Shape from shading in pigeons

Light is the origin of vision. The pattern of shading reflected from object surfaces is one of several optical features that provide fundamental information about shape and surface orientation. To understand how surface and object shading is processed by birds, six pigeons were tested with differentially illuminated convex and concave curved surfaces in five experiments using a go/no-go procedure. We found that pigeons rapidly learned this type of visual discrimination independent of lighting direction, surface coloration and camera perspective. Subsequent experiments varying the pattern of the lighting on these surfaces through changes in camera perspective, surface height, contrast, material specularity, surface shape, light motion, and perspective movement were consistent with the hypothesis that the pigeons were perceiving these illuminated surfaces as three-dimensional surfaces containing curved shapes. The results suggest that the use of relative shading for objects in a visual scene creates highly salient features for shape processing in birds.     

Conjoint measurement of gloss and surface texture

The image of a material's surface varies not only with viewing and illumination conditions, but also with the material's surface properties, including its 3-D texture and specularity. Previous studies on the visual perception of surface material have typically focused on single material properties, ignoring possible interactions. In this study, we used a conjoint-measurement design to determine how observers represent perceived 3-D texture ("bumpiness") and specularity ("glossiness") and modeled how each of these two surface-material properties affects perception of the other. Observers made judgments of bumpiness and glossiness of surfaces that varied in both surface texture and specularity. We quantified how changes in each surface-material property affected judgments of the other and found that a simple additive model captured visual perception of texture and specularity and their interaction. Conjoint measurement is potentially a powerful tool for analyzing perception of surface material in realistic environments.     

Light direction from shad(ow)ed random Gaussian surfaces

Three human observers estimated the illumination direction for samples of random Gaussian surfaces illuminated by a collimated beam from random directions. These stimuli appear as 'texture' due to shading and shadowing (the surface on the microscale was Lambertian of uniform albedo; thus texture appears only through shading and shadowing). We found that observers were able to estimate the azimuth of the source with remarkable accuracy. In the shading regime (no shadows) the observers committed 180 degrees azimuth errors with 50% probability, whereas in the shadow-dominated regime they were able to avoid this convex/concave confusion to a large extent. They evidently relied on second-order statistics in the shading regime and used an unidentified first-order cue in the shadow regime. The elevations of the source were also estimated with remarkable precision. We attribute this to the statistical homogeneity of the sample which can apparently be exploited by the observers. Likely cues are the fraction of shadowed surface, average intensity and rms contrast. The ability of human observers to estimate the illumination direction from surface texture no doubt contributes to the ability to estimate the light field in scenes, which is a prerequisite to the photometric parsing of scenes (shape from shading, and so forth).     

The perception of lightness in 3-D curved objects

Lightness constancy in complex scenes requires that the visual system take account of information concerning variations of illumination falling on visible surfaces. Three experiments on the perception of lightness for three-dimensional (3-D) curved objects show that human observers are better able to perform this accounting for certain scenes than for others. The experiments investigate the effect of object curvature, illumination direction, and object shape on lightness perception. Lightness constancy was quite good when a rich local gray-level context was provided. Deviations occurred when both illumination and reflectance changed along the surface of the objects. Does the perception of a 3-D surface and illuminant layout help calibrate lightness judgments? Our results showed a small but consistent improvement between lightness matches on ellipsoid shapes, relative to flat rectangle shapes, under illumination conditions that produce similar image gradients. Illumination change over 3-D forms is therefore taken into account in lightness perception.     

The influence of object size and surface shape on shape constancy from stereo

The failure of shape constancy from stereoscopic information is widely reported in the literature. In this study we investigate how shape constancy is influenced by the size of the object and by the shape of the object's surface. Participants performed a shape-judgment task on objects of five sizes with three different surface shapes. The shapes used were: a frontoparallel rectangle, a triangular ridge surface, and a cylindrical surface, all of which contained the same maximum depth information, but different variations in depth across the surface. The results showed that, generally, small objects appear stretched and large objects appear squashed along the depth dimension. We also found a larger variance in shape judgments for rectangular stimuli than for cylindrical and ridge-shaped stimuli, suggesting that, when performing shape judgments with cylindrical and ridge-shaped stimuli, observers rely on a higher-order shape representation.     

