Topological perception: Holes in an experiment

Chen (1982) reported three experiments to support his claim that a primitive function of visual systems is to extract the topological structure of objects (for example, connectedness, closedness, and number of holes). Chen's result was later synopsized for a large readership.' Here we reinterpret one of Chen's three experiments and comment on the other two. After successfully replicating Chen's first result, we added a condition in which we controlled for luminous flux. Data from our control condition suggest that Chen's findings were due to a confounding of luminous flux with topological factors. In Chen's first experiment, subjects were simultaneously shown a pair of figures and asked to respond "same" or "different." (The correct answer was always "different. ' ') Chen found that, under near-threshold conditions, a pair of topologically distinct figures (diskannulus) was more discriminable than pairs of topologically identical but geometrically distinct' figures (disksquare; disk-triangle). Chen concluded that the greater discriminability of the topologically distinct pair was due to the visual system's sensitivity to topological structure." However, the topological distinction was conflated with disparities in the luminous flux differences between the two figures of each pair. Indeed, the greater the flux difference, the better the discrimination. 4 To claim a visual sensitivity to topological properties, a pair of figures of different topology but identical flux must be shown to be highlydiscriminable in an experimental situation similar to Chen's. In an attempt to replicate Chen's results, we added such a control pair (Figure la). The black area of the annulus is identical to the black area of the topologically distinct disk-with-two-holes. Two other stimulus pairs (Figures lc and ld) are similar to Chen's. A fourth case, annulus-horseshoe (Figure lb), was added because it was topologically equivalent to the disk-annulus pair, yet had only a small (within-pair) difference in luminous flux. S Following Chen, we used 5-msec tachistoscopic presentation of the stimuli. Our displays closely matched Chen's in visual angle subtended." With five naive subjects, we replicated Chen's finding that discriminability of the diskannulus pair was significantly greater than that of the disksquare [t(4) = 2.9, P < .025V However, the control