Voluntarily controlled bi-stable slant perception of real and photographed surfaces

Abstract

We have quantified voluntarily selected perceived slant of real trapezoidal surfaces (a 'reverse-perspective' scene) and their photographed counterparts (pictorial space). The surfaces were slanted about the vertical axis and observers estimated slant relative to the frontal plane. We were particularly interested in those cases in which binocular disparity and monocular perspective provided conflicting slant information. We varied the monocularly and binocularly specified surface slants independently across stimulus presentations. To eliminate texture and shading cues we used sand-blasted aluminium trapezoidal surfaces illuminated from all directions. When disparity-specified slant and perspective-specified slant were conflicting, observers were able to perceive the surfaces in two ways: they perceived either a trapezoid or a rectangle. Our main finding is twofold. First, when subjects chose to perceive the trapezoid, the slant estimates followed the disparity-predicted slant with only a slight underestimation, as if they selected a pure binocular representation of slant governed only by disparity. Second, when subjects chose to perceive the rectangle their estimates for real surfaces were similar to those for photographed surfaces, as if they selected a representation of slant governed by perspective foreshortening.

Figure 1

The reverse-perspective phenomenon. (a) How to construct a 3D replica of a reverse-perspective scene. The main characteristic that makes reverse-perspective scenes attractive, both in art and in research, is that those scenes bring about a conflict between the depth specified by perspective and the depth specified by disparity. (b) An explanation of the foreshortening (linear perspective) of the portrayed door that specifies that the door’s right side is receding in depth. Because, in fact, the door’s right side is protruding the disparity-specified slant is opposite to the perspective-specified slant. The stereogram in (c) illustrates what observers perceive when viewing one panel of the 3D replica. After fusion of the stereogram two relatively stable percepts can be distinguished. In the first percept, the door recedes in depth with its right side further away (it is perceived as a normal slanted rectangular door). In the other percept, the left side of the door is further away (it is perceived in reverse perspective: as a trapezoidal door with the near-edge shorter than the far-edge). Each of the percepts can be selected and maintained at will in a relatively controlled way. When the left two images are being fused in a crossed way (or the right two images in an uncrossed way), perspective and disparity specify similar slants and the observer perceives a single stable slanted rectangular door with its right side further away. Adapted from the ‘Cloudy Doors’ 3D model of Wade and Hughes (http://www.perceptionweb.com/perc0999/wade.html) with the permission of the authors and Pion Limited, London.

Figure 2

The stimuli used. Each of the depicted stimuli is a sand-blasted aluminium trapezoid for a specific combination of foreshortening and disparity. Some of the stimuli are both slanted and a little rotated relative to the black table on which they are lying. This gives rise to the apparent deformations on this picture.

Figure 3

The geometry of reverse perspective. To create an aluminium trapezoid with disparity-specified slant and perspective-specified slant that differ from one another, we varied the stimulus heights and widths on its left (Hl, Wl) and right (Hr, Wr) sides. We show an example of a stimulus for which perspective specified zero slant (left column) under different disparity-specified slants (right column). We kept the horizontal visual angle that the trapezoid subtended (grey area) constant across stimuli. Note that this means that the Wl and the Wr of a stimulus are generally unequal.

Figure 4

Experimental set-up. (a) The illumination booth. The subject views the stimulus through an aperture while he/she matches the slant of the rotatable device that is visible on the foreground (b). The booth has a door that can be opened to enable the experimenter to place the stimuli in the booth (c). Note that the depicted trapezoid recedes in depth with its right side further away (c). In fact, its slant is 70°. However, the perspective-specified slant in (b) strongly indicates that the left side recedes in depth. In other words, we have here a reverse-perspective scene (compare with figure 1) under well-controlled visual conditions.

Figure 5

Data from experiments 1 and 2 for the subjects who completed both experiments. Perceived slant is plotted as a function of disparity-specified slant for a range of different perspective-specified slants. The trapezoid-shaped icons above the plots depict the perspective-specified slant. (a(i),b(i)) and ((a(ii),b(ii)) depict binocularly (filled symbols), and monocularly (open symbols) perceived slant, respectively. The slants that were geometrically present in the stimulus are represented by the dashed prediction lines. The data of experiment 1 are represented by the square and triangle symbols: subjects perceived either a slanted rectangular surface (squares) or a slanted trapezoid (triangles). The data of experiment 2 are represented by the diamond symbols: subjects perceived a slanted rectangular surface on the pictures. (a) The mean data of MS, NK and SV. (b) The mean data of GK and SP. Error bars, which are often smaller than the symbol, represent ±1 s.d. in the mean across the participating subjects.

Figure 6

Data from experiment 1 for subjects who did not participate in the pictorial slant estimation of experiment 2. The symbols and the error bars denote the same as in figure 5. (a) Both the mean binocular and the mean monocular data of subjects RR and TV. Their data resembles the data of MS, NK and SV depicted in figure 5a. (b) MK’s binocular data. Her slant estimations are hardly based upon disparity-specified slant.