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.     

Figure embeddedness depends on contour orientation

The “oblique effect” was studied using an embedded figures task in which complex patterns and hidden forms were rotated into different orientations. One set of stimuli (Series I) used patterns consisting either entirely of depending on rotation) horizontal and vertical line segments or entirely of obliques. A second set of stimuli (Series II) used patterns composed of horizontal, vertical, and oblique segments in equal proportions. With Series I, both form and complex pattern orientations changed with rotation. In Series II, rotation changed the orientation of the hidden forms, but not the relative proportion of contour orientations in the complex patterns. Significantly longer search times were required to find forms embedded within the obliquely oriented patterns of Series I. There were no significant differences in Series II. These results are discussed in terms of the role contextual contours may play in the detection of differently oriented form.     

The spacing illusion: a spatial aperture problem?

A geometrical illusion in which the horizontal spacing between adjacent parallel lines in a row is underestimated when the lines are tilted away from vertical in a chevron configuration was investigated in two experiments. The perceived spacing was found to decrease as the tilt angle increased, consistent with the idea that separation judgements are influenced by the normal spacing between lines ie at right angles to the line orientation. It is proposed that this illusion reveals an analogue in spatial perception to the well-known aperture problem in motion perception. In establishing the separation of nearby or overlapping shapes in an image, the visual system cannot only rely upon the normal separation of contours belonging to each shape (as would be visible through small spatial apertures or receptive fields), since this varies with contour orientation. The system is therefore faced with a spatial aperture problem. The spacing illusion may arise because information usually available to solve the problem is absent in the illusion figure, or it may reflect a bias in favour of the orthogonal, which is adopted in the face of the ambiguity.     

Effects of surface markings on judgments of motion direction

The effects of surface markings on perceived motion direction were examined for a rotating sphere in a structure-from-motion display. The markings were dot patterns representing separate line segments or intersecting line segments (crosses) covering the surface of the sphere. The orientation of the surface markings and their intersection angles affected the perceived direction of motion, suggesting that the markings were not interpreted as geodesics or planar cuts on the surface. The perceived direction of motion was biased towards the mean orientation of the markings over the visible area of the surface. A similar bias was observed for translating planar stimuli covered with crosses, suggesting that the bias is not specific to curved surfaces or motion in depth. The deviation between the simulated motion direction and the external horizontal and vertical axes also affected the perceived motion direction. These results suggest that the average orientation of surface contours with respect to an external reference frame influences the perceived direction of motion.     

Three-dimensional interpretation of quadrilaterals.

The three-dimensional interpretation of two-dimensional images was studied by using quadrilateral patterns, and some relationships between their structure, depth, and shape interpretations were analyzed under various viewing conditions. We defined rectangular and nonrectangular viewing conditions as follows: the viewing condition in which the quadrilateral, including parallel sides, could be a projection from a rectangle and the viewing condition in which it could not be so. For 9 subjects, 10 measurements were made in each experiment. Analysis showed that a pair of parallel sides of a quadrilateral were viewed as parallel to the viewer's forehead when the sides were horizontal in the image plane and were seen as slanting in depth if they were slanted in the image plane. The quadrilateral composed of parallel and nonparallel sides was perceived as rectangular when viewed with foveal vision even though under the nonrectangular viewing condition, if that viewing condition was not so different from the rectangular viewing condition. The quadrilateral did not appear to be rectangular when viewed in peripheral vision even though the rectangular viewing condition was used.     

Displacement of the path of perceived movement by intersection with static contours

Observation of a moving dot gives rise to a perceived movement path, which has properties similar to those of real contours. If the dot crosses a line inclined to a horizontal direction of movement, it appears to undergo a vertical displacement. This displacement was found to be greatest for a line orientation of around 15° with respect to the movement. At other relative orientations, the size of the perceived displacement varied in the same manner as the perceived expansion of angles formed by intersection between static contours. Movement path distortions were measured with background fields like those that produce the Hering and Zöllner illusions with continuous lines. Illusory displacements of perceived movement were found to be equivalent to the static forms. The subjective contour formed by observation of movement can therefore give rise to illusions similar to those obtained with real lines.     

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.     

Perception of the head transversal plane and the subjective horizontal during gondola centrifugation

The subjective visual horizontal (SVH) and the subjective head transversal plane (STP) were measured by means of an adjustable luminous line in darkness during centrifuging. Subjects (N = 10) were seated upright, facing forward in a swing-out gondola. After acceleration of the centrifuge to 2G (vectorial sum of the earth's gravity and the centrifugal force; gondola inclination 60 degrees), subjects had to set the line either so that it was perceived as gravitoinertially horizontal (SVH) or so that it was perceived as parallel with the transversal ("horizontal") plane of the head (STP). Initially after acceleration, the SVH was tilted with respect to the gravitoinertial horizontal of the gondola (M = 16.6 degrees). This tilt was compensatory with respect to the gondola inclination. However, the STP was tilted in the opposite direction (M = 12.4 degrees), which might suggest a vestibular-induced distortion of the mental representation of one's own body. Similar results were obtained when measuring the subjective visual vertical (SVV) and the subjective midsagittal plane (SSP) in 5 subjects. The perceived roll angle (obtained as SVH-STP or SVV-SSP) was considerably larger than had previously been reported. Time constants for exponential decay of the tilt of the SVH or SVV were often 2-3 min, indicating a memory for semicircular canal information on changes in head orientation--a position-storage mechanism.     