Illusory 3-D rotation induced by dynamic image shading

Observers' perceptions of the three-dimensional structure of smoothly curved surfaces defined by patterns of image shading were investigated under varying conditions of illumination. In five experiments, observers judged the global orientation and the motion of the simulated surfaces from both static and dynamic patterns of image shading. We found that perceptual performance was more accurate with static than with dynamic displays. Dynamic displays evoked systematic biases in perceptual performance when the surface and the illumination source were simulated as rotating in opposite directions. In these conditions, the surface was incorrectly perceived as rotating in the same direction as the illumination source. Conversely, the orientation of the simulated surfaces was perceived correctly when the frames making up the apparent-motion sequences of the dynamic displays were presented as static images. In Experiment 6, moreover, the results obtained with the computer-generated displays were replicated with solid objects.     

Perception of illumination direction in images of 3-D convex objects: influence of surface materials and light fields

We investigated the perception of illumination direction in images of 3-D convex objects under variations of light field and surface material properties. In a first experiment, we used an illumination-matching procedure in order to measure observers' ability to estimate the direction of illumination in images of 3-D polyhedra rendered under different light fields and illumination directions. Match deviations were larger in frontal direction than in rear directions, mainly counterclockwise in azimuth component, and diverged, in elevation component, from the image plane. In a second experiment, we examined whether the direction estimate was affected by the surface material type (BRDF), the light field, and the illumination direction. Angular deviations varied with material surface type and were largest in the test elevation direction 0 degrees. Elevation component deviations also differed with surface type and were larger in hemispherical diffuse lighting than in collimated lighting. These results suggest that the direction estimation is better with images of evenly distributed intensity gradients than with those of drastically varying gradients, and that the visual system may not take intensity variations due to the surface material or the light field into account in estimating the direction of illumination.     

Footprints sticking out of the sand. Part 1: Children's perception of naturalistic and embossed symbol stimuli

The shading information in images that depict surfaces of three-dimensional objects cannot be perceived correctly unless the direction of the illuminating light source is known, and, in the absence of this knowledge, adults interpret such images by assuming that light comes from above. In order to investigate if children make use of a similar assumption, we analysed data from 171 children between the ages of 4.6 and 10.8 years using 10 images (shown upright and upside-down) that could be perceived as either convex or concave. Each of five images depicted a naturalistic picture (e.g., a footprint), each of the other five depicted an embossed symbol (e.g., a square). On each of 20 trials, a child was presented with either an upright or upside-down image, and indicated whether the depicted shape appeared convex or concave. Our main findings are that (i) naturalistic stimuli are significantly more likely to be perceived as if light comes from above than symbol stimuli, and (ii) children's propensity to interpret stimuli as if light comes from above increases significantly with age, and at a similar rate for naturalistic and symbol stimuli. These results suggest that, irrespective of any innate competence, children's ability to interpret shading information is gradually refined throughout childhood.     

Smooth-shape assumption for perceiving shapes from shading

Humans can perceive three-dimensional shapes from shading, but reconstructing the original shape of an object from shading alone (luminance distribution) is mathematically impossible. Researchers have used different assumptions and reported that the human visual systems can resolve this difficulty. Here, we propose an assumption for perceiving shape from shading: that the object shape is assumed to be smooth rather than angular. In experiment 1, we investigated the effect of shape smoothness by manipulating the shading profile of the test region. In experiment 2, we further investigated the effect of shape smoothness by manipulating shapes of the regions bordering on the test region using binocular disparity. Each stimulus in our experiments is interpretable from shading as having either smooth or angular edges. Observers responded to the perceived shape while viewing the stimuli, and most tended to perceive smooth rather than angular edges. These results support the idea that the smooth-shape assumption is effective for perceiving shape from shading.     

Perception of surface curvature and direction of illumination from patterns of shading

Three experiments examine the perceptual salience of shading information for the visual specification of three-dimensional form. The observers in these experiments were required to estimate the surface curvature and direction of illumination depicted in computer-synthesized images of cylindrical surfaces, both with and without texture. The results indicate that the shininess of a surface enhances the perception of curvature, but has no effect on perceived direction of illumination; and that shading is generally less effective than texture for depicting surfaces in three dimensions. These and other findings are used to evaluate the psychological validity of several mathematical analyses of shading information that have recently been proposed in the literature.     

