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.

Binocular disparity and motion parallax are powerful cues to the relative depth between objects. However to recover absolute depth, either additional scaling parameters are required to calibrate the information provided by each cue, or it can be recovered through the combination of information from both cues (Richards, W. (1985). Structure from stereo and motion. Journal of the Optical Society of America, 2, 343 -- 349). However, not all tasks necessarily require a full specification of the absolute depth structure of a scene and so psychophysical performance may vary depending on the amount of information available, and the degree to which absolute depth structure is required. The experiments reported here used three different tasks that varied in the type of geometric information required in order for them to be completed successfully. These included a depth nulling task, a depth-matching task, and an absolute depth judgement (shape) task. Real world stimuli were viewed (i) monocularly with head movements, (ii) binocularly and static, or (iii) binocularly with head movements. No effect of viewing condition was found whereas there was a large effect of task. Performance was accurate on the matching and nulling tasks and much less accurate on the shape task. The fact that the same perceptual distortions were not evident in all tasks suggests that the visual system can switch strategy according to the demands of the particular task. No evidence was found to suggest that the visual system could exploit the simultaneous presence of disparity and motion parallax. 2000 Elsevier Science Ltd. All rights reserved.

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depth ambiguities. Without promoting the cues, their raw data (e.g., disparities and velocities) are in different units so that simple cue-combination strategies, such as averaging the depth estimates made using each cue, are impossible. When the missing parameters are the eye positions (vergence, gaze directions, and torsions), the promotion process is referred to as depth scaling. In particular, in central gaze, the raw sensory data for the cue (velocities, disparities, etc.) are scaled by (that is, multiplied by, or multiplied by the square of) an estimate of the fixation distance. To the extent that this scaling is done accurately, the result is depth constancy: perceived depth that is independent of changes in viewing conditions. In this hapter we will limit our discussion of cue promotion to the issue of scaling by the fixation distance. We review a number of ways in which depth scaling may be accomplished. Micha

The ratio of the vertical sizes of corresponding features in the two eyes' retinal images depends both on the associated object's distance and on its horizontal direction relative to the head (eccentricity). It is known that manipulations of vertical size ratio can affect perceived distance, size, depth and shape. We examined how observers use the vertical size ratio to determine the viewing distance. Do they use the horizontal gradient of vertical size ratio, or do they combine the vertical size ratio itself with the eccentricity at which it is found? Distance scaling (as measured by having subjects set an ellipsoid's size and shape to match a tennis ball) was no better when the judged object was 30 to the right of the head (where vertical size ratios vary considerably with distance) than when it was located straight ahead. Distance scaling improved when vertical disparities were presented within larger visual fields, irrespective of where this was relative to the head. Our results support the proposal that subjects use the horizontal gradient of vertical size ratio to estimate the distance of an object that they are looking at.

Convergence of the real or virtual stereoscopic cameras is an important operation in stereoscopic display systems. For example, convergence can shift the range of portrayed depth to improve visual comfort; can adjust the disparity of targets to bring them nearer to the screen and reduce accommodation-vergence conflict; or can bring objects of interest into the binocular field-of-view. Although camera convergence is acknowledged as a useful function, there has been considerable debate over the transformation required. It is well known that rotational camera convergence or ‘toe-in’ distorts the images in the two cameras producing patterns of horizontal and vertical disparities that can cause problems with fusion of the stereoscopic imagery. Behaviourally, similar retinal vertical disparity patterns are known to correlate with viewing distance and strongly affect perception of stereoscopic shape and depth. There has been little analysis of the implications of recent findings on vertical disparity processing for the design of stereoscopic camera and display systems. We ask how such distortions caused by camera convergence affect the ability to fuse and perceive stereoscopic images.

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