The projected image of a textured surface contains multiple texture cues to three-dimensional (3D) surface orientation. Previous studies have reported conflicting findings about the roles of various texture cues. We tested the influence of texture compression relative to other texture cues using a cue conflict paradigm. Observers viewed images of textured planar surfaces with varied slants (0°–70°) and estimated 3D slant by aligning their hand with the virtual surface. Conflicts between texture cues were created by stretching or compression the texture along the surface, which selectively changes the slant specified by texture compression. The texture distortions were relatively small (±10% or ±20%) to limit the size of the cue conflicts. Across three experiments, we varied the field of view (10° vs. 20°), texture regularity (circles vs. Voronoi), and availability of binocular cues. In monocular conditions, slant estimates were strongly affected by texture distortions. Analyses of cue weighting found that texture compression had more influence on slant settings than other texture cues and the relative influence of texture compression decreased with larger field of view and less regular textures. In binocular conditions, we also observed effects of texture distortion, and the influence of texture compression relative to information from stereo and other texture cues increased with slant. Our results provide evidence that texture compression contributes to perceived slant, in addition to other texture cues such as texture scaling. The observed effects of simulated slant, field of view, and texture regularity on cue weighting were all consistent with a model that integrates multiple sources of information according to their reliability.

*S*). In the example shown in Figure 1, the spatial frequencies in the vertical direction are higher than in the horizontal direction (middle panel). If texture is assumed to be isotropic, the anisotropy in the projected texture can be used to compute the local 3D orientation relative to the viewer. This computation could be applied at multiple locations in the visual field to derive a map of local 3D orientations.

*SD*) and aspect ratios (±26%

*SD*). The variability in aspect ratios might especially interfere with use of texture compression, which involves comparing spatial frequencies at different orientations within local image regions. FOV also affects the reliability of texture cues but would be expected to primarily affect the slant information provided by texture scaling or other gradient cues, as discussed previously. Thus, texture regularity and FOV differentially affect the slant information from texture scaling and texture compression. If both texture cues were used for slant perception and integrated in an approximately optimal manner, one would expect less use of texture compression for the Voronoi textures than for the circles textures, and less use of texture compression with a larger FOV.

*S*

_{comp}= arccos(α cos(

*S*)), where

*S*is the simulated slant and α is the stretching ratio of the surface texture. For example, when simulated slant was 40° and the texture was compressed by 10% (α = 0.9), local compression at the center of the stimulus was consistent with a slant of 46.4°.

*y*-

*z*plane (i.e., vertical tilt direction). When finished with the alignment, subjects held their hand still and pressed the spacebar again with their left hand to conclude the trial. If the tilt of the palm was more than 5° away from vertical, a warning beep would cue observers to readjust their hand and confirm again. Trials were self-paced and typically took 1 to 2 seconds to complete.

*F*(7, 77) = 127.19,

*p*< 0.001, partial η

^{2}= 0.920. Additional tests of polynomial contrasts found that there was a significant linear trend:

*F*(1, 11) = 166.22,

*p*< 0.001, partial η

^{2}= 0.938. There were also significant quadratic and cubic trends: quadratic,

*F*(1, 11) = 86.48,

*p*< 0.001, partial η

^{2}= 0.887; cubic,

*F*(1, 11) = 15.76,

*p*= 0.002, partial η

^{2}= 0.589. These results confirm that the psychometric functions were nonlinear.

*F*(1, 11) = 0.288,

*p*= 0.602, partial η

^{2}= 0.025, and no significant interaction between FOV and slant,

*F*(7, 77) = 0.785,

*p*= 0.602, partial η

^{2}= 0.067.

*y*-intercept and found that the intercepts from individual subjects were correlated across display conditions. This suggests that the non-zero intercepts are due to general response biases, which varied across individuals. There may also be bias in the overall scale of responses, but our data do not provide a way to evaluate the accuracy of scaling. Thus, the reported slant estimates should be interpreted as measures of relative perceived slant, which might differ from perceived slant by some scaling and constant bias.

*F*(4, 44) > 11.48,

*p*< 0.001, partial η

^{2}> 0.51. The conditions show a consistent general pattern of higher slant estimates for compressed textures than for stretched textures.