The perception of surface curvature from optical motion

Observers viewed the optical flow field of a rotating quadric surface patch and were required to match its perceived structure by adjusting the shape of a stereoscopically presented surface. In Experiment 1, the flow fields included rigid object rotations and constant flow fields with patterns of image acceleration that had no possible rigid interpretation. In performing their matches, observers had independent control of two parameters that determined the surface shape. One of these, called the shape characteristic, is defined as the ratio of the two principle curvatures and is independent of object size. The other, called curvedness, is defined as the sum of the squared principle curvatures and depends on the size of the object. Adjustments of shape characteristic were almost perfectly accurate for both motion conditions. Adjustments of curvedness, on the other hand, were systematically overestimated and were not highly correlated with the simulated curvedness of the depicted surface patch. In Experiment 2, the same flow fields were masked with a global pattern of curl, divergence, or shear, which disrupted the first-order spatial derivatives of the image velocity field, while leaving the second-order spatial derivatives invariant. The addition of these masks had only negligible effects on observers’ performance. These findings suggest that observers’ judgments of three-dimensional surface shape from motion are primarily determined by the second-order spatial derivatives of the instantaneous field of image displacements.     

The combined influence of binocular disparity and shading on pictorial shape

The combined influence of binocular disparity and shading on pictorial shape was studied. Stimuli were several pairs of stereo photographs of real objects. The stereo base was 0, 7, or 14 cm, and the location of the light source was varied over three positions (one from about the viewpoint of the camera, one about perpendicular to the line of sight, and one in between the two). Therefore, in total, nine different combinations were studied. Subjects had to perform surface attitude settings at about 300 positions in the image plane. From the settings, depth maps were calculated on which a principal components analysis was performed. It was found that three components were enough to account for at least 97.8% of the variance in the data. The first component accounted for shape constancy. The effects of the two cues could be isolated as a linear combination of the other two components. The effects of the disparity and the shading cue variation were found to combine in almost linear fashion.     

The combined influence of binocular disparity and shading on pictorial shape

The combined influence of binocular disparity and shading on pictorial shape was studied. Stimuli were several pairs of stereo photographs of real objects. The stereo base was 0, 7, or 14 cm, and the location of the light source was varied over three positions (one from about the viewpoint of the camera, one about perpendicular to the line of sight, and one in between the two). Therefore, in total, nine different combinations were studied. Subjects had to perform surface attitude settings at about 300 positions in the image plane. From the settings, depth maps were calculated on which a principal components analysis was performed. It was found that three components were enough to account for at least 97.8% of the variance in the data. The first component accounted for shape constancy. The effects of the two cues could be isolated as a linear combination of the other two components. The effects of the disparity and the shading cue variation were found to combine in almost linear fashion.     

Color constancy: phenomenal or projective?

Naive observers viewed a sequence of colored Mondrian patterns, simulated on a color monitor. Each pattern was presented twice in succession, first under one daylight illuminant with a correlated color temperature of either 16,000 or 4000 K and then under the other, to test for color constancy. The observers compared the central square of the pattern across illuminants, either rating it for sameness of material appearance or sameness of hue and saturation or judging an objective property-that is, whether its change of color originated from a change in material or only from a change in illumination. Average color constancy indices were high for material appearance ratings and binary judgments of origin and low for hue-saturation ratings. Individuals' performance varied, but judgments of material and of hue and saturation remained demarcated. Observers seem able to separate phenomenal percepts from their ontological projections of mental appearance onto physical phenomena; thus, even when a chromatic change alters perceived hue and saturation, observers can reliably infer the cause, the constancy of the underlying surface spectral reflectance.     

The visual perception of length along intrinsically curved surfaces

The ability of observers to perceive three-dimensional (3-D) distances or lengths along intrinsically curved surfaces was investigated in three experiments. Three physically curved surfaces were used: convex and/or concave hemispheres (Experiments 1 and 3) and a hyperbolic paraboloid (Experiment 2). The first two experiments employed a visual length-matching task, but in the final experiment the observers estimated the surface lengths motorically by varying the separation between their two index fingers. In general, the observers' judgments of surface length in both tasks (perceptual vs. motoric matching) were very precise but were not necessarily accurate. Large individual differences (overestimation, underestimation, etc.) in the perception of length occurred. There were also significant effects of viewing distance, type of surface, and orientation of the spatial intervals on the observers' judgments of surface length. The individual differences and failures of perceptual constancy that were obtained indicate that there is no single relationship between physical and perceived distances on 3-D surfaces that is consistent across observers.     

