and rotated in steps of 45 deg around 2π. Haptically, the divided line of the ⊥ was generally underestimated, especially at a horizontal orientation. Verbal judgments also differed according to presentation condition and to which line was the target, with the overestimation of the undivided line ranging between 6.2 % and 15.3 %. The results are discussed with reference to the two-visual-systems theory of perception and action, neuroscientific accounts, and also recent historical developments (the use of handheld touchscreens, in particular), because the previously reported “haptic induction effect” (the scaling of haptic responses to the divided line of the ⊥, depending on the length of the undivided one) did not replicate.     

The effects of curvature on haptic judgments of extent in sighted and blind people

A series of experiments was carried out to examine the effect of curvature on haptic judgments of extent in sighted and blind individuals. Experiment 1 showed that diameters connecting the endpoints of semicircular lines were underestimated with respect to straight lines, but failed to show an effect of visual experience on length judgments. In experiment 2 we tested are lengths. The effects of curvature on perceived path length were weaker, but were still present in this experiment. Visual experience had no effect on path length judgments. Another experiment was performed to examine the effect of repeated tracing (1, 5, 9, or unlimited number of traces) on judgments of the lengths of straight lines and diameters of semicircles. Judgments of extent were more accurate when subjects engaged in larger numbers of traces. There was no effect of number of traces on curve-height judgments, suggesting that subjects were not using height estimates to judge diameters of semicircles. In a further experiment we tested the effect of number of traces on curves that varied in height. Restricting subjects to a single trace magnified the effect of path length on judgments of the distance between the endpoints of curves. Additional experiments showed that curvature effects on diameter judgments were not eliminated when stimuli were in the frontal plane or when the curves were explored with the use of two hands. Arm support had no effect on judged length in experiment 7. A final experiment showed a robust horizontal vertical illusion in haptic perception of convex curves, with overestimation of the heights of the curves compared with their widths. The practical and theoretical implications of the results are discussed.     

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.     

Length perception of horizontal and vertical bisected lines

In an inverted T figure, the vertical line is largely overestimated (Avery and Day in J Exp Psychol 81:376–380, 1969). This vertical overestimation results from the vertical and bisection biases. Line orientation biases length perception in the sense that the vertical line of a L shape is perceived as longer than the horizontal line of the same physical length. In the inverted T figure, the vertical line is overestimated because of its orientation but also because the horizontal line is bisected. In the current study, we used various two-line configurations to investigate the role of bisection a/symmetry in line length perception and its interaction with the vertical bias. Experiment 1 showed that symmetry and asymmetry of bisection have different consequences on line length perception, as previously shown by Wolfe et al. (Percept Psychophys 67:967–979, 2005). Experiments 2 focused on the relation between the vertical and bisection biases by manipulating orthogonally line orientation and bisection a/symmetry. The results provided evidence that bisection can prevent the manifestation of the vertical bias, so that when the two lines are bisected, vertical lines are not anymore overestimated. These results are discussed in the light of recent findings claiming that saccades could play an essential role in length perception.     

Ratio scale measurement of the perceived lengths of lines.

In Experiments 1 and 2, magnitude and category estimates of perceived line length difference were used to rank order 36 pairs of lines with respect to the psychological length difference between the lines forming a pair. In Experiment 3 magnitude estimates of line length ratios were used to order the same 36 pairs with respect to the psychological length ratio between the lines comprising a pair. A nonmetric analysis of the rank-order of the difference and ratio judgments was used to construct a ratio scale of perceived line length. Perceived line length was found to be a power function of physical line length with an exponent of .46. In Experiments 4 and 5, magnitude and category estimates of line length similarity were obtained. A nonmetric analysis of these data indicated that similarity judgments were monotonic inverses of judgments of psychological ratios.     

Seeing big things: overestimation of heights is greater for real objects than for objects in pictures

In six experiments we demonstrate that the vertical-horizontal illusion that is evoked when viewing photographs and line drawings is relatively small, whereas the magnitude of this illusion when large objects are viewed is at least twice as great. Furthermore, we show that the illusion is due more to vertical overestimation than horizontal underestimation. The lack of a difference in vertical overestimation between pictures and line drawings suggests that vertical overestimation in pictures depends solely on the perceived physical size of the projection on the picture surface, rather than on what is apparent about an object's represented size. The vertical-horizontal illusion is influenced by perceived physical size. It is greater when viewing large objects than small pictures of these same objects, even when visual angles are equated.     

