Among other cues, the visual system uses shading to infer the 3D shape of objects. The shading pattern depends on the illumination and reflectance properties (BRDF). In this study, we compared 3D shape perception between identical shapes with different BRDFs. The stimuli were photographed 3D printed random smooth shapes that were either painted matte gray or had a gray velvet layer. We used the gauge figure task (J. J. Koenderink, A. J. van Doorn, & A. M. L. Kappers, 1992) to quantify 3D shape perception. We found that the shape of velvet objects was systematically perceived to be flatter than the matte objects. Furthermore, observers' judgments were more similar for matte shapes than for velvet shapes. Lastly, we compared subjective with veridical reliefs and found large systematic differences: Both matte and velvet shapes were perceived more flat than the actual shape. The isophote pattern of a flattened Lambertian shape resembles the isophote pattern of an unflattened velvet shape. We argue that the visual system uses a similar shape-from-shading computation for matte and velvet objects that partly discounts material properties.

^{1}results in a perceptually matte object (Dror, Willsky, & Adelson, 2004; Pont & Te Pas, 2006). This effect is likely due to the absence of highlights for objects illuminated by a diffuse light field. The geometry of the light field dictates the distribution of highlights on a glossy surface. Indeed, it has recently been shown that for image-based illumination (Debevec, 1998) the geometry of the light field determines the level of perceived gloss (Doerschner, Boyaci, & Maloney, 2010; Olkkonen & Brainard, 2010), although the exact relation between light field geometry and gloss is still unknown. The direction of the illumination also affects material perception. It has been shown that surface roughness perception depends on the illumination direction (Ho, Landy, & Maloney, 2006): Increasing the angle between the illumination direction and surface normal results in an increased perceived roughness. Interestingly, this illusory roughness increase did not depend on the presence of contextual cues relating to the illumination direction. This does not mean that in general the interaction between light and material is one way. In fact, it has been shown that reflectance can also influence the perception of illumination direction (Khang, Koenderink, & Kappers, 2006; Pont & Koenderink, 2007).

*x*,

*y*) values of the triangulation vertices and perceived depth values

*z*. The depth values were compared to analyze perceptual differences between matte and velvet shapes. First, we quantified possible depth compressions for the velvet shapes by performing a linear regression between matte and velvet conditions. If the slope (

*a*) of the regression

*z*

_{velvet}=

*az*

_{matte}+

*b*is smaller than 1, depth is compressed; if

*a*> 1, depth is extended. This was analyzed within observers (between BRDF). Second, the interobserver similarity was quantified by calculating the adjusted

*R*

^{2}(coefficient of determination) of the regression between the depth values of each stimulus. The higher the adjusted

*R*

^{2}, the higher the similarity in perceived shape and the lower the level of ambiguity. Besides this “straight” regression that reveals depth compression (

*a*) and similarity (

*R*

^{2}), we also performed affine regressions. It has been proposed by Koenderink et al. (2001) that when one assumes that “planes can reliably be differentiated from curved surfaces, owing to cues such as shading and so forth,” image ambiguities are described by the affine transformation

*z*(

*x*,

*y*) =

*az*+

*b*+

*cx*+

*dy*. It is thus similar to the straight regression with the addition of a plane

*cx*+

*dy*. The affine regression basically captures all linear differences between perceived depths. If the adjusted

*R*

^{2}of the affine regression (taking into account the extra two parameters

*c*and

*d*) is significantly larger than the straight regression adjusted

*R*

^{2}, the difference between depths is attributed to the affine plane, since the compression/stretch parameter

*a*is already present in the straight regression.

*R*

^{2}of all six pairs of the four repetitions was 0.995 and 0.997 for shapes 1 and 2, respectively.

*t*-test:

*t*(7) = −3.74269,

*p*< 0.05 and

*t*(7) = −2.59789,

*p*< 0.05 for the first and second stimuli, respectively. To assess whether there is some kind of depth compression invariance across different shapes, we correlated the depth gains of the first and second stimuli. We found a surprisingly high correlation of the flattening effect (

*r*= 0.902,

*p*= 0.002), which is shown in Figure 5b.

*F*(1, 109) = 3.24058,

*p*= 0.0746). However, the velvet shapes yielded a significantly higher perceptual ambiguity, i.e., a lower coefficient of determination (

*F*(1, 109) = 8.70619,

*p*= 0.0039). Velvet shapes are, thus, perceived more ambiguously between observers than matte shapes.

*R*

^{2}) for each observer pair in Figure 7. In this figure, the gray bars denote the straight coefficient of determination and the white bars denote the affine coefficient of determination. The alternating grays help discriminate observers. The asterisks denote significant affine improvements. The total fraction of affine improvements over all observer pairs is expressed as a percentage. For the first shape, a relatively large difference is found for the amount of significant affine improvement between the matte (75%) and velvet (43%) stimuli. The difference between these proportions was significantly different (

*χ*

^{2}(1,

*N*= 54) = 5.976,

*p*= 0.014). For the second stimulus, the difference is qualitatively similar but much smaller (61% against 54%) and not significantly different (

*χ*

^{2}(1,

*N*= 54) = 0.292,

*p*= 0.589). A significant affine improvement reflects that the differences between observers are

*linear*. Thus, the differences between observers in perceiving the velvet shape seem to be of relatively

*nonlinear*nature for the first shape, but this difference is undetermined for the second shape.

*F*(1, 7) = 7.392,

*p*< 0.05). Furthermore, the ANOVA showed no significant effect for the stimulus factor or the interaction. The magnitude of the coefficients of determination (adjusted

*R*

^{2}) is of comparable size with those found in the between-subjects correlation as indicated by the dashed bars in Figure 9, although for shape 1 the correlation with veridical appears somewhat lower.

*x*

^{2}+

*y*

^{2}+ (

*λz*)

^{2}= 1, where

*z*is perpendicular to the image plane and

*λ*ranged from 0.25 (oblate spheroid) to 1 (sphere). In Figure 11, the top row represents the renderings, the middle row shows the isophote patterns, and the bottom row shows the luminance histograms. As can be seen, both the isophote pattern and the luminance histogram shape of the velvet sphere resembles the isophote pattern and histogram shape of the flattened Lambertian shapes more than that of the actual spherical Lambertian shape. Although there may be many differences between these simple, rendered shapes and our real, photographed stimuli, it is not unlikely that such shading pattern and histogram resemblances may be responsible for the flattening effect. Furthermore, we took photographs of the stimuli with collimated light and plotted the luminance histograms in Figure 12. As can be seen in that figure, there appears to be a systematic shift between the brightest modes of the matte and velvet shapes. However, in the photographs, we can see that these brightest modes are probably due to different optical mechanisms and the brightest pixels are located at different positions. For the matte stimuli, we see highlights, and for the velvet ones, we see bright contours. Thus, in order to explain shape perception, we need to take into account the spatial characteristics of the luminance distribution, e.g., the isophote pattern. The isophotes effectively represent the direction orthogonal to the shading gradients. It is, therefore, more likely that the isophote pattern affects shape inference.

*cx*+

*dy*) and not on the depth gain that is already present in the straight regression. Thus, while depth compression is present in shape 2, an additive plane does not improve the similarities. This possibly indicates that nonlinear differences in perception between objects with different BRDFs depend on the presence of high-frequency shape variations.