Free
Article  |   August 2011
The perception of gloss depends on highlight congruence with surface shading
Author Affiliations
Journal of Vision August 2011, Vol.11, 4. doi:10.1167/11.9.4
  • Views
  • PDF
  • Share
  • Tools
    • Alerts
      ×
      This feature is available to Subscribers Only
      Sign In or Create an Account ×
    • Get Citation

      Juno Kim, Phillip Marlow, Barton L. Anderson; The perception of gloss depends on highlight congruence with surface shading. Journal of Vision 2011;11(9):4. doi: 10.1167/11.9.4.

      Download citation file:


      © 2016 Association for Research in Vision and Ophthalmology.

      ×
  • Supplements
Abstract

Studies have shown that displacing specular highlights from their natural locations in images reduces perceived surface gloss. Here, we assessed the extent to which perceived gloss depends on congruence in the position and orientation of specular highlights relative to surface shape and the diffuse shading from which surface shape is recovered. The position and orientation congruence of specular highlights with diffuse shading was altered while preserving their compatibility with physical surface shape (Experiment 1). We found that perceived gloss diminished as the position of highlights became incompatible wit h the surface's global diffuse shading maxima. In a subsequent experiment, we constrained highlight proximity near the global luminance maxima in diffuse shading. When we disrupted the consistency in the local position and orientation of specular highlights with respect to the diffuse shading and local surface meso-structure, a decline in perceived gloss was still observed (Experiment 2). This decline in perceived gloss caused by misaligning the positions and orientations of specular highlights relative to diffuse surface shading could not be explained by differences in orientation fields alone (Experiments 3 and 4). These results suggest the visual system assesses both position and orientation congruence between specular highlights and diffuse shading to estimate surface gloss.

Introduction
Surfaces reflect light that carries information about their material properties. Glossy surfaces generate specular reflections of the illumination environment, but little is known about how the visual system distinguishes specular highlights from other sources of luminance variation, such as surface shading or texture. It has been suggested that the visual system may use statistical properties of images (Motoyoshi, Nishida, Sharan, & Adelson, 2007; Sharan, Li, Motoyoshi, Nishida, & Adelson, 2008), motion characteristics of surface highlights (Doerschner, Kersten, & Schrater, 2011; Hartung & Kersten, 2002; Wendt, Faul, Ekroll, & Mausfeld, 2010), information about the position of surface highlights in depth (Blake & Bülthoff, 1990), and the alignment of highlights relative to the surface's diffuse shading profile (Anderson & Kim, 2009; Beck & Prazdny, 1981; Todd, Norman, & Mingolla, 2004) to distinguish specular reflections from other sources of luminance variation. Here, we further investigate how the relationship between specular highlights and diffuse shading influences perceived gloss. 
Although it was recently proposed that the visual system uses simple image statistics—histogram or subband skew—to estimate surface gloss (Motoyoshi et al., 2007; Sharan et al., 2008), we argued that such statistics are incapable of distinguishing luminance variations that are due to surface specularity from luminance variations that are due to 3D surface shape, surface pigmentation, or the illumination field (Anderson & Kim, 2009; Kim & Anderson, 2010). We argued that surfaces only appear glossy when specular highlights are positioned in the “right place” which cannot be determined from either histogram or subband skew. This argument is consistent with previous work that demonstrated the dependence of perceived gloss on the compatibility between surface highlights and surface geometry. Beck and Prazdny (1981) showed that rotating the highlights on a glossy vase led to a percept of a matte vase overlaid with light pigment or surface markings. Blake and Bülthoff (1990) manipulated the 3D position of a specular highlight for a convex surface and found that the highlight only appeared as the specular reflection of a glossy surface, when the highlight appeared at the geometrically correct depth. More recently, Anderson and Kim (2009) showed that the perception of gloss was abolished when highlights were rotated or translated in the image plane, which disrupted the alignment of specular highlights with surface shading. All of these studies reveal that surface gloss depends critically on the position of luminance extrema (highlights) and surface geometry, not merely on the presence of local image features that can be measured with simple image statistics. 
The natural question that arises from this work is: what does it mean for highlights to appear in the “right place” in 2D images of glossy surfaces? The generative (physical) answer to this question is relatively straightforward. Surface regions with high curvature are more likely to contain surface normals oriented toward the brightest illumination sources and will generate higher diffuse shading intensities (Lambert's Law). As the viewing direction deviates from the illumination direction, the amount of displacement between specular highlights and luminance maxima in diffuse shading decreases according to a cosine rule. For this reason, specular highlights will tend to appear in regions near, but not precisely at, luminance maxima in diffuse shading (Fleming, Torralba, & Adelson, in press; Koenderink & van Doorn, 1980). No such positional constraint applies to surface pigments, which can appear anywhere on a surface. Hence, a specular highlight's position relative to the luminance maxima in diffuse shading could theoretically be used to distinguish specular highlights from surface texture. 
From the perceptual side of the problem, it remains an open question how the visual system distinguishes specular highlights from other forms of luminance maxima. At least two possible sources of information can be distinguished: a position or brightness congruence between the luminance maxima of specular highlights with the luminance maxima generated by diffuse shading and an orientation congruence between the shading flow and the shape of highlights elongated along minimal lines of surface curvature. A number of researchers have argued that perceived gloss depends on congruence in the orientation of specular highlights with diffuse shading gradients. The distribution of local orientation responses—or orientation fields—that arise in response to local gradients in diffuse surface shading can provide low-level information about surface structure (Ben-Shahar & Zucker, 2001; Breton & Zucker, 1996). Fleming, Torralba, and Adelson (2004) noted that the orientation fields for specular highlights tend to be aligned with the orientation fields for diffuse shading in natural images (see Figure 1). In contradistinction, surface pigments can generate edges in any orientation relative to 3D surface shape. Consistency in the orientation of bright highlights with the orientation fields of surrounding diffuse shading could be used to identify specular highlights, as in Figure 1A (left). Inconsistency in the orientation of bright highlights with the orientation fields of surrounding diffuse shading could indicate the presence of textural markings, as in Figure 1B (left). In support of this view, when specular highlights are rotated or translated from their rendered locations, they appear as surface pigment or paint on a completely matte surface (Anderson & Kim, 2009; Beck & Prazdny, 1981; Todd et al., 2004). Recent work from our laboratory showed that rotating specular highlights in the image as little as 5° substantially reduced perceived gloss and caused the highlights to appear as pigment overlaying the surface (Anderson & Kim, 2009). This decline in perceived gloss was also associated with a decrease in the correlation between the local orientation fields for specular highlights and underlying diffuse shading. 
Figure 1
 