*w*= (45° – 40°)/(46.4° – 40°), which is approximately 0.78.

*f*(

*S*). For the conflicting cue conditions, we assumed that slant estimates varied around

*f*(

*S*+

*wΔS*), where

*ΔS*is the difference between the slant specified by texture compression and texture scaling (

*S*

_{comp}–

*S*), and

*w*is a linear weight representing the relative influence of texture compression for a given base slant and FOV condition. We excluded conditions where projected texture is vertically elongated (stretched textures with 0° or 20° slant) because texture compression does not specify a slant in the vertical direction in these cases. Other details of the cue weight analysis are provided in the Appendix.

*SD*of 0.4 cm. The size of the cells measured in the vertical and horizontal directions had ratios between 0.5 and 2.1, with a mean of 1.03 and

*SD*of 0.26. As in the previous experiment, we added random variations to the overall size of the texture on each trial to discourage the use of projected size as a direct cue to slant. On each trial, the base texture was uniformly scaled by a random amount between 0.875 and 1.125.

*F*(7, 77) = 87.27,

*p*< 0.001, partial η

^{2}= 0.888. Tests of polynomial contrasts found a significant quadratic trend,

*F*(1, 11) = 58.31,

*p*< 0.001, partial η

^{2}= 0.841, confirming that the psychometric functions were nonlinear, in addition to a significant linear trend:

*F*(1, 11) = 114.17,

*p*< 0.001, partial η

^{2}= 0.912.

*F*(1, 11) = 0.859,

*p*= 0.374, partial η

^{2}= 0.072, but there was a significant interaction between simulated slant and FOV:

*F*(7, 77) = 5.19,

*p*< 0.001, partial η

^{2}= 0.320. At low slants, the slant estimates in the two FOV conditions were similar, but, at high slants, the slant estimates were lower with the smaller FOV. Pairwise tests for individual slant conditions found significant differences between the FOV conditions at slants of 60°,

*t*(11) = 3.274,

*p*= 0.007, Cohen's

*d*= 0.945, and 70°,

*t*(11) = 2.744,

*p*= 0.019, Cohen's

*d*= 0.792, as well as a trend toward a difference at 50°:

*t*(11) = 2.016,

*p*= 0.069, Cohen's

*d*= 0.582. At other slants, there was no detectable effect of FOV:

*t*(11) < 0.798,

*p*> 0.442, Cohen's

*d*< 0.230. These results indicate that the Voronoi textures appeared less slanted with the smaller FOV, but only at high slant conditions.

*y*-intercepts of the psychometric functions were not zero, which can be attributed to response bias. The simulated surfaces with low slants clearly appear frontal, so the deviation from zero in the slant estimates would be due to errors in matching the orientation of the hand to the perceived slant, rather than indicating a non-zero perceived slant. There may also be some bias in the overall scaling of responses, which cannot be assessed from our data.

*F*(4, 44) > 9.08,

*p*< 0.001, partial η

^{2}> 0.45. As in Experiment 1, we also observed asymmetric effects of compression and stretching for slants of 0° and 20° but not for higher slants.

*F*(1, 11) = 154.74,

*p*< 0.001, partial η

^{2}= 0.934; no quadratic trend,

*F*(1, 11) = 0.005,

*p*= 0.946, partial η

^{2}< 0.001; and a small but significant cubic trend,

*F*(1, 11) = 10.98,

*p*= 0.007, partial η

^{2}= 0.500.

*F*(1, 11) = 3.59,

*p*= 0.085, partial η

^{2}= 0.246, and no interaction between texture type and slant,

*F*(7, 77) = 1.20,

*p*= 0.313, partial η

^{2}= 0.098. Slant estimates were higher for the circles textures than for the Voronoi textures, although the magnitude of this difference was small (0.79° ± 1.45°).

*dCor*= 0.76) or slant from compression (

*dCor*= 0.90). Although scaling contrast can account for a large portion of the overall variance in slant estimates, it does not accurately predict the observed effects of varying FOV and cannot account for the large observed effects of stretching and compressing the surface textures.

*Journal of Experimental Psychology,*81, 584–590.

