Three-space inference from two-space stimulation

Further Empirical Evidence on Patrick Hughes' Reverspectives: A Pilot Study

Reverspectives are paintings created by the English artist Patrick Hughes. They are 3D structures, for example, pyramids or prisms, which elicit an illusory depth perception that corresponds to the reverse of the physical depth layout. Rogers and Gyani state that “the perspective information provided by a simple grid of vertical and horizontal lines on a slanting surface can be just as powerful as the information provided by a rich, naturalistic scene”. The present experiment was aimed to further investigate this perspective reversal. Three independent variables were manipulated: (1) texture components (i.e., vertical, horizontal, and oblique lines components), (2) texture spatial arrangement (i.e., Hughes-type “perspective” grid vs. equidistant “no perspective” grid), and (3) illumination direction (i.e., homogeneous illumination, light from above, and light from below). The dependent variable was the “critical distance”, namely, the distance between an approaching observer and the stimulus at which the illusory depth perception of concavity/convexity switched to the actual perception of convexity/concavity. The results showed that a stronger illusion is elicited by: (a) a Hughes-type texture spatial arrangement; (b) a complete grid texture composition, having both vertical and horizontal, and oblique components; and (c) illumination from below, as opposed to the condition in which light is coming from above.

Perspectival reversals of a solid: a phenomenal description

The paper presents a phenomenal investigation of monocular perception of perspectival reversal of a conical shell. The inverted shell is seen as shorter than the stimulus, and both relative size of elements within it and movement within it appear to be affected by reversal. Similarity of the observed effects to those recorded in studies of afterimages are noted, as is similarity to reversals of Mach's Book.

Spatial judgments in the horizontal and vertical planes from different vantage points

Todorović (2008 Perception 37 106-125) reported that there are systematic errors in the perception of 3-D space when viewing 2-D linear perspective drawings depending on the observer's vantage point. Because these findings were restricted to the horizontal plane, the current study was designed to determine the nature of these errors in the vertical plane. Participants viewed an image containing multiple colonnades aligned on parallel converging lines receding to a vanishing point. They were asked to judge where, in the physical room, the next column should be placed. The results support Todorović in that systematic deviations in the spatial judgments depended on vantage point for both the horizontal and vertical planes. However, there are also marked differences between the two planes. While judgments in both planes failed to compensate adequately for the vantage-point shift, the vertical plane induced greater distortions of the stimulus image itself within each vantage point.

Alignment with the horizontal plane: evidence for an orientation constraint in the perception of shape

In order to convert a 2-D image to a 3-D percept, the visual system must apply constraints that maximize the chances that the result will be unique and veridical. Previously proposed constraints include one that maximizes the symmetry of the percept, and one that maximizes its compactness (Li et al, 2009 Vision Research 49 979-991). Analysis of the 3-D percepts elicited by certain 2-D forms suggests the action of an additional constraint, favoring the alignment of the surfaces and/or axis of symmetry of the perceived object with the horizontal plane.

Is pictorial perception robust? The effect of the observer vantage point on the perceived depth structure of linear-perspective images

Every image of a scene produced in accord with the rules of linear perspective has an associated projection centre. Only if observed from that position does the image provide the stimulus which is equivalent to the one provided by the original scene. According to the perspective-transformation hypothesis, observing the image from other vantage points should result in specific transformations of the structure of the conveyed scene, whereas according to the vantage-point compensation hypothesis it should have little effect. Geometrical analyses illustrating the transformation theory are presented. An experiment is reported to confront the two theories. The results provide little support for the compensation theory and are generally in accord with the transformation theory, but also show systematic deviations from it, possibly due to cue conflict and asymmetry of visual angles.

