The Effect of Material Properties on the Perceived Shape of Three-Dimensional Objects

Observers

Eight adult observers participated in the experiment, all of whom had normal or corrected-to-normal vision. The participants ranged in age from 22 to 44 years. Informed consent was obtained from all participants. Procedures were approved by the Toyohashi University of Technology ethics committee. All research was performed in accordance with the relevant guidelines and regulations.

Stimuli

All the stimuli were rendered using the open-source rendering package Blender 3D (Ver. 2.78b). The 3D geometry was created in Blender 3D by taking an initial Ico Sphere with 20,480 triangle faces and 10,242 vertices (i.e., subdivisions = 6). Bumpy surface relief was created by generating a Clouds texture (Size = 0.25, Depth = 0, Nabla = 0.03). This texture was applied to the geometry as a height map using the Displace Modifier (Midlevel = 0.5, Strength = 0.2). The Ico Sphere shape and Clouds texture and Displace Modifier are included in Blender 3D. The number of bumps along the circumference was 5–12, and its peak amplitude was 5% to 7% of the diameter of the object, based on Fourier power analyses of the radial distance of the object silhouette image (Figure 1A). All the stimuli were rendered with Cycles Render in Blender 3D. Cycles Render is a physically based ray tracing render engine designed for high-quality animation. The objects were rendered after they were multiplicatively scaled in depth over five levels (0.25, 0.5, 1.0, 1.5, and 2.0; hereafter referred to as convexity).

We rendered images without tone mapping; the intensity of the specular highlights was limited by setting the exposure, and any values exceeding the dynamic range of our standard RGB rendering were set to 255. The monitor’s calibrated gamma for displaying these images was 2.2 (mean absolute error was 5.7%, measured by a color and luminance meter CS-200, Konica Minolta).

We used two light fields for rendering, either the Eucalyptus Grove or the St Peters Basilica (Figure 1C; source: http://www.pauldebevec.com/Probes/). There were four surface material properties: Matte, Specular, Refraction (RI = 1.51), and 50% Refraction (RI = 1.51) + 50% Specular (Figure 1B). We also used three sizes of 3D objects that were small, normal, or large in diameter: length of 0.5, 1.0, and 2.0 Blender Units (BU), with the corresponding display size of 6.2, 12.4, and 24.8 deg, respectively. These were made by scaling the object’s shape multiplicatively equally along the X, Y, and Z directions.

The camera position was fixed to 10 BU away from the 3D object’s center. Light fields were represented on a sphere with infinite diameter. Objects were oscillated sinusoidally along the horizontal axis at 1.0 Hz (amplitude = 2 BU, corresponding display size: 24.8 deg) for 5 seconds beginning from the center and moving rightwards. All movie presentations of horizontal object oscillation were rendered using a custom Python script executed in the Blender environment. All movies were rendered at 60 fps.

Procedure

Visual stimuli were presented using custom psychophysical software called Psymat (ver. 0.35; http://juno3d.com/software/) running on a PC (OS: Windows 10 Pro, CPU: Intel Core i7-6700, Graphic card: GeForce GTX 960).

Observers were seated, and their head fixed by a chin rest. Stimuli were presented on an LCD flat-panel display (HP E242) situated 30 cm in front of the observers. Stimulus size was 28.6 × 28.6 cm, 51 × 51 deg, 800 × 800 pixels including the object and background of the light fields, and screen area other than the stimulus movie was midgray (red = green = blue = 0.5). Observers were given a minute at the start of the experiment to practice a small number of randomly presented trials, before moving on to the formal testing session. In a block of trials, observers were shown stimulus movies for 5 seconds with both eyes open, and then they were asked to attend to the curvature of objects in depth. Participants were specifically asked to rate how flat or elongated the objects appeared on a global scale.

Following each 5-second movie presentation, the scene was replaced with a metric scale for observer ratings. The vertical bar on the left was used to indicate the length, and the oval on the right corresponds to the profile of the 3D object when it was viewed from above. The rating bar and 2D outline were modulated simultaneously when the observer pressed either the UP/DOWN arrow key to respectively increase or decrease the matched profile length. The observer was asked to report the 3D object’s appearance as more elongated (like a rugby ball) or flatter (like a pancake). No feedback on their response accuracy was provided.

Once the observer was satisfied with their match, they pressed the space bar to log the response and advance to the next trial. The order of stimuli was randomized within a block of 80 conditions (4 materials × 5 convexity levels × 2 bump levels × 1 size in diameter × 2 light fields). Observers performed three repeats for each stimulus condition. On another day, observers participated in the same experiment, but the size of the objects was modified to small or large size with the order of object sizes randomly intermingled between blocks of trials.