Perceived path of oblique motion: horizontal-vertical and stimulus-orientation effects

Subjects adjusted the path of moving stimuli to produce apparent slopes of 45 degrees with respect to horizontal. The stimulus was either a single moving dot or a vertical or horizontal bar. In separate experiments either the stimuli were tracked or fixation was maintained on a stationary fixation target positioned 8 deg to the right of the center of stimulus motion. In both experiments the selected path slopes were in general more horizontal than 45 degrees. This pattern indicates that subjects overestimate the vertical component of motion along an oblique path, and is interpreted as a manifestation of the spatial anisometropy generally termed the 'horizontal-vertical illusion'. Additionally, paths selected for horizontal bars were more vertical than those for vertical bars. This finding is interpreted in the context of a previous report of the influence of stimulus orientation on perceived velocity.     

On a changing perspective illusion within Vermeer's The Music Lesson

The effect of line of sight on the perception of spatial configuration has been investigated in a well-known painting (The Music Lesson by Vermeer) and in two control patterns. In experiment 1, subjects indicated the perceived inclination of two major contours which defined the sidewall-floor and backwall-floor joints in (i) a projected image of the painting, (ii) a three-line representation of the major spatial elements of the painting, and (iii) a three-dimensional wire model of these same contours, when standing in each of eighteen positions on a line running parallel to the surface of the screen. Results indicated a significant change in the perception of the sidewall-floor, but not of the backwall-floor contour, as viewing angle changed, in both the painting and the three-line representation. However, the angular setting in the latter case was significantly less than when the painting was used, ie subjects underestimated the depicted inclination. Settings for the wire model did not deviate with viewing angle and reflected geometrically correct adjustments. In experiment 2, the results of experiment 1 were confirmed using enantiomorphs. These findings are discussed in the light of other view-dependent illusions in paintings.     

The role of the centre of projection in the estimation of slant from texture of planar surfaces

Displays were presented consisting of a perspective projection of a regular square grid, made up of vertical and horizontal equally spaced white lines, that was slanted in depth. The surface was viewed monocularly, through a circular aperture. A range of slants was shown (0 degree, 10 degrees, 20 degrees, 30 degrees, 40 degrees, 50 degrees, or 60 degrees) and the observers' task was to match the slant by means of a mouse-driven probe. The viewing distance (50, 75, or 100 cm) as well as the focal distance (25, 50, 75, 100, or 125 cm) were varied. We expected the estimation error to be smallest when the viewing distance and the focal distance coincided. This was not the case. Instead, subjects seemed to use the perspective deformation of the texture elements in the stimulus display to make a slant estimation, regardless of the specific combination of viewing distance and focal distance.     

Angular induction as a function of contact and target orientation

The Poggendorff effect is seen as misalignment of two obliques, or misprojection of one, when the obliques are placed outside a set of parallel lines. To understand better the mechanisms behind this effect, the orientation of the lines which are normally parallel was systematically manipulated. The results indicate that projection bias is affected by the orientation of either line, is at a minimum where the line is orthogonal to the oblique, and is maximal at small angles. This is in line with classic theories which attribute the illusion to misperception of angular size. However, such explanations presuppose that in order to be effective the induction line must be proximal to the oblique so that an angle can be formed. Results are reported which show that the angle formed by the oblique and a line placed at a distance from the oblique, serving as the target of the projection, follows an angular rule of effectiveness similar to what is seen when the line is placed directly in contact with the oblique. The underlying process is described as 'angular induction'.     

Perceived spatial organization of cutaneous patterns on surfaces of the human body in various positions

The perceived spatial organization of cutaneous patterns was examined in three experiments. People identified letters or numbers traced on surfaces of their body when the relative spatial orientations and positions of the body surfaces and of the stimuli were varied. Stimuli on the front or back of the head were perceived with respect to a frame of reference positioned behind those surfaces, independent of the surfaces' position and orientation. This independence may relate to the way in which the sensory apparatus on the front of the head is used in planning action. Stimuli on other surfaces of the head and body were perceived in relation to the position and orientation of the surface with respect to the whole body or trunk (most of which was usually upright). Stimuli on all transverse/horizontal surfaces were perceived with respect to frames of reference associated with the head/upper chest area. These frames were also used for stimuli on frontoparallel surfaces in front of the upper body. These observations may result from the use of "central" frames of reference that are independent of the head and are associated with the upper body. Stimuli on surfaces in other positions and orientations (with two exceptions) were perceived "externally"--that is, in frames of reference directly facing the stimulated surface. The spatial information processing we found may be fairly general because several of our main findings were also observed in very young children and blind adults and in paradigms studying perception by "active touch" and the spatial organization of the motor production of patterns.     