Footprints sticking out of the sand. Part 2: children's Bayesian priors for shape and lighting direction

The shading information in images that depict surfaces of 3-D objects cannot be perceived correctly unless the direction of the illuminating light source is known and, in the absence of this knowledge, perception in adults is consistent with a light-from-above Bayesian prior assumption. In order to investigate if children make use of a similar assumption, 171 children between the ages of 4.6 and 10.8 years were tested with 20 images containing shading information, where the shape depicted in each image could be perceived as either convex or concave. Each child's Bayesian prior probability that light comes from above was estimated, and (assuming that decision-noise is approximately the same in all children) regression analyses revealed a significant increase in this prior probability of 0.034-0.035 per year, and predict a neutral prior (0.5) at 1.6 years for naturalistic picture stimuli and 3.6 years for abstract symbol stimuli. Additionally, each child's prior probability for perceiving shapes as being convex/concave was estimated, and was found to be close to a neutral value of 0.5 for all ages. Together, these results indicate that children have a neutral prior for shape convexity, and that their prior probability for lighting direction gradually shifts towards an adult-like prior value as they grow older. Finally, the status of these one-dimensional priors is discussed in relation to marginal distributions of high-dimensional priors implicit in the statistical structure of the physical word.     

The proximity structure of achromatic surface colors and the impossibility of asymmetric lightness matching

In asymmetric lightness matching tasks, observers sometimes report that they cannot achieve satisfactory matches between achromatic surfaces under different neutral illuminants. The surfaces appear different, yet no further adjustment of either surface improves the match. There are evident difficulties in interpreting data from a task that the observer cannot always do, and these difficulties likely affect the interpretation of a large number of previous studies. We investigated, as an alternative to asymmetric matching, the direct use of proximity judgments in the study of surface lightness perception. We asked observers to rate the perceived dissimilarity of pairs of achromatic surfaces that were placed in identical scenes and viewed under different neutral illuminants. We develop a parametric model that accurately predicts perceived dissimilarity in terms of physical light intensities and surface albedos. The parameters of this model are readily interpretable. In particular, the ratio of the influence of changes in illuminant intensity and changes in surface albedo is a measure of the extent to which the observer discounts the illuminant. Asymmetric lightness matching can be interpreted as an unachievable limiting case of proximity judgment.     

The absence of depth constancy in contour stereograms

Stereoscopic surfaces constructed from Kanizsa-type illusory contours or explicit luminance contours were tested for three-dimensional (3-D) shape constancy. The curvature of the contours and the apparent viewing distance between the surface and the observer were manipulated. Observers judged which of two surfaces appeared more curved. Experiment 1 allowed eye movements and revealed a bias in 3-D shape judgment with changes in apparent viewing distance, such that surfaces presented far from the observer appeared less curved than surfaces presented close to the observer. The lack of depth constancy was approximately the same for illusory-contour surfaces and for explicit-contour surfaces. Experiment 2 showed that depth constancy for explicit-contour surfaces improved slightly when fixation was required and eye movements were restricted. These experiments suggest that curvature in depth is misperceived, and that illusory-contour surfaces are particularly sensitive to this distortion.     

Perception of local shape from shading

Theoretically, metric solid shape is not determined uniquely by shading. Consequently, human vision has difficulty in categorizing shape when shading is the only cue. In the present research, subjects were required to categorize shaded quadric surfaces. We found that they were rather poor at this task; they confused hyperbolic and elliptic (both convex and concave) shapes easily. When a cast shadow visually indicated the direction of the illuminant, they were able to notice the concavity or convexity of elliptic shapes. However, they still confused elliptic and hyperbolic ones. Finally, when an animated sequence of eight intensity patterns belonging to one quadric shape had been displayed, the subjects were able to categorize the quadrics. However, the results are still quite moderate. Our experiments indicate that local shading structure is only a weak shape cue when presented in the absence of other visual cues.     

Shape constancy from novel views

Prior experiments on shape constancy from novel views are inconclusive: Some show that shapes of objects can be recognized reliably from novel views, whereas others show just the opposite. Our analysis of prior results suggests that shape constancy from novel views is reliable when the object has properties that constrain its shape: The object has volumetric primitives, it has surfaces, it is symmetrical, it is composed of geons, its contours are planar, and its images provide useful topological information about its three-dimensional structure. To test the role of some of these constraints, we performed a set of experiments. Solid shapes (polyhedra) were shown on a computer monitor by means of kinetic depth effect. Experiment 1 showed that shape constancy can be reliably achieved when a polyhedron is represented by its contours (most of the constraints are present), but not when it is represented by vertices or by a polygonal line connecting the vertices in a random order (all the constraints are absent). Experiments 2 and 3 tested the role of individual constraints. Results of these experiments show that shape constancy from novel views is reliable when the object has planar contours and when the shapes of the contours together with topological information about the relations among the contours constrain the possible interpretations of the shape. Symmetry of the object and the topological stability of its image also contribute to shape constancy.