(A) An elongated surface region generates a congruent specular highlight that is stretched along lines of minimal change in diffuse shading (left), which also conforms to the direction of minimal surface curvature (right). (B) Rotating the specular highlight by 90° relative to the surface makes it incongruent with surrounding diffuse shading gradients (left) and 3D surface curvature (right).
Figure 1
 
(A) An elongated surface region generates a congruent specular highlight that is stretched along lines of minimal change in diffuse shading (left), which also conforms to the direction of minimal surface curvature (right). (B) Rotating the specular highlight by 90° relative to the surface makes it incongruent with surrounding diffuse shading gradients (left) and 3D surface curvature (right).
Although orientation incongruence between diffuse shading and specular highlights can potentially explain the decline in gloss experienced when highlights are rotated relative to the underlying surface geometry, this is not the only explanation possible. Rotation of highlights will also cause specular highlights to appear near the luminance minima of diffuse shading, which would generate brightness incongruences as well as orientation incongruences. In a companion study, we parametrically translated and rotated a single anisotropic specular highlight within the image plane to vary its position and orientation congruence relative to the surrounding diffuse shading (Marlow, Kim, & Anderson, in press). We found that both forms of incongruence contributed to the decline in surface gloss experienced when highlights were displaced from their naturally occurring positions. Thus, although orientation congruence plays some role in the decline in perceived gloss that occurs when highlights are rotated into the wrong positions, the effects of brightness incongruence also contribute to a decline in perceived gloss. This point was anticipated by Beck and Prazdny (1981), who noted that perceived gloss will not arise simply because highlights have the same orientation as the surrounding shading. They proposed that perceived gloss also depends on the luminance gradient around the highlight appearing to have arisen from the curvature of a surface. Consistent with this proposal, Todd et al. (2004) argued that the perceptual recovery of surface gloss and the recovery of 3D shape from shading are interdependent. Anderson and Kim (2009) argued that the visual system may identify specular highlights by assessing whether their orientations are congruent with the recovered 3D surface structure. Specular highlights are usually produced at local points of high surface curvature and tend to be elongated along lines of minimum surface curvature. Therefore, the appearance of specular highlights may depend on their position and orientation congruence with the structure of the recovered 3D surface shape; the appearance of specular reflections may require that bright highlights lie along lines of minimum surface curvature as in Figure 1A (right) rather than across such lines as in Figure 1B (right). Anderson and Kim showed that orientation field differences between the diffuse and specular images could provide a good account of the decline in perceived gloss that was observed by rotating and translating highlights but did not explore the possible contribution of the brightness incongruence that may have also contributed to the decline in perceived gloss. In the experiments presented below, we further explore how the visual system determines whether luminance extrema are specular reflections of a glossy surface or pigmentation by varying the congruence of the specular reflections with that of the diffuse surface reflectance. 
In addition to the information available in single images, the motion of 3D surfaces can also provide information for distinguishing specular highlights from surface textures. When a glossy surface moves or is viewed by a moving observer, specular highlights slide rapidly across surface regions with low curvature and “cling” to surface regions with high curvature (Koenderink & van Doorn, 1980). Perceived gloss is enhanced by dynamic changes in the appearance of specular highlights generated by rotating surfaces (Wendt et al., 2010). Hartung and Kersten (2002) demonstrated that a stationary smooth object appeared ambiguous as either glossy or matte when the reflection of the surrounding world was mapped onto the surface as a texture. The surface always appeared glossy when it rotated and dynamically distorted the reflected illumination field seen through the surface, but appeared completely matte when the reflection rotated with the 3D surface-like pigment. Doerschner et al. (2011) more recently showed that the spatial distribution of specular highlight velocities can provide diagnostic information about material properties of completely specular or diffuse objects. Given the rich information provided by motion, it is unclear to what extent perceived gloss depends on the compatibility of highlights with the diffuse shading of moving surfaces. 
In the following experiments, we sought to ascertain the degree to which perceived surface gloss depends on highlight congruence with diffuse surface shading in both static and moving images. We also examined the relative contributions of position and orientation congruence on perceptual estimates of surface glossiness. Our goal is to provide further insight into how the visual system distinguishes specular highlights from other forms of luminance maxima. 
Experiment 1
In Experiment 1, we evaluated the degree to which perceived gloss depends on specular highlights being correctly aligned with diffuse surface shading. In previous studies (e.g., Anderson & Kim, 2009), the orientation of highlights relative to the surface's diffuse shading profile was altered using simple image-wise displacements of the specular highlights. However, these manipulations also rendered the highlights' positions incongruent with 3D surface shape. In Experiment 1, we preserved highlight compatibility with physical surface shape while altering their position relative to the peak luminance in diffuse shading generated by different illumination fields. We used three illumination fields that systematically varied in their global isotropy in diffuse shading. As shown in Figure 2, the diffuse shading profile rendered in the St. Peter's Basilica light field is globally more isotropic than the same surface rendered in the outdoor illumination fields (Uffizi and Eucalyptus Grove). The two outdoor illumination fields generate larger anisotropies in global diffuse shading, evident in the difference in diffuse intensity between the top and bottom parts of these surfaces. If highlight proximity to the peak luminance in diffuse shading is used to estimate surface gloss, then specular highlights displaced relative to highly anisotropic diffuse shading should make the surface appear less glossy. In contradistinction, the nearly uniform diffuse shading profile generated by the St. Peter's illumination field should reduce the information available to differentiate highlight positions relative to diffuse shading. Perceived surface gloss should therefore be less affected by displacing highlights relative to the diffuse shading generated with this more isotropic illumination field. 
Figure 2
 