Thermally activated plastic glide

The two main theories of thermally activated plastic glide in ductile crystals, that of Becker and that of Mott and Nabarro, differ in their predictions of the stress exponent of the activation energy. But when the Becker theory is applied to the problem of the Mott-Nabarro theory, that is the overcoming of a single localized obstacle by a short segment of dislocation line, and account is taken of the stress relaxation brought about by the movement of the segment up to the obstacle, this modified Becker theory gives the same stress exponent as the Mott- Nabarro theory. The realistic situation, however, is that of long dislocation lines making their way through a forest of obstacles. In this case the interactions between different segments of these lines considerably modify the problem. They lead to load shedding, mechanical activation and large glide avalanches. Under these conditions the original form of the Becker theory, with an unmodified stress exponent, is applicable.     

Attentional effects on concurrent psychophysical discriminations: Investigations of a sample-size model

In two experiments, a concurrent discrimination paradigm was used to study the effects of visual attention on psychophysical judgments and the consistency of these effects with a sample-size model in which attention influences the variance of the internal representation used to make psychophysical judgments. Two pairs of lines were presented simultaneously—one on each side of fixation—and subjects had to indicate for each pair separately whether or not the lines had the same length. Attention was manipulated by instructing subjects to pay 100%, 75%, 50%, 25%, or 0% of their attention to the discrimination on one side, with the complementary amount of attention to the other side. In the first experiment, the relationship between attention and discrimination accuracy was consistent with the sample-size model both when attentional allocation varied from trial to trial and when it varied between blocks, and the relationship held over more widely varying attentional allocations than had previously been studied. In addition, discriminations were more accurate overall with varied than with blocked attentional allocation, suggesting that the two types of allocation do not merely differ in the degree to which attention is focused. The second experiment examined the effects of attentional allocation and stimulus variance, the latter being manipulated by randomly incrementing or decrementing line lengths. These manipulations had additive effects on total Thurstonian variance, and a version of the samplesize model gave an excellent quantitative fit to the obtained results. Besides supporting the samplesize model, the results of Experiment 2 suggest that criterion variance is at least as large as sensory variance and that criterion but not sensory variance increases with stimulus variance.     

Titchener’s ⊥ with its lines tilted—A partial replication and extension of Cormack and Cormack (1974)

Following Cormack and Cormack (Perception & Psychophysics, 16, 208–212, 1974), modified versions of Titchener’s (Experimental Psychology, Vol. 1, Pt. 1, 1901) ⊥, in which the ⊥’s lines were tilted (Experiment 1), or tilted and dissected into two separate lines (Experiment 2), were used as stimuli. In Experiment 1, the overestimation of the length of the ⊥’s vertical, undivided line tended to decrease with its tilt relative to the horizontal, divided line. For ⊥s rotated 90° or 270°, the divided line was tilted, and the overestimation of the length of the now horizontal, undivided line vanished except for ⊥s with orthogonal lines. Separation of the ⊥’s lines in Experiment 2 led to an attenuation of the overestimation of the length of the undivided line for the default ⊥, and an underestimation of the length of this line for rotated ⊥s. Results only partly confirm Cormack and Cormack, probably because of the different psychophysical methods used. Findings support the notion of a T-schema as a coherent unit in midlevel visual processing, but also suggest medium- and long-range interactions between orientation-sensitive neural mechanisms.     

Stimulus control and generalization of point-loss punishment with humans

Two experiments demonstrated stimulus control and generalization of conditioned punishment with humans. In both studies, responses first were reinforced with points exchangeable for money on a variable-interval schedule in the presence of one line length (S(D)). Next, a second line length was introduced, and point loss followed every response in the presence of that line (S(D)p). In the final training condition, points were deducted at session end. Response rate was lower in the presence of the S(D)p despite equal rates of points for money in the presence of both stimuli. In generalization testing for Experiment 1, the two lines were included in a 10-line continuum; S(D)p fell in the middle and the trained SD was at one end. Lines were presented randomly, and point delivery and loss contingencies were as in training but with points available in the presence of all lines. For all subjects, response rates were lowest around S(D)p and increased towards the SD end of the continuum. Because testing included only one or two lines beyond S(D), this pattern did not rule out S(D) generalization. Thus, in Experiment 2, stimuli beyond S(D) were added to generalization tests. Response rates did not decrease as a function of distance from S(D), clarifying the demonstration of punishment generalization.     

