Three-space inference from two-space stimulation.

Oblique contours sloping at 30 degrees with respect to the horizontal were presented alone, in combination to form chevrons, or with a vertical line to form arrowhead or Y patterns; they were projected onto a screen in the frontal parallel plane and viewed from positions that gave viewing angles of 90 degrees (normal to the screen's surface), 53 degrees, or 34 degrees. The perceived orientation of the contours, as assessed by a movable arm that the subjects set to be parallel to the obliques, changed monotonically as a function of viewing angle. The change was as great for single obliques as for combinations of obliques within the chevron, arrowhead, and Y patterns. The results of Experiment 1 were extended in Experiment 2, in which obliques at 30 degrees and 50 degrees with respect to the horizontal were presented singly or in combination as chevron patterns. It is argued that the results of both experiments indicate that single two-space oblique lines are immediately interpreted as lying in three-space and that the changes in perceived orientation are a consequence of this perceptual inference.     

Three-space inference from two-space stimulation

Oblique contours sloping at 30° with respect to the horizontal were presented alone, in combination to form chevrons, or with a vertical line to form arrowhead or Y patterns; they were projected onto a screen in the frontal parallel plane and viewed from positions that gave viewing angles of 90° (normal to the screen’s surface), 53°, or 34°. The perceived orientation of the contours, as assessed by a movable arm that the subjects set to be parallel to the obliques, changed monotonically as a function of viewing angle. The change was as great for single obliques as for combinations of obliques within the chevron, arrowhead, and Y patterns. The results of Experiment 1 were extended in Experiment 2, in which obliques at 30° and 50° with respect to the horizontal were presented singly or in combination as chevron patterns. It is argued that the results of both experiments indicate that single two-space oblique lines are immediately interpreted as lying in three-space and that the changes in perceived orientation are a consequence of this perceptual inference.     

The corner Poggendorff

With the classic Poggendorff illusion a set of parallel 'induction lines' will cause a set of oblique line segments to look misaligned even though they are collinear. A different kind of misalignment can be produced by placing the induction lines so that they form a corner. Under these conditions the obliques will appear to be angled slightly, one relative to the other. The effects are small, but can be seen and reliably reported by a group of naive subjects. The influence of the induction lines drops sharply as their relative position is moved from parallel to orthogonal, but there is a small residual influence which may be called the corner Poggendorff effect.     

Foreshortening and the perception of parallel projections

Does picture perception follow polar projective geometry? Parallel projection drawings, which are not produced by using rules of polar projection, are widely regarded as visually acceptable representations of three-dimensional (3-D) objects in free viewing. One explanation is that they are perceived by means of a system in which there is no foreshortening. If so, edges of a 3-D block in 1∶1 proportions should be denoted by lines in 1∶1 proportions on the picture surface. However, three experiments suggest that the perception of parallel projections of a block involves foreshortening. In Experiment 1, 90 subjects were shown a set of parallel projections of a cube, in which each drawing depicted three sides of the cube, drawn as a square with obliques—a frontal square with receding edges shown by parallel obliques of various lengths. The subjects preferred a drawing with a receding side length that was considerably foreshortened in relation to the front side. In Experiments 2 and 3, subjects viewed drawings of three blocks that differed in the ratios of the lengths of their receding edges to their frontal edges (1∶1, 1∶2, and 1∶0.65). In Experiment 2, the subjects were shown square-with-obliques drawings of the three blocks with receding edges shown by parallel obliques of various lengths. Again, the subjects preferred drawings with a receding side that was foreshortened. In Experiment 3, the drawings showed two sides of a block. The receding dimension was drawn with parallel or converging lines. The preferred foreshortening was not a fixed ratio of the dimensions of the 3-D blocks. We suggest that square-with-obliques parallel projections showing cubes are taken by vision to be approximations to projections using foreshortening. We suggest also that as the line showing the receding edge elongates, foreshortening becomes less of a factor.     

The relative contribution of contact and target lines in the magnitude of the Poggendorff effect

It is well known that a set of parallel lines can cause misperception of the projected path of an oblique. Most studies of this effect have emphasized either the proximal or the distal stimulus components--the line with which the oblique makes contact, or the line that serves as the target of the projection. An experiment is reported in which the relative contribution of the contact and target lines was examined. The results indicate that rotation of either line can determine the magnitude of the projection error.     