Static Presentations

To identify the effect of static cues on the perception of surface convexity, we presented the same stimuli statically in a follow-up experiment to determine whether there were any declines in perceptive convexity. In this follow-up experimental session, stimulus objects did not move and were presented statically at either the center, left, or right side of the stimuli locus traversed in the dynamic viewing experiment. A total of 240 randomized trials were presented to each observer (4 materials × 5 convexity levels × 2 bump levels × 2 light probes × 3 stimuli positions).

Statistical Analysis

The results were analyzed using MATLAB (Ver. R2016b). We tested for a main effect of light probe, bump level, physical convexity, and material property. The analysis of variance (ANOVA) treated physical convexity as a continuous factor but was treated as a categorical factor in post hoc testing. The other factors were treated as categorical factors in all analyses. We also tested for interaction effects between physical convexity and material property.

Effect of Dynamic Material Properties on Shape Perception

In our first task, observers estimated the perceived convexity of moving objects with different physical convexity, bumpiness, and material properties rendered under two light fields (Figure 2). Perceived convexity increased significantly with physical convexity—four-way ANOVA, main effect of physical convexity: F(1, 1919) = 1445.23, p < .001, partial η² = 0.4332. Generally, objects with convexity larger than 1.0 (i.e., greater than spherical) were underestimated relative to ground truth, and objects with convexity smaller than 1.0 (i.e., flatter than spherical) were overestimated relative to ground truth (dashed line). Thus, the slope of perceived convexity with respect to physical convexity was smaller than the ground truth (Slope = 0.377, linear regression of all material properties). Perceived convexity also differed depending on material properties—four-way ANOVA, main effect of material properties: F(3, 1919) = 16.91, p < .001, partial η² = 0.0262. Across all convexity levels, objects that were purely refractive were perceived significantly flatter than specular objects of identical convexity (post hoc test, Tukey honest significance test [HSD], p < .001, within all other materials). The average difference in perceived convexity between the purely refractive and the other materials was approximately 0.166. A complete description of the statistics is shown in Table S1 in Supplemental Material.

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Figure 2.

Perceived convexity for different material properties and lighting conditions for middle-sized dynamic stimuli. A: Plots show mean perceived convexity as a function of physical convexity of objects with different simulated material properties. The dashed line shows perception equating to ground truth. B: Results were shown separately by different illumination conditions and different surface bumpiness. Error bar shows standard error of mean of all trials.

The Refraction (50%) + Specular (50%) surface was perceived as comparable in convexity to the specular surface. Presumably, this occurred because the specular reflection component dominated observer’s estimates of convexity. The flattest (convexity = 0.25) matte object was perceived significantly flatter than the specular object of equivalent convexity (post hoc test, Tukey HSD, p = .018).

The effect of changing material properties on perceived convexity was generally consistent across different light fields and surface bumpiness (Figure 2B). In all four subplots, perceived convexity significantly increased with physical convexity (post hoc test, Tukey HSD, p < .001, convexity = 0.25 vs. convexity = 2.0). Again, across all convexity levels in the Eucalyptus Grove light field, smooth objects that were purely refractive were perceived significantly flatter than other materials of identical convexity (post hoc test, Tukey HSD, p < .001, within all other materials), but not for all stimulus and viewing conditions (result shown in Table S1 in Supplemental Material). There were no significant differences between the flattest matte object and the specular object of equivalent flatness (post hoc test, Tukey HSD, p = .786 [Grove–Smooth], p = 1 [Grove–Bumpy], p = 0.057 [St Peters–Smooth], p = 1 [St Peters–Bumpy]). Results were reproduced for different object sizes (Figure S1 and Table S2 in Supplemental Material).

Effect of Static Perspective Cues on Perceived Convexity

Moving objects provide several cues to infer their convexity, including motion cues and viewing perspective in addition to image cues (e.g., specular distortions). We performed another task in attempt to isolate these cues, but this time the stimuli were static images of the object placed at the center, extreme left, or extreme right of the image plane. We raise the hypothesis that looking at the sides (the left/right condition) might provide strong enough cues to shape, and then the result might be worse in the center condition and better in left/right condition.

Results are shown separately for the three positions of the object (Figure 3). Because left and right positions induced similar results, they were averaged. We performed a five-way ANOVA on these data to test the main effects of object position × light probe × bump level × convexity × material property. Slopes were smaller than in the motion condition, and the slopes of the center condition were smaller than left/right conditions (slope, center = 0.102, left/right = 0.161: linear regression across all material properties). The difference between positions was not significant (five-way ANOVA, main effect of positions: p = .35). Again, we found the effect of material properties on perceived convexity (p < .001, details shown in Table S3 Supplemental Material). Perceived convexity increased as physical convexity increased (main effect of convexity). The flattest (convexity = 0.25) matte object was perceived significantly flatter than the specular object of equivalent convexity (post hoc test, Tukey HSD, both center and the left/right: p < .001). Across all convexity levels, objects that were purely refractive or purely matte were perceived significantly flatter than objects with specular reflectance and identical convexity (post hoc test, Tukey HSD: p < .001; Figure 3A and C).

