How does the visual system combine information from different depth cues to estimate three-dimensional scene parameters? We tested a maximum-likelihood estimation (MLE) model of cue combination for perspective (texture) and binocular disparity cues to surface slant. By factoring the reliability of each cue into the combination process, MLE provides more reliable estimates of slant than would be available from either cue alone. We measured the reliability of each cue in isolation across a range of slants and distances using a slant-discrimination task. The reliability of the texture cue increases as |slant| increases and does not change with distance. The reliability of the disparity cue decreases as distance increases and varies with slant in a way that also depends on viewing distance. The trends in the single-cue data can be understood in terms of the information available in the retinal images and issues related to solving the binocular correspondence problem. To test the MLE model, we measured perceived slant of two-cue stimuli when disparity and texture were in conflict and the reliability of slant estimation when both cues were available. Results from the two-cue study indicate, consistent with the MLE model, that observers weight each cue according to its relative reliability: Disparity weight decreased as distance and |slant| increased. We also observed the expected improvement in slant estimation when both cues were available. With few discrepancies, our data indicate that observers combine cues in a statistically optimal fashion and thereby reduce the variance of slant estimates below that which could be achieved from either cue alone. These results are consistent with other studies that quantitatively examined the MLE model of cue combination. Thus, there is a growing empirical consensus that MLE provides a good quantitative account of cue combination and that sensory information is used in a manner that maximizes the precision of perceptual estimates.

Depth information from focus cues--accommodation and the gradient of retinal blur--is typically incorrect in three-dimensional (3-D) displays because the light comes from a planar display surface. If the visual system incorporates information from focus cues into its calculation of 3-D scene parameters, this could cause distortions in perceived depth even when the 2-D retinal images are geometrically correct. In Experiment 1 we measured the direct contribution of focus cues to perceived slant by varying independently the physical slant of the display surface and the slant of a simulated surface specified by binocular disparity (binocular viewing) or perspective/texture (monocular viewing). In the binocular condition, slant estimates were unaffected by display slant. In the monocular condition, display slant had a systematic effect on slant estimates. Estimates were consistent with a weighted average of slant from focus cues and slant from disparity/texture, where the cue weights are determined by the reliability of each cue. In Experiment 2, we examined whether focus cues also have an indirect effect on perceived slant via the distance estimate used in disparity scaling. We varied independently the simulated distance and the focal distance to a disparity-defined 3-D stimulus. Perceived slant was systematically affected by changes in focal distance. Accordingly, depth constancy (with respect to simulated distance) was significantly reduced when focal distance was held constant compared to when it varied appropriately with the simulated distance to the stimulus. The results of both experiments show that focus cues can contribute to estimates of 3-D scene parameters. Inappropriate focus cues in typical 3-D displays may therefore contribute to distortions in perceived space.

Typical stereo displays provide incorrect focus cues because the light comes from a single surface. We describe a prototype stereo display comprising two independent fixed-viewpoint volumetric displays.Like autostereoscopic volumetric displays, fixedviewpoint volumetric displays generate near-correct focus cues without tracking eye position, because light comes from sources at the correct focal distances. (In our prototype, from three image planes at different physical distances.) Unlike autostereoscopic volumetric displays, however, fixed-viewpoint volumetric displays retain the qualities of modern projective graphics: view-dependent lighting effects such as occlusion, specularity, and reflection are correctly depicted; modern graphics processor and 2-D display technology can be utilized; and realistic fields of view and depths of field can be implemented. While not a practical solution for general-purpose viewing, our prototype display is a proof of concept and a platform for ongoing vision research. The design, implementation, and verification of this stereo display are described, including a novel technique of filtering along visual lines using 1-D texture mapping.

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Typical stereo displays provide incorrect focus cues because the light comes from a single surface. We describe a prototype stereo display comprising two independent fixed-viewpoint volumetric displays.Like autostereoscopic volumetric displays, fixedviewpoint volumetric displays generate near-correct focus cues without tracking eye position, because light comes from sources at the correct focal distances. (In our prototype, from three image planes at different physical distances.) Unlike autostereoscopic volumetric displays, however, fixed-viewpoint volumetric displays retain the qualities of modern projective graphics: view-dependent lighting effects such as occlusion, specularity, and reflection are correctly depicted; modern graphics processor and 2-D display technology can be utilized; and realistic fields of view and depths of field can be implemented. While not a practical solution for general-purpose viewing, our prototype display is a proof of concept and a platform for ongoing vision research. The design, implementation, and verification of this stereo display are described, including a novel technique of filtering along visual lines using 1-D texture mapping.