by Joseph L Brooks, Kevin Lai,
and Stephen Palmer
Palmer Perception Laboratory
University of California, Berkeley
We investigated a size illusion first reported by Kanizsa (1979) in which a figure bounded by an occluding edge looks larger than the same figure not bounded by an occluder. We call this phenomenon an occlusion illusion. We conducted a series of experiments to document the magnitude of this illusion and distinguish between two hypotheses about its perceptual basis. The size-distance relation (Emmert's Law) predicts that the farther of two objects with equally-sized retinal projections should be seen as larger. Because occlusion implies relative distance order, the size-distance relation serves as one explanation of the occlusion illusion. Alternatively, the illusion may reflect an extension of the occluded surface at the occluding border without a uniform increase in the perceived size of the figure. The distinctive prediction between these two theories is whether the occlusion illusion reflects a change in the overall size of the figure (size-distance theory) or a shape change in which the occluded edges perceptually extend beyond their intersection points with the occluder. This extension would form a greater area of a slightly different shape. To test this, we first used a staircase procedure to measure the magnitude of the occlusion illusion under various occlusion conditions and various occluding and occluded shapes. We found that the strength of the illusion varied with the strength of the cue to occlusion. In a second experiment we specifically addressed the two hypotheses about the origin of the illusion. In the first phase of this experiment each participant completed two staircase procedures. One staircase measured the point of subjective equality (PSE) for the overall size of the figure in comparison to the partially-occluded figure. The other staircase measured the PSE for extension of the edges beyond their intersection points with the occluder. The two figures representing the PSEs for each of these procedures were then compared to the partially occluded figure showing the illusion. Participants were significantly more likely to judge the figure with the extended edges as more similar to the example of the illusion. This suggests that the occlusion illusion includes a modal extension of edges that intersect with an occluding object.
In this example of the occlusion illusion, the partially occluded semi-circle in the upper-left corner should appear larger than the semi-circle in the lower-right corner. Both semi-circles are the same size.
To demonstrate that the illusion is dependent on the amount of evidence for occlusion, we have used three different occlusion conditions. On each trial, participants were shown two stimuli, one experimental stimulus as well as a reference stimulus that consisted of a semi-circle alone. They were asked to make a 2AFC judgement about whether the lone semi-circle or the experimental stimulus one appeared larger. Condition A shows the classic occlusion illusion in which the semi-circle appears to be the visible portion of a circle occluded by a square. Condition B shows a condition that we called "in front" because it appears that the semi-circle is on top of the square. In this case, the semi-circle does not appear to be occluded and does not show evidence of the illusion. Condition C was the final condition. We called this condition "on" because to many observers the semi-circle appeared to be laying on the rectangle. These participants showed no evidence of the occlusion illusion in their size judgements. However, a subset of participants said that they saw this stimulus as a circle inserted into a slit on the surface of the rectangle. In this case, the circle would be partially occluded by the rectangle. Consistently, their size responses showed evidence of the occlusion illusion effect. These results show that evidence for occlusion produces the occlusion illusion effect.
|Condition A||Condition B||Condition C|
Although our results above make it clear that the illusion is produced by information about occlusion, it does not inform us which mechanism (of those named above) is at work. That is, does the size illusion arise from the size-distance relation or is some line extension mechanism giving rise to a modal perception of some of the occluded space? In another experiment, each observer made judgements to find the point of subjective equality on two staircase. In one staircase, the overall size of the experimental semi-circle (the stimulus with an occluder present) was changed through a dilation until it appeared to be the same size as the reference semi-circle. In the other staircase, the experimental semi-circle was changed by extending the endpoints of the semi-circle. The point of subjective equality was found for both of these staircase. Then, the observer was asked to judge whether the extended version POS or the dilated POS was more similar to the reference semi-circle. Observers were significantly more likely to choose the extended version of the stimulus. This suggests that the contour extension mechanism plays a role in the occlusion illusion.
Updated: January, 19, 2004