This experiment investigates whether the effect persists following the manipulation o f the local brightness contrast effects observed in Figure 6.1. As noted earlier, the higher luminance gradient of the right-hand background sphere in Figure 6.1 contrasts sharply with the lower luminance gradient of the embedded central patch. Consequently, the lower part of the central patch appears brighter and, therefore, less curved than it actually is. The opposite relationship between the background sphere and patch on the left results
in the left central patch appearing more curved than it actually is. If, through some manipulation, this contrast-induced change in brightness was reversed for the stimuli on the right of Figure 6.1, one might expect that the illusion would be abolished - or even reversed.
Figure 6.6 shows such a manipulation. In this figure each background sphere has been replaced with a group of fifteen spherical patches identical in size to the test patch which they surround. The "surround" patches on the left o f Figure 6.6 are less curved than the test patches, while the surround patches on the right are more curved than the test patches. Following this manipulation, the contrast in luminance gradients o f the right test patch and its adjacent surround patches is now reversed. The top part o f the test patch is now adjacent to the darker area of the surround patch, while the bottom part is now adjacent to the brighter area of the surround patch. A similar brightness relationship can be observed for the test and surround patches on the left of Figure 6.6, although the contrast is not as strong. If local contrast-induced interactions are solely responsible for the occurrence of 3D curvature contrast, then one would expect the effect to either be removed or, alternatively, reversed following this manipulation. Furthermore, because the test and surround patches no longer overlap, but are spatially separated, any local interactions should be eliminated.
Subjects were tested using the above paradigm. The apertures bounding the test and surround patches had radii of 30 pixels (0.86cm). The mean curvature of the surround patches remained fixed at 0.81cm \ The curvature of the two groups of surround patches differed by either 0, 0.3, or 0.61cm^; thus the radii o f the left and right surround spheres
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F ig u re 6.6. An exam ple o f the stim uli used in experim ent sixteen. The background spheres used in the previous experim ents w ere replaced with tw o arrays o f spherical patches that w ere either m ore or less
curved than the patches being com pared. Subjects were asked to make curvature discrim ination
Judgem ents between the second and seventh patch in the third row from the top. In the above exam ple the array o f surrounding patches on the left have a curvature o f 0.5 cm ', the surrounding patches on the right have a curvature o f 1.1 cm ', and the tw o patches being discrim inated by subjects have a curvature o f .81 cm '. N ote that the local brightness contrast has been reversed, yet the spherical patch on the left appears m ore curved than that on the right.
varied from 1.24cm to 2cm and from 0.9cm to 1.24cm, respectively. As in the earlier experiments, the curvatures o f the two test patches were set with the constraint that their mean curvature was equal to the mean curvature of the surround patches. The patches were presented against a random grey-level noise background. Subjects were instructed to make curvature discrimination judgments between the second and seventh patch in the third row o f the array. The surround patches remained on the monitor throughout the experiment; the test patches were replaced by a random grey-level noise pattern between test stimuli presentations, thus making explicit to subjects the spatial location o f the patches being compared. Four psychometric functions were obtained from each subject for each of the three curvature-difference conditions above.
6.5.1 R esults. The results of experiment sixteen are shown in Figure 6.7. It is apparent from these results that, despite manipulating the local luminance contrasts in this way, varying the curvature of the surround patches has a measurable effect on subjects’ perceived curvature of the test patches. Note that the effect is in the same direction as the previous experiments. That is, when both test patches were of equal curvature, as in Figure 6.6, the left test patch appeared more curved than the right test patch.
The results obtained from experiment sixteen are compelling evidence that 3D curvature contrast cannot be explained simply in terms of local contrast-induced changes in brightness. However, it is possible that the persistence of the effect under the above manipulation may be explained in terms of either texture or spatial interactions in apparent contrast (Cannon & Fullenkamp, 1991; Cannon & Fullenkamp, 1993; Cannon & Fullenkamp, 1994; Chubb, Sperling & Solomon, 1989; Solomon, Chubb & Sperling,