Anisotropy in diffuse shading profiles of the same 3D surface placed in the three different illumination fields. The global pattern of diffuse surface shading is more circularly symmetric in the illumination context of the St. Peter's Basilica light field compared to the outdoor illumination fields of the Uffizi and Eucalyptus Grove.
Figure 2
 
Anisotropy in diffuse shading profiles of the same 3D surface placed in the three different illumination fields. The global pattern of diffuse surface shading is more circularly symmetric in the illumination context of the St. Peter's Basilica light field compared to the outdoor illumination fields of the Uffizi and Eucalyptus Grove.
Highlights were displaced relative to diffuse shading using a two-stage computer rendering technique: The specular reflections were rendered with the illumination field upright and the diffuse shading rendered with the same illumination field rotated counterclockwise by varying amounts. These illumination field rotations also altered the layout of orientation fields for diffuse shading surrounding specular highlights, while ensuring that diffuse shading and specular highlights were both consistent with the underlying physical 3D surface geometry. If perceived gloss primarily depends on specular highlights being positioned near surface regions with high curvature, then perceived gloss should be less affected by displacing specular highlights in ways that preserve their natural geometric alignment with physical 3D surface shape. Alternatively, if perceived gloss depends on highlights being co-aligned with the orientation fields of diffuse shading, then altering the direction of diffuse illumination to become incompatible with the orientation fields of specular highlights should reduce perceived gloss. 
In addition to the local consistency between the orientations of highlights and diffuse shading, perceived gloss may also depend on variations in the pattern of highlight velocities generated by the shape of moving surfaces (Doerschner et al., 2011; Koenderink & van Doorn, 1980). Because our manipulations preserved highlight compatibility with physical 3D surface shape, they should also retain much of the natural variation in the pattern of specular highlights' velocities. Therefore, we included conditions where observers viewed each surface rotating around its vertical axis. The purpose of these conditions was to further assess whether perceived gloss depends on a highlight's dynamic consistency with 3D shape, compared with orientation field information alone. 
Observers
Fourteen first-year undergraduate psychology students with normal or corrected-to-normal color vision participated in the study. All were naive to the experimental procedures and research rationale until they were debriefed at the conclusion of the experiment. 
Stimuli
Three-dimensional artificial surfaces were generated using the open-source software Blender 3D. A geodesic sphere consisting of 327,680 triangular polygons was created by subdividing an icosahedron and coercing the interpolated vertices to form a sphere. Surface relief was introduced using displacement mapping, which systematically transformed the sphere's shape by altering vertex heights according to the luminance values of a pink noise texture. Texture synthesis was performed using the internal procedural texture feature in Blender (version 2.49). Procedural textures are seamless noise bases that can be used to generate smooth changes in surface curvature. A pink noise (cloud) texture was generated in Blender using the original noise basis with a value of 0.5 for noise size. This texture essentially comprised a 1/f power spectrum generated by adding components that had random orientations and phases. Due to the limited number of vertices in the 3D model that were used to sample texture detail, only the lower frequency band of the cloud texture displaced surface vertices. This resulted in the generation of a globally round surface with smooth variation in local relief. 
The 3D surface model was exported to Radiance (Ward, 1994) where an image-based lighting (IBL) algorithm produced photorealistic rendering (Debevec, 2002). The specific IBL parameters we used in Radiance were one ambient reflection and 256 ambient divisions to simulate the appearance of surfaces in real-world illumination environments. We also used the Ward model for rendering specular reflections of the illumination environment (specularity = 0.2). The observer's simulated vantage point was fixed at the side of the surface. Chromatic images in 512 × 512 high dynamic range (HDR) format were rendered for different angular orientations of the surface rotated around its vertical axis over a 0° to 360° range at 2° steps. Rendering was performed twice for each viewing orientation to obtain a diffuse rendering and another (glossy) rendering with both diffuse and specular components. An image mask with the surface blacked out against the background was also computed. Subtracting the mask from the surface images removed the background from test images. 
The specular highlight map for each glossy image was obtained by subtracting the luminance values in the diffuse image away from the corresponding luminance values in the glossy image with the same surface geometry. As shown in Figure 3, separate diffuse images were rendered with the illumination direction now rotated counterclockwise around the visual axis at known angles. Five angular offsets were used in this experiment (0°, 15°, 45°, 90°, or 180°). The specular highlight map was then added to these comparable surfaces rendered with the rotated diffuse illumination field to produce a single stimulus image. Figure 4 shows sample images for three levels of highlight offset in the three illumination fields. The procedure was repeated for the three illumination fields with each view of the surface over the 0° to 360° rotational range. Chromatic images were linearly tone mapped to 8-bit grayscale for presentation using experimental control software written in Visual C++ 6. 
Figure 3
 