The perception of surface folding in static and animated displays

How do we interpret outline drawings of surfaces? Although pictorial depictions are projectively ambiguous, observers demonstrate definite preferences of interpretation. Additionally, they commit typical errors. A study is reported of one specific arrangement of surfaces as it is represented in outline drawings, namely the arrangement that results when two arbitrary surfaces are joined at a common edge to form an angle in 3-D ('phenomenic folding'). With some of these arrangements, observers report that the angle formed by the two surfaces is zero (complete folding). With others, they report that the angles are greater than zero (incomplete folding). Both interpretations are actually valid. Several investigators have proposed that observer preferences such as these are due t a tendency to prefer a 3-D interpretation that will make the depicted 3-D shape regular. Three experiments were performed to test this regularisation hypothesis. In the first, observers were shown pairs of four-sided polygons joined at one equal side. Their task was to imagine how the smaller polygon could be folded completely towards the larger, and, subsequently, to report on its position after the ('mental folding'). Reported positions were consistent with 3-D interpretations that caused figural regularisations, In the second and third experiments, observers were shown drawings of diamonds and parallelograms folded along a number of differently positioned and oriented segment ('folding edge'). Their task was to estimate verbally the extent of the dihedral angle formed by the two surfaces. Results indicated that the perception of incomplete folding is determined by 3-D interpretation of the orientation of the drawing with respect of the picture plane. In a fourth experiment, observers were asked whether projective equivalences might be disambiguated by animating two kinds of displays that yield the 'incomplete folding' effect but that should be distinguishable on the basis of the trajectories of the vertexes of the folding parts. Results demonstrated that even in these conditions observers are unable to interpret the foldings correctly. These results might be taken to indicate that projective, static information leading to a simpler and more regular interpretation of the display can prevail over explicit motion information that should force the system to achieve a nonregular solution.

The depiction of distance: a Bartelian analysis

Work by Bartel has shown that observers make systematic errors when attempting to set a receding row of staves at equal intervals, and make even-more-pronounced errors in the same direction when drawing a similar row; consequently, the factors that contribute to this systematic distortion in spatial representation were examined. The results indicate that the tendency to overestimate nearer distances and underestimate further distances in pictorial space may be enhanced both by increasing the size ratio of the nearest and furthest pictorial elements and by increasing the angle of convergence of represented parallel contours. However, it is clear that size ratio is the more powerful independent variable. The reasons for this discrepancy are discussed and an explanation of the pattern of pictorial distortion, in terms of a compromise between an objective representation of the relative estimated distance of the depicted distances and an inaccurately anticipated optical projection, is proffered.

Viewing angle and the perceived orientation of pictorial elements: geometric or representational effects?

The role of geometric shape properties in determining the perceived orientation (heading) change of picture elements was investigated in four experiments. In experiment 1 the systematic change in perceived heading of each of a depicted team of horses which projected irregular geometric shapes was measured. In experiment 2, involving silhouettes, the perceptual axes of these same horse shapes, together with those of a pair of enantiomorphic deltoid shapes, were derived. These derived shape axes were used in experiment 3, along with single oblique contours, to determine the degree of heading shift as a function of the complexity and orientation of the shape. The degree of heading shift was remarkably similar for both silhouette shapes and the single contours when the axes were oblique but, whereas vertical orientation was predicted to abolish heading shift, this was only true for the deltoid shapes. In experiment 4 a possible explanation of the nonpredicted heading shift for the vertically oriented horse silhouettes was investigated. Subjects' individual estimates of the axes of the horse shapes, rather than a group mean value, were used to set the horse shapes to the vertical. When viewing was from two positions no significant heading change with view was found. Taken as a whole the data suggest that the geometric properties of patterns, rather than their representative nature, determine the very obvious heading shift when pictures are viewed from different angles.

The frame turns also: factors in differential rotation in pictures

When pictures of simple shapes (square, diamond) were seen frontally and obliquely, (1) the shapes with a deeper extent into pictured space underwent more rotation (Goldstein, 1979), which is an apparent turning to keep an orientation toward an observer's changing position; (2) there was little effect of whether the observer knew the picture surface's orientation in real space, except that such knowledge could prevent multistability; and (3) depicted picture frames also rotated. In other experiments, figural and frame rotations were independent of each other, and rotation was shown for real frames. The rotation of depthless depictions suggests that at least two rotational factors exist, one that involves the object's virtual depth and one that does not. The nature of this second factor is discussed. Frame rotation appeared to subtract from object rotation when the two were being compared; this could explain a paradox in picture perception: Depicted orientations often seem little changed over viewpoints, despite (apparent) rotations with respect to real-space coordinates.