An optimal linear system for integrating visual cues to 3D surface geometry weights cues in inverse proportion to their uncertainty. The problem of integrating texture and stereo information for judgments of planar surface slant provides a strong test of optimality in human perception. Since the accuracy of slant from texture judgments changes by an order of magnitude from low to high slants, optimality predicts corresponding changes in cue weights as a function of surface slant. Furthermore, since humans show significant individual differences in their abilities to use both texture and stereo information for judgments of 3D surface geometry, the problem admits the stronger test that individual differences in subjects' thresholds for discriminating slant from the individual cues should predict individual differences in cue weights. We tested both predictions by measuring slant discrimination thresholds and stereo/texture cue weights as a function of surface slant for multiple subjects. The results bear out both predictions of optimality, with the exception of an apparent slight under-weighting of texture information. This may be accounted for by factors specific to the stimuli used to isolate stereo information in the experiments. Taken together, the results are consistent with the hypothesis that humans optimally combine the two cues to surface slant, with cue weights proportional to the subjective reliability of the cues.

In most models of heading from optic flow a rigid environment is assumed, yet humans often navigate in the presence of independently moving objects. Simple spatial pooling of the flow field would yield systematic heading errors. Alternatively, moving objects could be segmented on the basis of relative motion, dynamic occlusion, or inconsistency with the global flow, and heading determined from the background flow. Displays simulated observer translation toward a frontal random-dot plane, with a 10 deg square moving independently in depth. The path of motion of the object was varied to create a secondary focus of expansion (FOE') 6 deg to the right or left of the actual heading point (FOE), which could bias the perceived heading. There was no effect when the FOE was visible, but when the object moved in front of it, perceived heading was biased toward the FOE' by approximately 1.9 degrees with a transparent object, and approximately 3.4 degrees with an opaque object. The results indicate that scene segmentation does not occur prior to heading estimation, which is consistent with spatial pooling weighted near the FOE. A simple template model based on large-field, center-weighted expansion units accounts for the data. This may actually represent an adaptive solution for navigation with respect to obstacles on the path ahead.

How visual feedback contributes to the on-line control of fast reaching movements is still a matter of considerable debate. Whether feedback is used continuously throughout movements or only in the "slow" end-phases of movements remains an open question. In order to resolve this question, we applied a perturbation technique to measure the influence of visual feedback from the hand at different times during reaching movements. Subjects reached to touch targets in a virtual 3D space, with visual feedback provided by a small virtual sphere that moved with a subject's fingertip. Small random perturbations were applied to the position of the virtual fingertip at two different points in the movement, either at 25% or 50% of the total movement extent. Despite the fact that subjects were unaware of the perturbations, their hand trajectories showed smooth and accurate corrections. Detectable responses were observed within an average of 160 ms after perturbations, and as early as 60% of the distance to the target. Response latencies were constant across different perturbation times and movement speed conditions, suggesting that a fixed sensori-motor delay is the limiting factor. The results provide direct evidence that the human brain uses visual feedback from the hand in a continuous fashion to guide fast reaching movements throughout their extent.