Method used to render specular highlights consistent with surface geometry while altering diffuse shading. Specular highlights rendered for the upright light probe were added to different radial profiles of diffuse shading produced by counterclockwise rotation of the light probe used for diffuse illumination (e.g., 0°, 45°, 90°, and 180°). The specular highlight map generated by the Eucalyptus Grove illumination field is shown in the center.
Figure 3
 
Method used to render specular highlights consistent with surface geometry while altering diffuse shading. Specular highlights rendered for the upright light probe were added to different radial profiles of diffuse shading produced by counterclockwise rotation of the light probe used for diffuse illumination (e.g., 0°, 45°, 90°, and 180°). The specular highlight map generated by the Eucalyptus Grove illumination field is shown in the center.
Figure 4
 
Effect of rendering specular reflections consistent with the geometry of a 3D surface where the orientation of the illumination field providing diffuse shading is the same (0°) or rotated counterclockwise by 90° (middle row) and 180° (lower row).
Figure 4
 
Effect of rendering specular reflections consistent with the geometry of a 3D surface where the orientation of the illumination field providing diffuse shading is the same (0°) or rotated counterclockwise by 90° (middle row) and 180° (lower row).
Procedure
Visual stimuli were presented in pairs on either side of a CRT display (21″ Sony Trinitron) using a two-alternative forced choice (2AFC) paired comparison approach. The monitor had a maximum realizable intensity of 82 cd/m2 and its luminance gamma was calibrated to 2.2. We showed our observers the images of St. Matthew obtained from Anderson and Kim (2009, Figure 4) to demonstrate the difference in the appearance between specular reflections and surface pigmentation. The observer's attention was directed toward differences in the way the similarly bright features appeared as gloss or paint between the images. 
During the experiment, observers were instructed to study test images for 5 s and then push either the left or right directional key on a standard keyboard to select the image containing highlights that appeared to arise from the glossier surface. Six blocks of trials were performed with the three illumination fields and two levels of surface motion (i.e., 3 × 2 within-subjects design). Each paired presentation trial comprised two stimuli that differed in offset between specular highlights and diffuse shading. The presentations were counterbalanced such that each unique pair was presented twice with each image appearing on both sides of the display. A 2-min rest break was provided after each block of trials to reduce any effects arising from prolonged exposure to the stimuli. The probability that an image was selected as glossy was determined as the number of times it was selected as glossier divided by the total number of times it was presented. 
Highlight orientation was assessed using the correlation between the orientation fields for the edges of specular highlights and surrounding diffuse shading. Figure 5 exemplifies the procedure used to identify specular highlight edges for the original glossy image where highlights are compatible with both diffuse shading and physical surface shape. We first transformed the stimulus images with added highlights using a simple edge detector applied to images with specular highlights added to diffuse shading. For edge detection, the image's horizontal and vertical derivatives were determined, and the sum of squares between the two derivatives was then computed. Sum-of-square values above a threshold of 45 were taken as the locations of highlight borders as this value conformed to the edges of the most intense highlights on the basis of visual inspection. Polar orientations were determined at highlight borders from the local magnitudes of horizontal and vertical derivatives. Local orientations were pooled over a small local neighborhood using a Gaussian filter (sigma = 24). These estimates of local polar orientation fields were computed for matte images and images with added highlights obtained for several views of the surface over the 360° rotational range (at 20° steps; i.e., 18 equally spaced measurements). Pearson's correlations between the orientation fields for matte and glossy images provided an estimate of local orientation field consistency between specular highlights and diffuse shading at specular highlight borders. 
Figure 5
 
Edge detection was used to identify edges of specular highlights generated by glossy surfaces. The insets on the right show the corresponding orientation fields for the diffuse shading and the edge of a highlight for the same surface region.
Figure 5
 
Edge detection was used to identify edges of specular highlights generated by glossy surfaces. The insets on the right show the corresponding orientation fields for the diffuse shading and the edge of a highlight for the same surface region.
Results and discussion
Means and 95% confidence intervals plotted in Figure 6 show the estimated probabilities that surfaces appeared glossy within the three illumination fields. Separate axes show perceptual judgments for static (blue) and moving (red) stimuli. Rotating the illumination field for diffuse shading relative to specular highlights resulted in a general decline in perceived gloss. Declines in perceived gloss coincided with transformations in the appearance of surface highlights from specular reflections to light surface pigmentations. Perceived gloss decreased continuously over the entire 0° to 180° rotational range in diffuse lighting with the outdoor illumination fields but only decreased over a limited rotational range in diffuse lighting with the St. Peter's illumination field (0° to 15°, approximately). 
Figure 6
 