The poggendorff illusion with subjective contours

Gregory (1972) has claimed that the Poggendorff misalignment effect occurs when the collinear obliques are separated by subjective rather than real contours. He used two figures to demonstrate this variant of the illusion. Two experiments to test the claim are reported. The first showed that apparent misalignment in one of the two original figures is no greater than that with two obliques alone (the oblique line effect), but misalignment in the other is greater than with two oblique lines and than with a control without subjective contours. The second experiment showed that apparent misalignment in the second figure was less than in two control figures without subjective contours. Since this reduced effect was probably due to the nature of the intersection between the oblique and a semi-circular element, the role of subjective contours remains unsettled.     

Eliminating the haptic oblique effect: influence of scanning incongruity and prior knowledge of the standards

Although the oblique effect has been conceptualized as a purely visual phenomenon, recent studies report its occurrence in a haptic matching task and present the hypothesis that differences in haptic orientational sensitivity might be responsible for the results. The possibility that procedural variables could be responsible was investigated. Specifically, the effect of prior knowledge of the stimulus orientation standards and of use of bilateral haptic exploration of standard and comparison orientations was examined. The results indicate that the reported oblique effect is reduced either when subjects are not informed which orientations will be tested, or when a unilateral matching procedure instead of a bilateral one is used. When both conditions are combined, the haptic oblique effect is eliminated. It is concluded that this particular manifestation of the oblique effect is not related to haptic sensitivity, but stems from the use of well-established imagery as referent for a match (imagery for oblique stimulus orientations is inferior) and the inherently different scanning patterns required in bilateral exploration of obliques (percepts of standard and comparison obliques will be necessarily different).     

The role of contextual cues in the haptic perception of orientations and the oblique effect

Blindfolded right-handed participants were asked to position, with the right hand, a frontoparallel rod to one of three orientations: vertical (0°) and left 45° and right 45° obliques. Simultaneously, three different backgrounds were explored with the left hand: smooth, congruent stripes (parallel to the orientation to be produced), or incongruent stripes (tilted relative to the orientation to be produced). The analysis of variable errors showed that the oblique effect (higher precision for the vertical orientation than for the oblique orientations) was weakened in the presence of contextual cues, because of an improvement in oblique precision. Moreover, the analysis of constant errors revealed that the perception of orientations erred in the direction of the stripes, similar to the effect that has been found with vision, where visual contextual cues (tilted frame or lines) divert the perception of the vertical. These results are discussed in relation to a patterncentric frame of reference hypothesis or as a congruency effect.     

Angular subtense effects on perception of polar and parallel projections of cubes

Many authors contend that the perception of 2-D drawings of a 3-D object is governed by polar projective geometry. A problem for this position is that observers accept parallel projections, which are not produced with polar projective geometry, as accurate representations of 3-D objects. In Experiments 1 and 2, we used two different standards of comparison to study the perceptions of three line drawings of cubes—correct polar projections of cubes with subtenses of 15° and 35°, and a parallel projection—at five different angular subtenses. In Experiment 1, 14 observers judged each drawing when it subtended about 35°, 15°, 5°, 4°, and 2° in width. Subjects used an 8-point rating scale to compare each drawing with a correct polar projection of a cube subtending 35°, viewed with the drawing subtending 15°. As predicted, both polar projections had their highest ratings at their correct vantage points. Ratings for the parallel projection were highest at small angular subtenses and decreased when it subtended 35°. These findings were supported by a second experiment in which the 15° polar projection was set at a 5° viewing angle as a standard. In Experiment 3, 15 observers compared the three drawings, viewed at a second set of angular subtenses (30°, 35°, 40°, 45°, and 50°), with a standard, the 35° polar set at 45°. Ratings fell with increases in viewing angle, and the parallel projection was rated lowest. The results indicate that parallel projections are assessed as polar projections that are correct for objects at a small angular subtense. Furthermore, projections at a small angular subtense are robust; that is, they are acceptable over a wide range of angular subtenses. We suggest that robustness can be explained by the modest variability in the proportions of pictures of cubes subtending small angles.     

