S. Nishida and M. Shinya (1998) found that observers have only a limited ability to recover surface-reflectance properties under changes in surface shape. Our aim in the present study was to investigate how the degree of surface-reflectance constancy depends on the availability of information that may help to infer the reflectance and shape properties of surfaces. To this end, we manipulated the availability of (i) motion-induced information (static vs. dynamic presentation), (ii) disparity information (with the levels “monocular,” “surface disparity,” and “surface + highlight disparity”), and (iii) color information (grayscale stimuli vs. hue differences between diffuse and specular reflections). The task of the subjects was to match the perceived lightness and glossiness between two surfaces with different spatial frequency and amplitude by manipulating the diffuse component and the exponent of the Phong lighting model in one of the surfaces. Our results indicate that all three types of information improve the constancy of glossiness matches—both in isolation and in combination. The lightness matching data only revealed an influence of motion and color information. Our results indicate, somewhat counterintuitively, that motion information has a detrimental effect on lightness constancy.

*x, z*)-plane and a complexly shaped height profile (

*y*-coordinate), consisting of a combination of a number of sinus gratings with random orientations and phases (see 1 for details on stimulus construction). The shape of the stimuli was controlled by two parameters

*f*and

*a,*which determined the spatial frequency and the amplitude of the height profile, respectively (see Figure 3). The projection of the square base of the surfaces on the monitor screen had a side length of 6.5 cm. The viewing distance was 50 cm.

*I*

_{ R },

*I*

_{ G },

*I*

_{ B })

^{T}—where the indices refer to the relative intensities of the three monitor lights—was an additive mixture consisting of three different reflection components, namely the ambient, diffuse, and specular components. The relative amount to which each component contributes to the total intensity is determined by the parameters

*k*

_{a},

*k*

_{d}, and

*k*

_{s}, respectively, and by the intensity of two different light sources: The intensity of the ambient light (

*I*

_{a}) and the intensity of a point-light source (

*I*

_{p}). The diffuse component is scaled by the cosine of the angle between the surface normal and the direction of the light source (

*θ*), as defined by Lambert's law. The specular component is scaled by the cosine to the power of

*n*of the angle between the cardinal direction of the reflected light and the viewing direction (

*α*): The size of the exponent

*n*determines the spread of the specularly reflected light (“shininess”). Additionally, each component contains a triple of color weighting factors for the R, G, and B channels of the monitor that were used to assign different hues to the single reflection components.

*A*

_{ R }=

*D*

_{ R }= 1.0,

*A*

_{ G }=

*D*

_{ G }= 1.0,

*A*

_{ B }=

*D*

_{ B }= 0.0) while the specular color was kept unchanged as white light. When we used such chromatic stimuli we paid heed to equate them in luminance to corresponding grayscale stimuli.

*k*

_{d}) and the Phong exponent

*n*in the latter (however, in our experiments we transformed

*n*into the “Phong index” parameter

*m*=

*n*

^{0.25}, which provides an approximately equidistant scale of perceived shininess, cf. Wendt et al., 2008). During the stimulus presentation, these two parameters could be manipulated by the observer using the arrow keys on the keyboard. For the diffuse component (

*k*

_{d}), values within the interval [0.0, 0.7] in steps of 0.02 could be chosen, and for the Phong index

*m,*values within the interval [1.0, 3.5] in steps of 0.05 could be chosen. Figure 4 illustrates the perceptual effect of manipulating the Phong index. The test surface was presented with 9 different reflection parameter combinations (the cartesian product of

*k*

_{d}= {0.2, 0.3, 0.4} and

*m*= {1.35, 1.8, 2.35}) for each shape condition that was tested. All other parameters in Equation 1 were kept constant with

*I*

_{a}= 0.2,

*k*

_{a}= 0.3,

*I*

_{p}= 1.0,

*k*

_{s}= 0.2 in Experiments 1 and 2 and

*k*

_{s}= 0.45 in Experiment 3.

*y*-axis of the virtual space, and in the 90° end position, the global surface normal was parallel to the

*z*-axis (=observer direction; see Figure 5, left).

*x*= 0.0,

*y*= 70.71,

*z*= −70.71). In the observer motion condition, the surface rotated in exactly the same way, but in this case the light source followed the motion of the surface: In each frame, the point-light source was positioned in the same direction as the global surface normal, with a constant distance of 100 cm to the center of the surface.

*f*= 3.0 and an amplitude of

*a*= 0.2 (see surface no. 4 in Figure 3). The match surface was presented in one of 7 different shape conditions with the shape parameter combinations (

*f, a*) = (1.5, 0.2), (1.5, 0.4), (3.0, 0.1), (3.0, 0.2), (3.0, 0.4), (6.0, 0.1), and (6.0, 0.2).

*k*

_{d}× 3 values for the Phong index

*m*× 2 rotation conditions) whereby each condition was presented 4 times. The total of 504 randomly ordered trials was subdivided into 4 blocks that were completed by each observer in 4 separate sessions.

*k*

_{d}and

*m,*respectively) of the test stimuli (open circles) and the corresponding pairs of the mean settings (arrowheads). The error ellipses are based on the covariance matrices of the samples.

*f*= 3.0 and

*a*= 0.2). Thus, one would expect that the data points of the settings in our diagrams will correspond to the effects found by Nishida and Shinya, if the latter are point reflected at the coordinates of the test. This is roughly the case.