Means and 95% confidence intervals showing the estimated probabilities of a surface being selected as glossier after different levels of angular offset in diffuse illumination relative to the natural specular highlights rendered with each of the three illumination fields (across columns). Results obtained with static images (blue) and dynamically rotating movies (red) in separate axes down each column.
Figure 6
 
Means and 95% confidence intervals showing the estimated probabilities of a surface being selected as glossier after different levels of angular offset in diffuse illumination relative to the natural specular highlights rendered with each of the three illumination fields (across columns). Results obtained with static images (blue) and dynamically rotating movies (red) in separate axes down each column.
We performed separate regression analyses to determine whether the relationship between perceived gloss and misalignments in diffuse lighting varied across illumination environments. There was a highly significant inverse linear relationship between perceived gloss and misalignment in the direction of diffuse illumination with the Uffizi light field (t 136 = 12.58, p < 0.000001). Similarly, there was a significant inverse linear relationship between perceived gloss and misalignment in diffuse illumination with the Eucalyptus Grove light field (t 136 = 14.67, p < 0.000001). There was also a significant, though comparatively weaker, linear relationship between perceived gloss and misalignment in diffuse illumination with the St. Peter's Basilica illumination field (t 136 = 2.30, p < 0.05). 
Surface motion had little influence on the changes in perceived gloss produced by displacing the specular highlights' positions relative to diffuse shading. As shown in Figure 6, the psychometric curves were similar in shape across moving (red) and static (blue) presentations of surfaces rendered in the same illumination field. Regression analyses showed no significant difference in the slope coefficients for the curves between static and moving conditions when stimuli were rendered with the Uffizi illumination field (t 136 = 0.63, p = 0.53) or the Eucalyptus Grove illumination field (t 136 = 1.72, p = 0.09). However, there was a significant interaction effect between motion conditions and misalignments in diffuse shading using the St. Peter's Basilica light probe (t 136 = 2.53, p < 0.05). This interaction effect seems to be due to the lack of significant (negative) decline in perceived gloss with increasing misalignment in the diffuse surface shading using the St. Peter's Basilica light field (r = +0.15, t 13 = 1.11, p = 0.29). There was a small initial decline in perceived gloss with small phase offsets in static presentations, but this was reduced during surface motion. This appears to suggest that small positional inconsistency between displaced specular highlights and the global isotropy in diffuse shading is harder to identify in moving surfaces. 
Angular displacement between specular and diffuse illumination fields misaligned specular highlights with respect to the local orientation fields of diffuse shading but should have preserved highlight compatibility in shape and orientation with physical 3D surface curvature. The corresponding decline in perceived gloss of surfaces rendered in the outdoor environments supports the notion that perceived gloss depends on highlight orientation relative to the orientation fields of diffuse shading. This suggests that perceived gloss depended on the alignment between local orientation fields for specular highlights and surrounding diffuse shading in the current experiment. Figure 7 shows the means and 95% confidence bands for correlations between the local orientation fields for specular highlights and the diffuse shading at highlight borders. Misalignments in diffuse illumination relative to specular highlights reduced the correlation between the local orientation fields for specular highlights and diffuse shading around the perimeter of the highlights. The paint-like appearance of highlights produced by misaligning specular highlights with diffuse shading could be caused by these inconsistencies between the orientation fields for specular highlights and surrounding diffuse shading. Orientation field correlations also account for the limited falloff in perceived gloss of surfaces rendered with the St. Peter's Basilica light field. 
Figure 7
 
Means and 95% confidence bands of correlations between local orientation fields at the edges of specular highlights in images of a glossy surface and the corresponding locations on purely diffuse surface with identical 3D structure. Correlation between local orientation fields for specular highlight edges and adjacent diffuse shading is seen reduced with increasing angle of misalignment in diffuse illumination.
Figure 7
 
Means and 95% confidence bands of correlations between local orientation fields at the edges of specular highlights in images of a glossy surface and the corresponding locations on purely diffuse surface with identical 3D structure. Correlation between local orientation fields for specular highlight edges and adjacent diffuse shading is seen reduced with increasing angle of misalignment in diffuse illumination.
Although orientation field differences provide a good account for the decline in perceived gloss that arises when specular highlights are displaced relative to diffuse shading, this is not the only explanation possible. Highlight displacements alter the positions of specular highlights relative to the luminance maxima in diffuse shading, which will cause specular highlights to lie in darker regions of diffuse shading. We determined highlight proximity to the luminance maxima in diffuse shading heuristically as the diffuse shading intensity around specular highlights relative to the maximum luminance in diffuse surface shading. The average diffuse shading intensity was computed around highlight regions identified with the same edge detector used for orientation field computations. Figure 8 plots the relative diffuse shading intensity around the perimeter of specular highlights as a function of misalignment in diffuse illumination (in degrees) for the three illumination fields. The model roughly accounts for the rates of decline in perceived gloss as a function of the misalignment between specular and diffuse illumination fields. Although there were some inconsistencies in shape between the curves, these variations may simply reflect the limited spatial scale over which diffuse luminance was computed in the model. The model generally supports the interpretation that perceived gloss depends on highlights appearing near luminance maxima in diffuse shading. 
Figure 8
 
Means and 95% confidence bands for the average intensity of diffuse shading around specular highlights represented as a ratio of the maximum intensity of diffuse surface shading in the image. The intensity of diffuse shading around specular highlights is seen to reduce with increasing angle of misignment in diffuse illumination.
Figure 8
 