*Vision Research,*36(8), 1163–1176.

*Journal of vision,*19(4), 7–7.

*Journal of Experimental Psychology: General,*113(2), 198–216.

*SIAM Journal on Numerical Analysis,*17(2), 238–246, doi:10.1137/0717021.

*Journal of Mathematical Imaging and Vision,*2(4), 327–350.

*Journal of Vision,*9(9), 8.1–8.20.

*Journal of Vision,*4(12), 967–992.

*Vision Research,*38, 1683–1711.

*Vision Research,*38, 2635–2656.

*Vision Research,*38, 1655–1682.

*Vision Research,*43, 2539–2558.

*Vision Research,*35(3), 389–412.

*Perception & Psychophysics,*71(1), 116–130.

*Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003)*(p. 10). Vienna, Austria: R Foundation for Statistical Computing.

*Vision Research,*44(13), 1511–1535.

*Vision Research,*37(16), 2283–2293.

*Perception,*32(2), 211–233.

*Journal of Vision,*6(9), 882–897.

*Journal of Vision,*15(2), 14.

*Annals of Statistics,*35(6), 2769–2794.

*PLoS One,*8(5), e64958.

*Perception,*30(2),185–193.

*Journal of Vision,*10(2), 20.1–20.18.

*Vision Research,*45, 1501–1517.

*Journal of Vision,*7(12), 1–16.

*f*(

*S*), plus noise due to trial-to-trial variability in perceived slant and responses. Slant estimates on conflicting cue trials were assumed to vary around

*f*(

*S*+

*wΔS*), where

*ΔS*is the difference between the slant specified by texture compression and texture scaling, and

*w*is an unknown cue weight representing the relative influence of texture compression.

*t*-distribution around the expected mean response for a subject and condition:

*R*∼ dt(

*f*(

*S*+

*wΔS*), σ

_{R}^{–2}, ν). The parameter σ

_{R}^{–2}is the inverse variance of responses around the mean across trials, and ν is the degree-of-freedom parameter for the

*t*-distribution representing deviation from normality. We used

*t*-distributions to model trial-to-trial variability rather than normal distributions to be more robust to outliers. The distributions of σ

_{R}^{–2}and ν across subjects in each condition were modeled as gamma distributions, with generic hyperpriors for the gamma parameters.

*f*

_{70}>

*f*

_{35}>

*f*

_{0}and that the derivatives be positive and less than three times the slope between endpoints. These constraints are sufficient to ensure monotonicity (Fritsch & Carlson, 1980). The range [0°, 70°] spans the set of slants used in our experiments, but the perceptually matching slant for cue conflict conditions (

*S*+

*wΔS*) could potentially be outside this range if

*w*is less than zero or much greater than one. For negative slants, we assumed symmetry around the zero point:

*f*(–

*S*) –

*f*

_{0}= –(

*f*(

*S*) –

*f*

_{0}). For slant values larger than 70°, we extended

*f*(

*S*) by linearly extrapolating from

*f*

_{70}and

*f*′

_{70}.

*f*

_{0}∼ dnorm(0, σ

^{–2}

_{zero})

*f*

_{70}∼ dgamma(α

_{max}, β

_{max})

*f*

_{35}/

*f*

_{70}∼ dbeta(α

_{mid}, β

_{mid})

*f'*

_{0}∼ dunif(0, 3·(

*f*

_{35}–

*f*

_{0})/35)

*f'*

_{35}∼ dunif(0, 3·min(

*f*

_{35}–

*f*

_{0},

*f*

_{70}–

*f*

_{35})/35)

*f'*

_{70}∼ dunif(0, 3·(

*f*

_{35}–

*f*

_{0})/35)

^{–2}

_{zero}is the variance of

*f*

_{0}across subjects, α

_{max}and β

_{max}are parameters for a gamma distribution fit to the distribution of

*f*

_{70}across subjects, and (α

_{mid}, β

_{mid}) are parameters for a beta distribution fit to the distribution of the ratio of

*f*

_{35}to

*f*

_{70}. We used separate distributional parameters for the different FOV and texture type conditions and uninformative hyperpriors on these parameters.