Various visual cues provide information about depth and shape in a scene. When several of these cues are simultaneously available in a single location in the scene, the visual system attempts to combine them. In this paper, we discuss three key issues relevant to the experimental analysis of depth cue combination in human vision: cue promotion, dynamic weighting of cues, and robustness of cue combination. We review recent psychophysical studies of human depth cue combination in light of these issues. We organize the discussion and review as the development of a model of the depth cue combination process termed modified weak fusion (MWF). We relate the MWF framework to Bayesian theories of cue combination. We argue that the MWF model is consistent with previous experimental results and is a parsimonious summary of these results. While the MWF model is motivated by normative considerations, it is primarily intended to guide experimental analysis of depth cue combination in human vision. We describe experimental methods, analogous to perturbation analysis, that permit us to analyze depth cue combination in novel ways. In particular these methods allow us to investigate the key issues we have raised. We summarize recent experimental tests of the MWF framework that use these methods. Depth Multiple cues Sensor fusion

A unified differential geometric framework for estimation of local surface shape and orientation from projective texture distortion is proposed, based on a generalization of the texture stationarity assumption introduced by Malik and Rosenholtz. This framework allows the information content of the gradient of any texture descriptor defined in a local coordinate frame to be characterized in a very compact form. The analysis is then specialized to three classes of texture descriptors; full affine descriptors, the classical "texture gradients" and second moment descriptors. For estimation of local surface orientation and curvature from uncertain observations of ane texture distortion, the proposed framework allows the dimensionality of the search space to be reduced from five to one.

The accuracy of depth judgments that are based on binocular disparity or structure from motion (motion parallax and object rotation) was studied in 3 experiments. In Experiment 1, depth judgments were recorded for computer simulations of cones specified by binocular disparity, motion parallax, or stereokinesis. In Experiment 2, judgments were recorded for real cones in a structured environment, with depth information from binocular disparity, motion parallax, or object rotation about the y-axis. In both of these experiments, judgments from binocular disparity information were quite accurate, but judgments on the basis of geometrically equivalent or more robust motion information reflected poor recovery of quantitative depth information. A 3rd experiment demonstrated stereoscopic depth constancy for distances of 1 to 3 m using real objects in a well-illuminated, structured viewing environment in which monocular depth cues (e.g., shading) were minimized. It has been pointed out that the geometric information supporting the perception of depth from binocular disparity is actually less determinate than that supporting the recovery of structure from object rotation or motion parallax

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

Li and Zaidi (Vision Research 40 (2000) 217; 41 (2001) 1519) have recentlyargued that there are two necessaryconditions for the perception of 3D shape from texture: (1) the texture pattern must have a disproportionate amount of energyalong directions of principal curvature; and (2) the surface must be viewed with a noticeable amount of perspective. In the present article we present evidence that these conclusions are onlyvalid under a limited set ofnon-fi'ylIW viewing conditions. Other relevant factors that need to be considered in this context include the distribution of curvature on an object's surface and the set of possible viewing directions from which it can be observed. For generic viewing directions and patterns of curvature, the perception of surface curvature from texture is onlyminimallya#ected bythe orientation spectrum of the texture pattern or the amount perspective in its opticalprojection.

Observers viewed large dichoptic patterns undergoing smooth temporal modulations or step changes in simulated slant or inclination under various conditions of disparity -- perspective cue conflict and concordance. After presentation of each test surface, subjects adjusted a comparison surface to match the perceived slant or inclination of the test surface. Addition of conflicting perspective to disparity affected slant and inclination perception more for brief than for long presentations. Perspective had more influence for smooth temporal changes than for step changes in slant or inclination and for surfaces presented in isolation rather than with a zero disparity frame. These results indicate that conflicting perspective information plays a dominant role in determining the temporal properties of perceived slant and inclination.

There are a variety of stereoscopic after-effects in which exposure to a stimulus with a particular slant or curvature affects the perceived slant or curvature of a subsequently presented stimulus. These after-effects have been explained as a consequence of fatigue (a decrease in responsiveness) among neural mechanisms that are tuned to particular disparities or patterns of disparity. In fact, a given disparity pattern is consistent with numerous slants or curvatures; to determine slant or curvature, the visual system must take the viewing distance into account. We took advantage of this property to examine whether the mechanisms underlying the stereoscopic curvature after-effect are tuned to particular disparity patterns or to some other property such as surface curvature. The results clearly support the second hypothesis. Thus, 3D after-effects appear to be caused by adaptation among mechanisms specifying surface shape rather than among mechanisms signaling the disparity pattern. © 2001 Elsevier

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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

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