Contrast-dependent interaction between steadily fixated lines

Disappearances of a steadily fixated line were shown to be reduced when it was paired with a like-oriented second line of the same luminance. The effect did not decline with 2.4 deg of separation between the lines. No such stabilization was obtained if the second line was either brighter than the reference line or decremental with respect to the background. It was found that this selective interaction was not the result of either a reduction in the apparent brightness of the dim Une by simultaneous contrast with the brighter one or of the different response requirements when viewing two dim Unes as opposed to one. Disappearances in steady fixation can therefore indicate the existence of processes that are not apparent in other forms of steady visual stimulation.     

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.     

Is target movement as well as target displacement a stimulus for saccadic eye movements?

The effects of visual movement on saccadic eye movement have been examined. In a classic apparent-movement demonstration with two successively exposed line-segment targets the quality of the movement is dependent on the relative orientation of the line segments. If saccadic eye movements are elicited between the targets in this situation, the configuration leading to optimal apparent movement also leads to the shortest-latency saccades. When a single line segment is succeeded by two line segments flanking it on opposite sides, and if one of these has the same orientation as the initial one and the other a different orientation, then apparent motion is seen between the two lines with the same orientation. However, the direction of saccades elicited in this configuration is not influenced by the relative orientations of the line segments. The two results together suggest that the effect of visual movement on saccadic eye movement is nonspecific.     

Measuring the effect of multiple eye fixations on memory for visual attributes.

Because of limited peripheral vision, many visual tasks depend on multiple eye fixations. Good performance in such tasks demonstrates that some memory must survive from one fixation to the next. One factor that must influence performance is the degree to which multiple eye fixations interfere with the critical memories. In the present study, the amount of interference was measured by comparing visual discriminations based on multiple fixations to visual discriminations based on a single fixation. The procedure resembled partial report, but used a discrimination measure. In the prototype study, two lines were presented, followed by a single line and a cue. The cue pointed toward one of the positions of the first two lines. Observers were required to judge if the single line in the second display was longer or shorter than the cued line of the first display. These judgments were used to estimate a length threshold. The critical manipulation was to instruct observers either to maintain fixation between the lines of the first display or to fixate each line in sequence. The results showed an advantage for multiple fixations despite the intervening eye movements. In fact, thresholds for the multiple-fixation condition were nearly as good as those in a control condition where the lines were foveally viewed without eye movements. Thus, eye movements had little or no interfering effect in this task. Additional studies generalized the procedure and the stimuli. In conclusion, information about a variety of size and shape attributes was remembered with essentially no interference across eye fixations.     

Measuring the effect of multiple eye fixations on memory for visual attributes

Because of limited peripheral vision, many visual tasks depend on multiple eye fixations. Good performance in such tasks demonstrates that some memory must survive from one fixation to the next. One factor that must influence performance is the degree to which multiple eye fixations interfere with the critical memories. In the present study, the amount of interference was measured by comparing visual discriminations based on multiple fixations to visual discriminations based on a single fixation. The procedure resembled partial report, but used a discrimination measure. In the prototype study, two lines were presented, followed by a single line and a cue. The cue pointed toward one of the positions of the first two lines. Observers were required to judge if the single line in the second display was longer or shorter than the cued line of the first display. These judgments were used to estimate a length threshold. The critical manipulation was to instruct observers either to maintain fixation between the lines of the first display or to fixate each line in sequence. The results showed an advantage for multiple fixations despite the intervening eye movements. In fact, thresholds for the multiple-fixation condition were nearly as good as those in a control condition where the lines were foveally viewed without eye movements. Thus, eye movements had little or no interfering effect in this task. Additional studies generalized the procedure and the stimuli. In conclusion, information about a variety of size and shape attributes was remembered with essentially no interference across eye fixations.     

What Is Line Bisection in Unilateral Spatial Neglect?: Analysis of Perceptual and Motor Aspects in Line Bisection Tasks

Three patients with unilateral spatial neglect could detect the difference of length between the right and left segments when a line had a transection mark. To examine the effect of response mode, the manual line bisection task and a new “line bisection task by fixation” were given to the patients. In tasks that used lines with no landmark, they showed apparent rightward errors. The results suggest that line bisection is not a task that examines the ability of patients with neglect to compare the right and left extents of a line. Where to fixate as the subjective midpoint may determine the rightward errors of bisection, whether manual response is used or not.