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.

this article online for further analysis.) study were more likely to use commonplace rather than Figure 4C shows the predicted and observed JNDs ad hoc strategies. The fact that nearly optimal cue inte- for small or zero conflicts for each observer and each gration was observed in all three studies suggests that stimulus orientation. The good agreement between prethe phenomenon is pervasive. dicted and observed shows that individual differences The observed and predicted PSEs in our experiment in intermodal discrimination can be largely explained by behavior in the within-modality experiments. were very similar (Figure 3D), but the observed and pre- 487 were otherwise transparent. Because element size and density were dicted JNDs differed consistently (Figures 4A and 4B). randomized, they were not a reliable cue to intersurface distance

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.

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.

similar in the parallel and perpendicular cases; so, in this situation, the precision of haptic estimates should not vary with orientation (see [3] for a counter example). Suppose the observer looks at and feels the surfaces simultaneously. The principle of maximum likelihood (ML) prescribes the strategy for combining visual and haptic estimates that produces the estimate of lowest variance [4–8]. If the visual and haptic estimates are independent and normally distributed, that strategy is weighted summation Vision and haptics have different limitations and advantages because they obtain information by different methods. If the brain combined information from the Sˆ VH � wVS ˆ V � wHS ˆ H, two senses optimally, it would rely more on the one

Abstract not found

When an organism estimates a property of the environment so as to make a decision (“Do I flee or do I fight?”) or plan an action (“How do I grab that salt shaker without tipping my wine glass along the way?”), there are typically multiple sources of information (signals or “cues”) that are useful. These may include different features of the input from one sense, such as vision, where a variety of cues—texture, motion, binocular disparity, and so forth—aid the estimation of the three-dimensional (3D) layout of the environment and shapes of objects within it. Information may also derive from multiple senses such as visual and haptic information about object size, or visual and auditory cues about the location of a sound. In most cases, the organism can make more accurate estimates of environmental properties or more beneficial decisions by integrating these multiple sources of information. In this chapter, we review models of cue integration and discuss benefits and possible pitfalls in applying these ideas to models of behavior. Consider the problem of estimating the 3D orientation (i.e., slant and tilt) of a smooth