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Huseyin Boyaci, Laurence T. Maloney; Binocular perception of shape from shading/contour is invariant under ordinal transformations of image intensities. Journal of Vision 2002;2(7):309. doi: 10.1167/2.7.309.
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How light interacts with a matte surface depends on the material structure of the surface, notably its roughness (Nayar & Oren, 1995, Science, 267, 1153). This dependence complicates the recovery of shape from shading since visual image intensities depend on not only object shape and lighting model, but also on the (unknown) surface material. A possible solution is to base shape reconstruction primarily on the (local) ordering of intensities in the visual image. Todd & Reichel (1989, Psychol Rev, 96, 643), among others, have suggested that human visual estimation of shape from shading in achromatic scenes depends primarily on this ordering information (and should, therefore, be insensitive to non-linear transformations of image intensity that preserve intensity order). We test this hypothesis for binocular shape from shading/contour.
Experiment 1: We rendered stereo image pairs of scenes each containing one of ten achromatic matte ellipsoids differing in shape. We transformed the normalized image intensities in both images of each stereo pair by a common power function with coefficient 0.75 or 1.25. Four observers viewed each of the twenty resulting stereo pairs in a Wheatstone stereoscope and estimated the surface orientation at one pre-selected point on each ellipsoid by adjusting a monocular gradient probe. Each setting was repeated 10 times. The order of presentation was randomized. We compared the gradient settings at corresponding points on each ellipsoid when the coefficient was 0.75 and when the coefficient was 1.25. We found no significant effect of transformation on observers' judgments of gradient.
Experiment 2: We repeated Experiment 1 with more extreme power transformations (0.5,1.5). Three observers participated. We again found no discernible effect of these transformations. Our findings are consistent with the claim that human observers use only the order of luminance values in binocular shape from shading and contour.
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