Spatial orientation from optic flow in the central visual field

Previous research has shown that stimulation of the central visual field with radial flow patterns (produced by forward motion) can induce perceived self-motion, but has failed to demonstrate effects on postural stability of either radial flow patterns or lamellar flow patterns (produced by horizontal translation) in the central visual field. The present study examined the effects of lamellar and radial flow on postural stability when stimulation was restricted to the central visual field. Displays simulating observer motion through a volume of randomly positioned points were observed binocularly through a window that limited the field of view to 15 degrees. The velocity of each display varied according to the sum of four sine functions of prime frequencies. Changes in posture were used to measure changes in perceived spatial orientation. A frequency analysis of postural sway indicated that increased sway occurred at the frequencies of motion simulated in the display for both lamellar and radial flow. These results suggest that both radial and lamellar optic flow are effective for determining spatial orientation when stimulation is limited to the central visual field.     

The orientation of a parallel-line texture between the verticals can modify the strength of the Poggendorff illusion.

In the present experiments, we attempted to evaluate the modification of the strength of the Poggendorff illusion as a function of the different orientation of a parallel-line texture filling the space between the vertical lines. In Experiment 1, the standard version of the Poggendorff configuration was tested against four different parallel-line textures oriented at 0 degrees, 45 degrees, 90 degrees, and 135 degrees with respect to the obliques. The results showed that the illusory effect was a linear function of the progressive discrepancy between the angle of the lines of the texture and that of the obliques. In Experiment 2, we tested the same textures used in Experiment 1 after the elimination of the two vertical lines. The data obtained approximated a linear function, as in the previous experiment, but the alignment errors were consistently lower. The statistical analysis performed on the data of all eight experimental conditions shows that both factors--texture and presence/absence of verticals--were significant, but most of the effect was due to the texture factor. The results may be interpreted through the "perceptual compromise hypothesis," originally proposed for the bisection forms of the Poggendorff illusion, but with important modifications. The data are also discussed in terms of their implications for other theories proposed for the Poggendorff illusion.     

Measurement and modelling of perceived slant in surfaces represented by freely viewed line drawings

Simple pictures under everyday viewing conditions evoke impressions of surfaces oriented in depth. These impressions have been studied by measuring the slants of perceived surfaces, with probes (rotating arrowheads) designed to respect the distinctive character of depicted scenes. Converging arguments indicated that the perceived orientation of the probes was near theoretical values. A series of experiments showed that subjects formed well-defined impressions of depicted surface orientation. The literature suggests that perceived objects might be 'flattened', but that was not the general rule. Instead, both mean slant and uncertainty fitted models in which slant estimates are derived in a relatively straightforward way from local relations in the picture. Simplifying pictures tended to make orientation estimates less certain, particularly away from the natural anchor points (vertical and horizontal). The shape of the object affected all aspects of the observed-object/percept relationship. Individual differences were large, and suggest that different individuals used different relationships as a basis for their estimates. Overall, data suggest that everyday picture perception is strongly selective and weakly integrative. In particular, depicted slant is estimated by finding a picture feature which will be strongly related to it if the object contains a particular regularity, not by additive integration of evidence from multiple directly and indirectly relevant sources.     

Contour symmetry detection: the influence of axis orientation and number of objects

Participants discriminated symmetrical from random contours connected by straight lines to form part of one- or two-objects. In experiment one, symmetrical contours were translated or reflected and presented at vertical, horizontal, and oblique axis orientations with orientation constant within blocks. Translated two-object contours were detected more easily than one, replicating a "lock-and-key" effect obtained previously for vertical orientations only [M. Bertamini, J.D. Friedenberg, M. Kubovy, Acta Psychologica, 95 (1997) 119-140]. A second experiment extended these results to a wider variety of axis orientations under mixed block conditions. The pattern of performance for translation and reflection at different orientations corresponded in both experiments, suggesting that orientation is processed similarly in the detection of these symmetries.     

Judgments of visually perceived eye level (VPEL) in outdoor scenes: effects of slope and height

When one looks up a hill from below, its peak appears lower than it is; when one looks at a hill across a valley from another peak, the peak of that hill appears higher than it is. These illusions have sometimes been explained by assuming that the subjective horizontal is assimilated to the nearby slope: when looking up a slope, the subjective horizontal is raised, diminishing the height of the peak above the subjective horizontal, and making the peak appear lower than it is. When looking down a slope towards another hill, the subjective horizontal is lowered, increasing the height of that hill above the subjective horizontal, and making its peak appear higher than it is. To determine subjective horizontals we measured visually perceived eye levels (VPELs) in 21 real-world scenes on a range of slopes. We found that VPEL indeed assimilates by about 40% to slopes between 7 degrees downhill and 7 degrees uphill. For larger uphill slopes up to 23 degrees, VPEL asymptotes at about 4.5 degrees. For larger downhill slopes, the assimilation of VPEL diminishes, and at 23 degrees is raised by about 1 degree. These results are consistent with the assimilation explanation of the illusions if we assume that steep downhill slopes lose their effectiveness by being out of view. We also found that VPEL was raised when viewing from a height, in comparison with ground-level views, perhaps because the perceived slope increases with viewing height.