Means and 95% confidence bands for the average intensity of diffuse shading around specular highlights represented as a ratio of the maximum intensity of diffuse surface shading in the image. The intensity of diffuse shading around specular highlights is seen to reduce with increasing angle of misignment in diffuse illumination.
The compatibility of specular highlights with the underlying physical 3D surface geometry was preserved in all of our conditions, so the decline in perceived surface gloss appears to relate to incongruence in specular highlight position and/or orientations relative to diffuse shading. This suggests that perceived gloss does not just depend on highlight compatibility with physical 3D surface shape but rather the consistency in the positions and orientations of highlights with respect to diffuse shading. The continuous decline in perceived gloss over the full range of highlight displacements appears to suggest that highlight proximity to the global anisotropy in diffuse shading contributed to estimates of surface gloss. This is because the relief in our surfaces generated both global and local maxima in diffuse shading luminance. If highlight congruence with the local pattern of shading generated by the meso-structure of the surfaces was important, then perceived gloss should have exhibited an initial steep falloff, followed by an asymptotic decline as highlights were displaced beyond the median bump size of the surface's meso-structure. This appears to have occurred to a limited extent with surfaces rendered in the St. Peter's Basilica light field, which lacked global anisotropy in diffuse shading. In the next experiment, we altered highlight consistency with the surface's meso-structure in ways that restricted their positions relative to the global luminance maxima in diffuse shading. 
Experiment 2
In the previous experiment, we found that displacing specular highlights relative to diffuse shading reduced perceived surface gloss, even though highlight compatibility with physical 3D surface shape was preserved. This suggests that the perception of surface gloss does not just depend on highlight consistency with 3D surface shape. The displaced highlights' local orientation fields were found to be misaligned with the local orientation fields of the surrounding diffuse shading. Although this finding supports the view that perceived gloss may depend on local orientation field consistencies between specular highlights and diffuse shading, the proximity of specular highlights to the local and global luminance maxima in diffuse shading was also disrupted by the highlight displacements. Hence, it is possible that global and local changes in a highlight's position and orientation congruence relative to diffuse shading account for the declines in perceived gloss. 
In Experiment 2, we examine whether perceived gloss depends on the local consistency between specular highlights and the diffuse shading associated with a surface's meso-structure. Specular highlights were displaced so that they were inconsistent with 3D surface shape (and local orientation fields of diffuse shading) but globally positioned near the luminance maxima in diffuse shading. Rather than manipulating highlight orientations within the image plane (i.e., as in Anderson & Kim, 2009), we offset the phase relationship between specular reflections and the 3D surface. Phase offsets involved adding the specular highlights for the surface viewed at one orientation to the diffuse shading for the surface viewed at progressively different angular orientations around the vertical axis. This ensured that the highlight's global position remained largely proximal to the most intense regions of diffuse shading at the top of the surface. Zero phase offset corresponded to the original glossy image where specular highlights were combined with diffuse shading for the same surface geometry and viewing orientation. The effect of phase offsets on perceived gloss was examined in both static and rotating surfaces. 
Observers
Twenty undergraduate psychology students with normal or corrected-to-normal vision participated in the study. All were naive to the experimental procedures and research rationale. All observers provided written and informed consent prior to their involvement in the study. 
Stimuli
As in the previous experiment, we presented static images or short movie segments where surfaces rotated around the vertical axis. Specular highlights were phase offset across movie frames with respect to the diffuse shading for the surface at different orientations around the vertical axis (Figure 9). We used the stimulus images rendered in Experiment 1 with the Eucalyptus Grove light probe because it depicts an illumination field of a natural arboreal environment that has a significant bias in the overall illumination direction. As the luminance is greatest from above, phase offsets around the vertical axis disrupt the normal position and orientation of specular highlights relative to the surface's local diffuse shading and 3D shape but constrain their general position near the global luminance maxima in diffuse shading. We imposed seven levels of phase offset in specular highlights relative to diffuse shading (0°, 4°, 8°, 16°, 46°, 90°, and 180°). We removed all specular highlight fragments that were displaced to regions in the image that fell outside the bounding contour of the surface's diffuse shading. 
Figure 9
 
Schematic showing the method used to add specular highlights to the diffuse shading profile rotated out of phase by known angles around the vertical axis (θ). Resulting stimulus images taken from the side of the surface with phase offsets in specular highlights of 0° (i.e., no offset) and 46° are shown against the black background.
Figure 9
 
Schematic showing the method used to add specular highlights to the diffuse shading profile rotated out of phase by known angles around the vertical axis (θ). Resulting stimulus images taken from the side of the surface with phase offsets in specular highlights of 0° (i.e., no offset) and 46° are shown against the black background.
Procedure
Display parameters and instructions to observers were identical to those used in Experiment 1. The paired comparisons procedure was used to present pairs of images comprising two different levels of phase offset. Each unique pair was presented twice for up to 5 s to counterbalance the display of images on either side of the CRT monitor (7 × 7 − 7 = 42 trials). Each observer performed the blocks of 42 paired comparison trials with either moving or static stimuli, where they selected the side of the display with the surface that appeared to contain the glossier highlights. After each block of trials, a rest period of up to 5 min was provided before observers recommenced the experiment with the alternative static or moving stimulus condition. 
Results and discussion
Figure 10 plots means and 95% confidence intervals for the estimated probability that surfaces appeared glossy as a function of phase offset between the specular highlights and diffuse shading. Both the static condition (blue trace) and motion condition (red trace) exhibited a clear asymptotic decline in perceived gloss over successive increases in angular phase offset between specular highlights and diffuse shading. A repeated-measures ANOVA performed on these data showed a significant effect of phase offset on perceived gloss (F 6,114 = 38.43, p < 0.00001). There was no significant interaction effect of phase offsets on perceived gloss between static and dynamic viewing conditions (F 6,114 = 1.44, p = 0.21), which suggests that motion did not alter the effects obtained in the static viewing conditions. 
Figure 10
 
