Color, lightness, and glossiness are perceptual attributes associated with object reflectance. For these perceptual representations to be useful, they must correlate with physical reflectance properties of objects and not be overly affected by changes in illumination or viewing context. We employed a matching paradigm to investigate the perception of lightness and glossiness under geometric changes in illumination. Stimuli were computer simulations of spheres presented on a high-dynamic-range display. Observers adjusted the diffuse and specular reflectance components of a test sphere so that its appearance matched that of a reference sphere simulated under a different light field. Diffuse component matches were close to veridical across geometric changes in light field. In contrast, specular component matches were affected by geometric changes in light field. We tested several independence principles and found (i) that the effect of changing light field geometry on the diffuse component matches was independent of the reference sphere specular component; (ii) that the effect of changing light field geometry on the specular component matches was independent of the reference sphere diffuse component; and (iii) that diffuse and specular components of the match depended only slightly on the roughness of the specular component. Finally, we found that equating simple statistics (i.e., standard deviation, skewness, and kurtosis) computed from the luminance histograms of the spheres did not predict the matches: these statistics differed substantially between spheres that matched in appearance across geometric changes in the light field.

*ρ*

_{d}controls the diffuse component (“albedo”),

*ρ*

_{s}controls the strength of the specular component (“glossiness”), and

*α*controls the spread of the specular component (“roughness”). All scenes were rendered with the RenderToolbox package for Matlab (http://rendertoolbox.org). RenderToolbox acts as an interface to the RADIANCE rendering software (Ward, 1994), allowing scenes to be rendered independently at different monochromatic wavelengths. This ensures that the spectral interaction between illuminants and surfaces is simulated in a physically correct manner. This feature was not critical here because the stimuli were grayscale, but it remained convenient to use this software.

*ρ*

_{d}= [0.15 0.35]) and three levels of specularity (

*ρ*

_{s}= [0 0.06 0.12]) for the reference stimuli. One set of spheres was rendered with a smooth specular component (

*α*= 0.001), while another was rendered with a rough specular component (

*α*= 0.1).

*XYZ*values on the assumption that the RGB values represented linearized RGB primary intensities with respect to the sRGB standard (International Electrotechnical Commission, 1999). A three-dimensional linear model for surface reflectance, computed in our laboratory from measurements of 462 Munsell papers (Newhall, Nickerson, & Judd, 1943; Nickerson, 1957; Nickerson & Wilson, 1950), was then used to convert the

*XYZ*values of each pixel to spectra. This was done by forming a 3 by 3 transformation matrix between

*XYZ*values and linear model weights, using standard linear model methods (e.g., Brainard, 1995). Spectra were produced by multiplying the basis functions by the obtained weights. The particular choice of linear model was not of deep theoretical significance and was motivated primarily by convenience; we currently know little about the spectral variation of real-world light fields. The rendering procedure resulted in an hyperspectral image with 31 planes, with each plane corresponding to one wavelength band. Sample wavelengths were between 400 and 700 nm at 10-nm steps. For the current experiment, only the 500-nm band resulting from this process was used. This single image plane was replicated three times to produce identical red, green, and blue image planes for display. Although the conversion to spectral light fields and subsequent hyperspectral rendering was not necessary for the current experiment, we implemented it in preparation for planned future experiments where the spectral properties of the stimuli will be manipulated.

^{2}. The minimum luminance was below the measurement range of our radiometer, but at least a factor of 10,000 below the maximum luminance. There were some deviations between desired and displayed chromaticities, due primarily to shifts in the chromaticity of the nominally neutral projected light as a function of luminance. These shifts were not corrected for by the display control software but were not readily apparent in the displayed images. Through analysis of the calibration data, we estimate that mean chromaticity of the scenes (i.e., the neutral point of the display) was

*x*= 0.306 and

*y*= 0.353 across all input RGB values and changed gradually as a function of luminance from

*x*= 0.307 and

*y*= 0.338 to

*x*= 0.302 and

*y*= 0.375 as luminance varied between 0.025 and 423 cd/m

^{2}, with additional shifts at very low luminances.

*x*-axis and the reference (Galileo) values on the

*y*-axis. This allows direct comparison between the two cases. The broad effect in the data is that the points fall well below the unity line. The slopes of the regression lines shown in Figure 4B for the simple context were 0.51 and 0.40, and for the complex context, 0.55 and 0.45 for VIL and BNW, respectively.

*t*-tests confirmed that none of the differences were significantly different from zero (the six uncorrected

*p*-values ranged from 0.05 to 0.93).

*t*-tests confirmed that none of the differences shown in Figure 8 were significantly different from zero (3 tests; uncorrected

*p*-values of 0.02, 0.36, and 0.78 for Figures 8A–8C, respectively). We attribute the significant uncorrected

*p*-value for Figure 8A to the outliers in the data.

*p*= 0.004 for specular comparison in Figure 9C; the other five uncorrected

*p*-values varied between 0.01 and 0.52).

*x*-axis) against the same statistics for the same spheres under the Galileo light field (

*y*-axis). As noted above, there was little effect of light field geometry on the histogram means because of the way we normalized light field intensities. For the other three statistics, the change in light field had a large effect. The bottom panels show the same statistics, but rather than computing them from the same physical spheres across the light field change, we computed them from the asymmetric matches. Each point represents the statistic value for a pair of spheres judged to match across the illuminant change. For an observer who matched spheres based on one of these statistics, the data in the bottom panel for that statistic would fall along the positive diagonal of the plot. This pattern is approximated only for the histogram mean, and this is not diagnostic since very little variation in the mean was produced by the light field change. For the other three statistics, the data deviate strongly from the positive diagonal. Specifically, these data falsify the hypothesis that specular component matches are predicted solely by luminance histogram skewness (second panel from the right).

^{2}. Whether performance is invariant with mean luminance is an aspect that requires future exploration.