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A number of models of depth-cue combination suggest that the final depth percept results from a weighted average of independent depth estimates based on the different cues available. The weight of each cue in such an average is thought to depend on the reliability of each cue. In principle, such a depth estimation could be statistically optimal in the sense of producing the minimum-variance unbiased estimator that can be constructed from the available information. Here we test such models by using visual and haptic depth information. Different texture types produce differences in slant-discrimination performance, thus providing a means for testing a reliability-sensitive cue-combination model with texture as one of the cues to slant. Our results show that the weights for the cues were generally sensitive to their reliability but fell short of statistically optimal combination-we find reliability-based reweighting but not statistically optimal cue combination.

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We measure the performance of five subjects in a two-alternative-forced-choice slant-discrimination task for differently textured planes. As textures we used uniform lattices, randomly displaced lattices, circles (polka dots), Voronoi tessellations, plaids, 1/f noise, "coherent" noise and a leopard skin-like texture. Our results show: (1) Improving performance with larger slants for all textures, (2) and some cases of "non-symmetrical" performance around a particular orientation. (3) For orientations sufficiently slanted, the different textures do not elicit major differences in performance, (4) while for orientations closer to the vertical plane there are marked differences among them. (5) These differences allow a rank-order of textures to be formed according to their "helpfulness"--that is, how easy the discrimination task is when a particular texture is mapped on the plane. Polka dots tend to allow the best slant discrimination performance, noise patterns the worst. Two additional experiments were conducted to test the generality of the obtained rank-order. First, the tilt of the planes was rotated by 90 degrees. Second, the task was changed to a slant report task via probe adjustment. The results of both control experiments confirmed the texture rank-order previously obtained. We then test a number of spatial-frequency-based slant-from-texture models and discuss their shortcomings in explaining our rank-order. Finally, we comment on the importance of these results for depth-perception research in general, and in particular the implications our results have for studies of cue combination (sensor fusion) using texture as one of the cues involved.