Means and 95% confidence intervals showing estimated probabilities of surface highlights being perceived as glossy reflections were found to decrease with increasing angle of phase offset around the vertical axis. Effects of phase offset are shown based on data obtained with both dynamically rotating (red) and statically viewed surfaces (blue). Similar falloff in the mean correlation between diffuse and specular orientation fields (green) and diffuse shading intensity around highlights (black) is also observed in the model predictions with increasing level of phase offset (green). The 95% confidence band denoted by dotted lines is based on 18 different views around the surface (i.e., 20° steps).
Figure 10
 
Means and 95% confidence intervals showing estimated probabilities of surface highlights being perceived as glossy reflections were found to decrease with increasing angle of phase offset around the vertical axis. Effects of phase offset are shown based on data obtained with both dynamically rotating (red) and statically viewed surfaces (blue). Similar falloff in the mean correlation between diffuse and specular orientation fields (green) and diffuse shading intensity around highlights (black) is also observed in the model predictions with increasing level of phase offset (green). The 95% confidence band denoted by dotted lines is based on 18 different views around the surface (i.e., 20° steps).
The decline in perceived gloss as a function of phase offset was qualitatively explained by both the orientation field analysis and positional differences between highlights and the luminance maxima of diffuse shading. The correlation between orientation fields for specular highlights and adjacent diffuse shading (Figure 10, green trace) was an excellent predictor of perceived gloss as a function of phase offsets in both static (r 2 = 0.97, t 5 = 12.34, p < 0.00005) and dynamic (r 2 = 0.88, t 5 = 5.96, p < 0.005) viewing conditions. The luminance-based model that computes the relative intensity in diffuse shading around specular highlights (as a proportion of the maximum diffuse luminance—Figure 10, black trace) also statistically accounted for the psychophysical responses obtained with phase offsets in both static (r 2 = 0.94, t 5 = 8.69, p < 0.0005) and dynamic (r 2 = 0.89, t 5 = 6.35, p < 0.005) viewing conditions. 
Although both types of models could account for the pattern of results obtained in this experiment, there was a substantial difference in the range over which the two sources of information varied. We constrained the range over which the specular highlights were shifted so that they always fell within the globally brightest regions of diffuse shading (i.e., the top of the surface). Consequently, the diffuse shading intensity around specular highlights only varied over a 4.4% range in proportion to the peak diffuse intensity. This was considerably smaller than in the previous experiment, where the diffuse shading intensity around specular highlights varied over a 47.6% range in proportion to the peak diffuse intensity. This suggests that highlights were globally more constrained near the maximum luminance in diffuse shading in Experiment 2. The decline in perceived gloss in Experiment 1 was more linear and continuous, compared with the more asymptotic decline in perceived gloss with small phase offsets imposed in Experiment 2. The comparatively rapid decline in perceived gloss found in Experiment 2 appears highly consistent with local incongruence in highlights relative to the surface's meso-structure. Most of the decline in perceived gloss occurred within the first 4° to 8° of phase offset, which is roughly on the order of the surface's median bump size in local relief. These data suggest that consistency in both highlight position and orientation relative to local variations in diffuse shading is important for the perception of surface gloss. 
In order to further assess the extent to which the relative highlight proximity to the global versus local patterns in diffuse shading may contribute to perceived gloss, we conducted a third experiment where we combined the phase offsets of Experiment 2 with changes in the direction of diffuse illumination used in Experiment 1. The goal of this experiment was to determine whether we could find evidence for the use of both position and orientation congruence of highlights with local and global diffuse shading in a context where both sources of information provide a robust signal that could contribute to the perception of gloss. 
Experiment 3
In Experiment 3, we combined phase offsets with changes in the direction of diffuse illumination and examined their effects on perceived gloss. Misalignments between the diffuse and specular light fields preserve a specular highlight's consistency with physical 3D surface shape. Phase offsets imposed in conjunction with these misalignments in diffuse illumination should destroy the local alignment between specular highlights and physical 3D surface curvature (and orientation fields). Therefore, if consistency in local specular highlight position and orientation relative to 3D surface shape influences perceived gloss, then these parametric phase offsets should consistently reduce perceived gloss regardless of misalignments between specular and diffuse illumination fields. However, if perceived gloss primarily depends on highlight position relative to the global luminance maxima in diffuse shading, phase offsets should have negligible effects on perceived gloss when combined with large misalignments in diffuse illumination. The logic of this prediction is based on the fact that 180° misalignments in diffuse illumination will produce the largest positional incongruence between specular highlights and the luminance maxima in diffuse shading, so no further incongruence in highlight position relative to diffuse shading should be reliably incurred by the addition of phase offsets. 
Observers
Nine undergraduate psychology students with normal or corrected-to-normal color vision participated in the study. All were naive to the experimental procedures and research rationale. 
Stimuli
We varied the direction of diffuse illumination provided by the Eucalyptus Grove light field relative to specular highlights (as in Experiment 1). Each frame in the animation sequence was tone mapped using a non-linear transformation in Radiance (Ward, 1994). Non-linear tone mapping allowed the HDR image values to be transformed to low dynamic range in a way that ensured the specular highlights did not saturate the intensity range of image pixels. In order to ensure all images were processed using the same non-linear transformation, a cumulative histogram was predetermined from images spanning the entire 360° range of surface orientations around the vertical axis. 
We parametrically imposed five levels of phase offset (0°, 4°, 8°, 16°, and 46°), which accounted for most of the decline in perceived gloss observed in Experiment 2. The number of trials was further reduced by limiting the counterclockwise rotation in diffuse illumination to three orientations (0°, 90°, and 180°). Sample stimulus images are shown in Figure 11 for three levels of phase offset (0°, 16°, and 46°). 
Figure 11
 
