We investigate how different depth cues are combined when one cue is ambiguous. Convex and concave surfaces produce similar texture projections at large viewing distances. Our study considered unambiguous disparity information and its combination with ambiguous texture information. Specifically, we asked whether disparity and texture were processed separately, before linear combination of shape estimates, or jointly, such that disparity disambiguated the texture information.

Vertical ridges of various depths were presented stereoscopically. Their texture was consistent (in terms of maximum likelihood) with both a convex and a concave ridge. Disparity was consistent with either a convex or concave ridge. In a separate experiment the stimuli were defined solely by texture (monocular viewing).

Under monocular viewing observers consistently reported the convex interpretation of the texture cue. However, in stereoscopic stimuli, texture information modulated shape from disparity in a way inconsistent with simple linear combination. When disparity indicated a concave surface, a texture pattern perceived as highly convex when viewed monocularly caused the stimulus to appear more concave than a “flat” texture pattern. Our data confirm that different cues can disambiguate each other. Data from both experiments are well modeled by a Bayesian approach incorporating a prior for convexity.

*equally*compatible with a convex or concave ridge. To ensure this, we randomly selected equal numbers of texture elements from ridges with equal and opposite depths (e.g., 100 texels from a +5-cm ridge and 100 texels from a −5-cm ridge). The texture likelihoods were calculated for these composite stimuli and the random sampling process was repeated until the two peaks of the resultant likelihood were approximately equal (within 10%). These likelihoods are shown in Figure 1.

*SE*of the mean. The abscissa gives the texture-specified depth and the ordinate shows the perceived ridge depth (the depth difference between the edges and peak of the ellipse, as indicated by the observers’ cross-sectional settings). The most important aspect of the data to note is that the means lie above zero. In fact, in all trials the stimuli appeared convex (with the exception of the 0-cm texture condition). In other words, the observers discounted the concave interpretation. This is consistent with a prior for convexity that has been noted previously (Mamassian & Landy, 1998; Langer & Bülthoff, 2001; Li & Zaidi, 2001). The second point is that the depth of the ridge was underestimated. This is consistent with a prior for fronto-parallel, and/or the effect of residual cues associated with using a flat monitor, such as accommodation, vergence, and blur cues (Watt, Banks, Ernst, & Zumer 2002; Watt, Akeley, & Banks, 2003).

*F*(6, 24)=37.5,

*p*< .01). What we are more interested in here, however, is the interaction between disparity and texture. We want to know how a texture cue, which is always interpreted as convex in the “texture only” condition, will be combined with a disparity cue, which signals either a convex or concave surface. Consider the solid light blue line (texture = ±7.5 cm) in Figure 5 and compare that to the dark blue dotted line (texture = 0 cm). On the right hand side of the plot, the solid line is above the dotted line, showing that the ±7.5 texture made the stimuli appear to be more convex than the 0-cm texture. This is reasonably straight-forward; a texture that was seen as convex when viewed alone, makes a disparity-specified ridge appear more convex compared to the effect of a flat texture. This is consistent with the data of Buckley and Frisby (1993) for texture and disparity cue combination in convex ridges.

*more*concave, despite the fact that this texture was seen as convex when viewed in isolation from disparity. This is inconsistent with a linear combination of independent cues. An intuitive way to think of this result is that the concave interpretation appears to be discarded or overruled when the textures were viewed monocularly. However, the concave interpretation of the texture cue was still available when that texture information was combined with disparity indicating a concave surface. This interaction between disparity and texture was significant (

*F*(18,72) = 7.5,

*p*< .05), but as expected from our model, there was no significant main effect of texture (

*F*(3,12) = 5.2,

*p*> .05). We have modeled this cue combination within a Bayesian framework.

Observer | Disparity Std Dev | Convexity Std Dev | Residual Std Dev |
---|---|---|---|

WJA | 0.378 | 2.96 | 0.404 |

EWG | 0.266 | 2.07 | 0.303 |

PAW | 0.205 | 0.415 | 0.292 |

LW | 1.85 | 100 | 0.326 |

ML | 0.472 | 1.31 | 0.357 |

*x*

_{s}is horizontal position and

*z*

_{s}is depth on the surface.

*a*,

*b*, and

*z*

^{0}are constants that give the maximum horizontal and depth extents of the ellipse and the distance of the center of the ellipse from the image plane, respectively. The center of the ellipse is offset from the image plane; the ridge comprises less than half of a full ellipse. The exact values of

*a*,

*b*, and

*z*

_{0}depend on the ridge depth (

*h*).

_{i},

*y*

_{i}) are calculated. The arc lengths on the surface corresponding to the top and bottom sides of a square image patch are calculated by integrating the differential of the curve between the relevant surface points (e.g.,

*x*

_{s1}and

*x*

_{s2}).

*φ*) at that location is given by The orientation,

*γ*, of an image line is then defined as where

*θ*is the orientation of the line on the surface,

*d*is viewing distance, and

*x*

_{s},

*y*

_{s}and

*z*

_{s}give the center of the line on the surface.

*θ*that corresponds to a particular range of

*γ*(in the image). Because the model assumes that

*γ*follows a uniform distribution on the original surface, the probability of finding an image line within the range of is proportional to the size of the corresponding range of

*θ*(Figure 7). The orientation likelihood for any particular image line is found by extracting the probability of that orientation,

*γ*, for the complete range of ridge depths. The overall likelihood

*p*(

*h|h*) for an observed image texture pattern (

*t*) is calculated by multiplying together all of the individual likelihoods for position and orientation for all texture elements.

*σ*

_{r}) is a free parameter relating to the reliability of the residual cues and the strength of the prior for frontoparallel:

*b*) and the texture information in the image (

*t*) are combined with the residual cues and prior(

*s*) to produce the posterior distribution. In the “texture only” condition, the disparity likelihood is omitted. The posterior gives the probability of a scene parameter (here ridge depth) given the available image information and prior assumptions. From Bayes’ rule, Following the assertion that the disparity and texture cues are independent, the expression becomes In our model, a response is extracted from the posterior distribution by calculating its