*both*shape parameters

*f*and

*a*from the test values and not just in one. Actually, the shape conditions 2, 4, and 6 are related to each other in a specific way: With regard to local curvatures, each of these shape conditions can be transformed into the others by a simple scaling of the underlying vertices. Therefore, it seems that surfaces whose structures only differ in scaling exhibit similar shading features in the proximal stimulus (when they have equal reflection properties) that are considered as equivalent by the visual system. A possible explanation for this result may be that the shape of the highlights remains approximately invariant under a scaling transformation. It would thus be interesting to explore to what extent the invariance of highlight shape actually holds.

*x*= 0.0,

*y*= 100.0,

*z*= 0.0) in the virtual space.

*k*

_{d}and the Phong index

*m*(see General methods section) and also the task and procedure were the same as before. In total, 108 different condition combinations resulted (3 levels of the factor “binocular information” × 2 levels of the factor “motion information” × 2 shape conditions for the match surface × 3 values for the diffuse component of the test × 3 values for the Phong index), which were each repeated four times. The set of 432 trials was randomized and split in four equally sized blocks that were completed by each observer in four different sessions.

*p*< 3 × 10

^{−9}for shape condition 1 and

*p*< 6 × 10

^{−8}for shape condition 3. The main effect of the factor “binocular information” was also significant under both shape conditions (

*p*< 0.00047 in shape condition 1 and

*p*< 0.00013 in shape condition 3). Compared to monocularly presented stimuli, the systematic error of the glossiness matches decreased considerably when the stimuli contained surface disparity. This systematic error was reduced further when in addition to surface disparity also highlight disparity was available in the stimuli. This indicates that the visual system takes both kinds of binocular information into account when it estimates the glossiness of a surface.

*f*= 3.0 and

*a*= 0.2 (shape condition 4 in Figure 3; cf. 1). In order to keep the total number of trials within a reasonable limit, we only used shape condition 1 (

*f*= 1.5;

*a*= 0.2) for the match surface. This restriction seems justified in light of the great similarity of the results with shape conditions 1 and 3 observed in Experiment 2.

*p*< 0.0056) and the lightness matches (

*p*< 4.42 × 10

^{−8}). With respect to the lightness matches, this trend seems to be reversed, i.e., the systematic errors seem to increase under the color conditions compared to the achromatic conditions. On closer inspection, however, this finding is the result of an inappropriate averaging of the data across all observers that ignored the fact that different observers show different polarities in their lightness settings. An inspection of the individual results of the four observers shown in Figure 9 reveals that the lightness matches benefit

*most*from the availability of color information. A further analysis of the individual data also reveals an effect of the factor “motion information” on the lightness matches: All observers show smaller systematic errors under static than under dynamic stimulus presentation. With regard to the glossiness matches, the diagrams for the single observers show a more heterogeneous pattern of results (left column in Figure 9): Observers LF and CG, for instance, seem to take color information more into account than observers GW and TK and while observer GW seems to make strong use of motion information in order to judge the glossiness of a surface, the other observers seem to use this kind of information to a much lesser degree—indicating that different observers show a different receptiveness to certain combinations of information.

*better*under static than under dynamic stimulus presentation is rather astonishing given our assumption that the presence of motion information facilitates a separation between specular and diffuse reflection components. As both components stand in a complementary relation to each other, this assumption implies that the estimation accuracy of both components benefits equally from the presence of motion information (a few studies, however, indicate that the presence of highlights or mirror images barely affects the perceived color of a surface; cf. Todd, Norman, & Mingolla, 2004; Xiao & Brainard, 2006). Furthermore, this finding seems to contradict our results from Experiment 1 where we found that the accuracy of the lightness settings was better under the surface motion condition (where dynamic changes of the diffuse light occurred) than under the observer motion condition (where the amount of diffuse light was constant for each surface point during the rotation).

*that*the visual system makes use of several cues in order to perform gloss constancy, it remains an open question in

*which way*these sources of information are used. An influence of two potential mechanisms was discussed above (see Introduction section): First, a cue (for instance motion and surface disparity information) may contribute to a better estimation of the 3D shape of a surface. This information could then be taken into account by the visual system to infer spatial properties of highlights, which depend on local surface curvature. Second, a cue (for instance, motion and color information, and highlight disparity) may contribute to a better segregation of the diffuse and specular reflection components, which are confounded at each point of a surface.

*x*and

*z*:

*x, y, z*) are the vertices of this surface. The surface is the sum of sinus gratings with frequencies in the range from 0 to 2

*f*cycles/sl, where sl is the side length of the square base. At each frequency, the orientation

*o*

_{ k }and the phase

*p*

_{ k }of the corresponding sinus grating was randomly chosen from the intervals [0,

*π*] and [0, 2

*π*], respectively. The exponential weighting function gives sinus gratings with high frequencies less weight. The height of the surface was normalized in such a way that an amplitude factor

*a*= 1.0 corresponded to a stimulus with a height range two times the side length of the square base.

*f*and the amplitude

*a*jointly determine the global shape of the surfaces and were varied in the experiments (see Figure 3).

*z*-axis. To display the surface, all vertices of the surface were scaled by the factor 0.12. This way, the stimuli (which were centered 10 cm behind the clipping plane in the virtual space) were brought to a size where the projection of the square base of the surfaces on the monitor screen had a side length of ca. 6.5 cm.

*ECVP Abstract Supplement,*77.