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Figure 3.

Effect of material properties on perceived convexity for static stimuli. Format is same as in Figure 2. A and B: Results for the object placed on center. C and D: Results for the object placed on either left or right.

These results are generally consistent across surface bumpiness and different light fields (Figure 3B and D). Across all convexity levels, objects that were purely refractive were perceived significantly flatter than specular objects of identical convexity except for bumpy objects in the St Peters Basilica for both the center and left/right conditions (post hoc test, Tukey HSD, p < .001).

It is possible these data could be explained by a learning effect because the same observers participated in the task with static images after the dynamic image task. The aforementioned hypothesis was rejected by the results; poor performance for both center and left/right, even if it had a learning effect.

The results together suggest that material properties generate static image cues for modulating the estimation of shape. However, in the absence of motion cues, the linear relationship between perceived and physical convexity was small. The decline in the slope of the relationship in the static viewing task does not appear to be due to increased uncertainty of object shape, because the error bars obtained for our perceptual estimates are similar to those of dynamic viewing tasks where a steeper slope was observed. These results suggest that dynamic and static cues contribute to the perception of shape, and these cues depend on the surface optics of different materials.

Image Analysis

We found that the surface properties of objects affect the perception of their shape. How do the image cues produced by the interaction of the light field with different material surfaces evoke different perception of shape? We examined a potential explanation for our observed results.

Curvature involves a change in surface orientation relative to the observer in depth that generates shading critical for shape perception (Fleming, Holtmann-Rice, et al., 2011; Ramachandran, 1988; Todd & Mingolla, 1983). This shading generates a variation in local contrast in image luminance that can be used to inversely estimate surface convexity. For example, consider a side view of either a flat or elongated (highly curved) object with matte surface properties embedded within an anisotropic light field (e.g., Eucalyptus Grove). The image of the flat surface will have a shallow diffuse shading gradient and lower local contrast at almost all visible surface regions—and thus, its luminance variation will be globally small. In contradistinction, the image of the elongated surface will have a steeper diffuse shading gradient and higher local contrast at the position where surface normals are oriented more obliquely to the primary lighting direction from above causing the regional variation in local contrast to be larger for the elongated surface compared with the flatter surface.

Curvature also generates variation in the scaling of texture gradients (Todd & Thaler, 2010), which influences the rate of change in luminance over finite regions of image space. Similar compression of environmental reflections occurs across specular surfaces (Fleming et al., 2004). The strength of local contrast cues generated by specular edge contours is known to be important for the perception of gloss (Kim, Tan, et al., 2016), which might also contribute to the perception of shape. It is possible that the perception of convexity can be modeled by computing variations in local contrast across the surface image. Therefore, we analyzed whether perceived surface convexity could be explained by the variations in local root-mean-square (RMS) contrast of the stimulus images by following formula:

RMS contrast = 1 N ∑ n = 1 N | x n 2 |

We computed local RMS contrast over finite image regions defined within 15 × 15 pixel (1.0 × 1.0 deg) square tiles (Figure 4). Then, we calculated the variance of RMS contrast over regions defined within 6 × 6 tiles. Thus, each variance was computed over 90 × 90 pixels (6.1 × 6.1 deg) of the stimulus image.

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Figure 4.

Correlation between local RMS contrast variability and perceived convexity. A: Normalized luminance image of an example stimulus. B: Local RMS contrasts over finite image regions defined within 15 × 15 pixels were computed. C: The variance of RMS contrast within the regions of 6 × 6 RMS contrast areas was computed. D: Correlation plots between the variance of RMS contrast of the region with highest correlation (denoted by red square in E) and perceived convexity. Color of symbols shows surface properties. Shape of symbol indicates the light probe and stimulus shape (circle: Grove–Smooth, diamond: Grove–Bumpy, square: St Peters–Smooth, triangle: St Peters–Bumpy). Symbols connected by lines indicate five levels of stimulus convexity (E). The Spearman’s rank correlation coefficient was calculated separately for each variance of RMS contrast. White outlined areas showed significant correlation (p < .05).

To assess the validity of our model, we computed the correlation coefficient between the variance of local RMS contrasts and perceived convexity (Figure 4D and E). The data for perceived convexity used here were for the condition with static stimuli presented at the center of the display. The large green symbol in Figure 4D indicates the data from the smooth sphere (convexity = 1) in the Eucalyptus Grove light probe (Figure 4A to C). Figure 4E shows the distribution of the correlation coefficients (Spearman’s R value) for each analyzed image area. Significant correlations were observed for the upper half of the image (significant correlation, p < .05). Highest correlation was found for right side of the image (R = 0.81, red outline in Figure 4E). A similar conclusion was obtained for different region size for calculating RMS contrast and tile size for calculating the variance (Figure S2 in Supplemental Material). These results suggest that perceived convexity can be explained by variance of local RMS contrasts at different parts of the image.