Perceptual learning of orientation judgments in oblique meridians

Fourteen daily training sessions in orientation discrimination of foveal lines in the 45-deg meridian improved thresholds in the trained meridian by an average of 25 % in five observers. A substantial amount of training transferred to the other obliques, but none to the cardinal meridians, with a consequent reduction in the oblique effect. The data were interpreted as showing perceptual learning at two levels: performance facilitation specific to the trained orientation and improved proficiency globally. The failure of the cardinal orientations to share in the benefit is likely to have its origin in the fact that contour orientation in these meridians is so well established that it had already reached maximum hyperacuity thresholds. The judgment of obliques depends much more than the judgment of cardinals on whether the comparison and test stimuli are shown simultaneously or in succession, but this effect is not changed by perceptual training.     

Perceptual similarity of mirror images in infancy

Perception of mirror images by three-to four-month infants was studied in five experiments using habituation paradigms. In the first experiment, babies discriminated right profiles of two different faces but not the left and right profile of the same face. In the second, babies discriminated a 45° oblique from a vertical line, but not the oblique from its mirror image. In the third, babies discriminated oblique lines that differed by 50° and were not mirror images. In the final experiments. 90° rotations of a ?-shape were discriminated but not 180° rotations that formed lateral or vertical mirror images. These results demonstrated that although babies were able to discriminate differences in orientation (even among obliques) they tended to view mirror images, especially lateral mirror images, as equivalent stimuli. We propose that the perceptual equivalence of mirror images reflects an adaptive mode of visual processing; mirror images in nature are almost always aspects of the same object, and they usually need not be discriminated. The relations of the perceptual similarity of mirror images to the ontogeny of the object concept and to the development of reading are discussed.     

Evidence for a general category of oblique orientations in four-month-old infants

Recent work on orientation perception and memory in infants suggest that oblique stimulus orientations are treated as members of a category. The two studies in this report support this hypothesis and extend previous findings by demonstrating that this category includes obliques on either side of vertical even when infants are previously exposed to obliques on only one side.     

Gradients of distortion seen in the context of the Ponzo illusion and other contours

It is suggested that the spatial distortion evident in the Ponzo figure is a special case of a more general illusion in which a gradient of attenuation appears within areas bounded by angular brackets. The magnitude of this gradient is measured in five lines seen against a number of angular contexts. A similar gradient appears also in the presence of single oblique lines. Accordingly, it is suggested that the distortions seen in the figures usually referred to as “the angle illusions” depend upon the presence of contours which do not necessarily define angles. The implications of these findings for certain existing theories which suggest that some illusions depend upon apparent-distortion of angular size and that they contain features usually associated with two-dimensional perspective projections of typical three-dimensional scenes are discussed.     

Errors towards the perpendicular in children's copies of angular figures: a test of the bisection interpretation

Children distort angular figures so that the constituent angles are nearer 90 degrees than they should be. This could be due to a perpendicular bias or a bisection bias, or to both. A study is reported which was designed to establish whether a perpendicular bias would appear independently of bisection. Twenty four-year-old children were tested on two types of angular figure: (i) a baseline with another line joining at the end at 45 degrees, 90 degrees, or 135 degrees and (ii) a baseline with another line joining at the middle at 45 degrees or 90 degrees. Perpendicular errors were obtained both for 'end' and for 'middle' figures, but overall more strongly for 'middle' figures. However, while 90 degrees 'middle' figures were copied more accurately than 45 degrees/135 degrees figures, this effect was only obtained for vertical and horizontal presentations of 'end' figures, and was reversed for oblique presentations. Also, for 'end' figures, directional errors varied with subtended-line orientation, whereas for 'middle' figures they varied with baseline orientation. It is concluded that although errors towards the perpendicular do occur with single-angle figures, angle equalisation may take place when there are two adjacent angles in the figure. One interpretation of the differing orientation effects is that in 'middle' figures strong internal relational forces produce a distortion that varies with the angle at which the figure is viewed, whereas in 'end' figures the absence of relational forces within the figure leads to a stronger influence from external cues.     

The Poggendorff Illusion and estimates of transverse extent.

