The wallpaper illusion explained

Abstract

In the wallpaper illusion, a repetitive pattern appears to shift from one depth plane to the plane nearest fixation. We measured the timing of this shift for a 6 degrees wide, 3-cpd sinusoidal grating presented in a rectangular envelope; the edges (envelope) of the grating were presented at 20 arcmin of disparity (one period) behind the fixation plane. We asked observers to signal when the segment appeared to move from the edge plane forward to the fixation plane. Initially, the shift from the edge plane took 4-6 s, but after many trials, the shift became faster. Additional experiments demonstrated that the envelope was adapting, thereby permitting the alternative match. Our measurements for a range of spatial frequencies and disparities showed that these shifts to the fixation plane occurred only if the envelope disparity was more than one-half period of the carrier; that is, phase disparity >180 degrees. We also found that stereoacuity for the initial envelope-based match was poor, as might be expected for a target presented far off the fixation plane. However, once the perceived shift in depth occurred, stereoacuity improved fivefold without any change in the physical stimulus. We speculate that access to the most sensitive V1 neurons depends on the extrastriate processes that determine perceived depth--in this case, second-order envelope mechanisms.

Figure 1

Diagram of wallpaper illusion demonstrating the new matching solution produced by convergence on a point in front of a repetitive pattern—in this example, a sinusoidal grating segment.

Figure 2

Average time taken for the apparent shift forward from the plane defined by the grating edges (uncrossed disparity of 20 arcmin) to the fixation plane for sequential blocks of 10 trials. The 3-cpd grating segment was 6° wide and 2° high and presented at 50% contrast. The time to shift decreased over blocks for all four observers. Note the difference in the y-axis scale for the upper and lower graphs.

Figure 3

Average time to shift for sequential blocks of five trials. After four blocks (20 trials), the 6°-wide, 3-cpd grating segment was repositioned laterally to the right or to the left. Edge disparity = 20 arcmin; contrast = 50%. Blue curve shows lateral shift right two periods after 20 trials, then left four periods after 40 trials. Red curve shows lateral shift right one period, then left two periods. Arrows show block when shift occurred.

Figure 4

Average time to shift for sequential blocks of 10 trials. The 3-cpd grating segment was 6° wide and 2° high and presented at 50% contrast. Blue squares: data taken from Figure 2; red circles: data for shift times after prolonged adaptation to large counter-phasing box of the same dimensions and disparity as test grating. Note scale differences between top and lower two graphs.

Figure 5

Left graphs: Average time taken for the apparent shift from the edge plane to an alternate matching plane as a function of edge disparity for four different spatial frequencies. Negative values = crossed disparity. Right graphs: Data transformed into disparity phase angle. The transformed data show that the time to shift depends on the strength of the competing match as defined by phase disparity. Each point based on a minimum of 25 trials.

Figure 6

Diagram of potential matching planes for grating segment, with each dash space representing one period. The number of periods matched is symmetrically arranged around the edge plane.

Figure 7

Average time to shift as a function of the width of the 3-cpd grating segment. Edges (envelope) of grating are presented at 20 arcmin uncrossed disparity (one period of the grating segment). Red point: 3-cpd grating, 1° wide, presented at 40 arcmin uncrossed disparity (two periods back). Twenty-five trials per point.

Figure 8

Diagram of experimental setup for measuring stereoacuity. The left side of the figure shows the stimulus arrangement for the three stereoacuity measurements. In Panel A, the grating edges and the probe are centered on the fixation plane. In Panel B, the grating edges are 20 arcmin (one period) behind the fixation plane, but the probe is centered on the fixation plane. In Panel C, the stimulus arrangements are identical to Panel B, but the observer waits until grating shifts forward to initiate a trial. The right side shows of the timing of the onset and offset of three features in the stimulus: fixation point (not drawn), grating segment, and test probe. The timing for Configurations A and B is diagrammed in Panel D; timing for Configuration C is shown in Panel E. Note that the onset of the probe occurs 500 ms after the fixation point has disappeared for all three configurations; probe duration = 200 ms. Grating spatial frequency = 3 cpd; contrast = 50%.

Figure 9

Disparity thresholds for the three stimulus configurations shown in Figure 8. Data for three observers.