The underestimation of transverse extent relative to longitudinal extent, in the Poggendorff Illusion, was tested by varying oblique line orientation, interparallel line distance, and presence or absence of obliques. 20 subjects made estimates of the transverse extent on both a longitudinal and transverse extent. The results indicated that, although underestimation was found for some stimulus conditions, overestimation was found for others. It was argued that even though presence of obliques affected judgmental error the longitudinal-transverse illusion could not form a basis for the Poggendorff Illusion.     

Children's memory for line orientation: A reexamination of the “oblique effect”

A theory of orientation memory is advanced to explain why 5- and 6-year olds fail to discriminate between mirror-image obliques. It is argued that children can code the left-right orientation of an oblique line in relation to an adjacent reference feature, but are limited in their ability to recognize this stimulus-referent relationship when it is altered by changes in frame location. According to this view simultaneous presentation of the correct and incorrect comparison, typical of traditional testing paradigms, leads to failure because of trial by trial shifts in the frame location of the target orientation. The findings of the two experiments reported are consistent with this hypothesis. In Experiment 1 kindergarteners who performed poorly under the simultaneous condition discriminated oblique orientations with ease when stimuli were successively presented. Moreover, performance was not significantly affected by variations in the plane of presentation. In Experiment 2 children who discriminated successively presented obliques when stimuli were shown in a constant frame location had great difficulty when the left-right frame location of the stimuli was varied over trials.     

The Poggendorff illusion: consider all the angles

In the Poggendorff display, which consists of parallel lines interrupting a transversal, one of the two transversal segments was replaced by a dot lying along the parallel. The angle between the remaining transversal segment and the parallels was varied in 15 degree increments, as was the orientation of the transversal with respect to the subject. Subjects set the dot to appear collinear with the transversal. Judgmental errors can be partitioned into additive components, one linearly related to the size of the obtuse angle between transversal and parallels and the other a sinusoidal function of transversal and parallels and the other a sinusoidal function of transversal orientation (collinearity settings err toward the horizontal or vertical, whichever is closer), plus a meridional effect, an interaction term that magnifies the errors of a given obtuse angle as the transversal approaches an oblique orientation.     

Spatial coding and oblique discrimination by children

Children from five to eight years of age learned to discriminate between mirrorimage oblique lines more readily when cards bearing the obliques were presented vertically than when they were presented horizontally. The difference in performance between the vertical and horizontal planes could not be accounted for by differences in either the external visual context or the availability of asymmetrical body information (e.g., left vs right hand). The superiority of the vertical plane was attributed to the congruence of objective, bodily, and retinal vertical axes for the vertical, but not the horizontal plane, It was concluded, on this basis, that at least part of children's difficulty discriminating between mirror-image obliques is due to their difficulty establishing the internalized vertical axis necessary for the left-right spatial coding of the obliques.     

The Poggendorff illusion: Apparent misalignment which is not attributable to apparent orientation of the transversals

Subjects while looking down were required to adjust a horizontal field of parallel lines (Experiment I) or a single line (Experiment II) to the apparent sagittal direction with and without a superimposed rectangle in the centre of a circular field. The rectangle was tilted at 20, 30 or 40° to the parallels and at 20° to the line. For the 20° condition the parallel lines were apparently oriented at about half a degree compared with the field without a rectangle but in the direction opposite to that necessary to account for the Poggendorff misalignment effect. For the 30 and 40° conditions the lines did not change in apparent orientation. The orientation of the single line did not change. Almost all subjects readily reported an apparent misalignment between the collinear parallels and line separated by the oblique rectangle. It is concluded that the Poggendorff misalignment illusion occurs without apparent regression of the lines to right angles with the figure.     

Why do children confuse mirror-image obliques?

Thirty-five children aged from 4.17 to 6.58 years were given a delayed-matching task in which they had to choose on each trial which of two lines was the same as a previously displayed standard line. Their choices were no better than random when the lines differed in degree of slope but not in left-right orientation and were only marginally more accurate when the lines were left-right mirror images. Performance improved significantly when the lines differed both in degree of slope from the vertical and in left-right orientation and improved still further if at least one of the lines was horizontal or vertical. The results suggest that young children have extreme difficulty encoding in memory either the degree of slope or the left-right orientation of an oblique line.