Non-linearly tone-mapped images generated after combining different levels of phase offset between diffuse and specular shading (along rows) with different levels of counterclockwise displacement in the illumination field providing diffuse shading (down columns).
Figure 11
 
Non-linearly tone-mapped images generated after combining different levels of phase offset between diffuse and specular shading (along rows) with different levels of counterclockwise displacement in the illumination field providing diffuse shading (down columns).
Procedure
The procedure was identical to the previous experiments. Two separate blocks of trials were performed where stimuli were presented either as dynamically rotating surfaces or static views at single random orientations. The order of blocks was counterbalanced across observers. We correlated local orientation fields and the relative peak intensity of diffuse shading around highlights with the psychophysical responses of observers. 
Results and discussion
Figure 12 plots means and 95% confidence intervals for the probability that surfaces appeared glossy as a function of the phase offset between specular highlights and diffuse shading. Separate curves represent different parametric misalignments in diffuse illumination. As in Experiment 2, phase offsets reduced perceived gloss when the illumination fields for specular and diffuse shading were aligned (0°; black traces in Figures 12A and 12B). A three-way repeated-measures ANOVA showed a significant effect of phase offset on perceived gloss (F 4,36 = 3.82, p < 0.05). There was a highly significant effect of misalignment in diffuse illumination direction on perceived gloss (F 2,18 = 21.81, p < 0.00005), which is evident in the vertical separation between the three colored curves in Figures 12A and 12B. There was also a significant interaction effect between phase offsets and diffuse illumination direction on perceived gloss (F 8,72 = 3.33, p < 0.005). This interaction is evident in the diminishment of the inverse relationship between perceived gloss and phase offsets when the diffuse illumination direction was misaligned with the specular highlights (90°, red traces in Figures 12A and 12B). The effect of phase offsets on perceived gloss was abolished when specular highlights were generated in the opposite direction to the most intense diffuse shading (180°, green traces in Figures 12A and 12B). There was no interaction effect between highlight motion and phase offsets on perceived gloss (F 4,36 = 1.18, p = 0.33). 
Figure 12
 
Means and 95% confidence intervals showing probabilities of perceived gloss for tone-mapped surfaces presented in (A) static images and (B) dynamically rotating presentations of stimuli. Results are shown for gloss percepts obtained with surfaces rendered with different angles of diffuse illumination: 0° (black), 90° (red), and 180° (green). (C) Model output from orientation field correlations between matte and glossy stimuli is shown as a function of phase offset for each of the three directions of diffuse illumination. (D) The prediction-based local diffuse intensity around specular highlights relative to the peak intensity of diffuse shading is also shown for the test conditions.
Figure 12
 
Means and 95% confidence intervals showing probabilities of perceived gloss for tone-mapped surfaces presented in (A) static images and (B) dynamically rotating presentations of stimuli. Results are shown for gloss percepts obtained with surfaces rendered with different angles of diffuse illumination: 0° (black), 90° (red), and 180° (green). (C) Model output from orientation field correlations between matte and glossy stimuli is shown as a function of phase offset for each of the three directions of diffuse illumination. (D) The prediction-based local diffuse intensity around specular highlights relative to the peak intensity of diffuse shading is also shown for the test conditions.
A specular highlight's alignment with 3D surface shape is disrupted when phase offsets are imposed between specular reflections and diffuse shading. Phase offsets reduced perceived gloss when specular highlights were initially compatible with the surface's diffuse shading and physical 3D shape. However, little or no consistent change in perceived gloss was observed when phase offsets were imposed with combined misalignments in diffuse illumination relative to specular illumination (e.g., at 90° and above). This result can be partially explained by the correlation between local orientation fields for diffuse and specular components at highlight borders (Figure 12C). However, the large vertical displacements between psychometric curves in Figures 12A and 12B are comparatively much smaller in the orientation field model prediction. This suggests that orientation field differences alone cannot explain changes in perceived gloss generated by misaligning the directions of diffuse and specular illumination fields (i.e., the large vertical separation of the three curves in each panel). These large differences appear to be due to the diffuse shading intensity around highlights. Based on the stimulus images used in the current experiment, Figure 12D plots the diffuse shading intensity around the specular highlights' perimeter as a proportion of the peak intensity in diffuse shading. The sustained separation between the curves across misalignments in diffuse illumination direction captures the large vertical separations in the psychophysical data (Figures 12A and 12B). This suggests that information about highlight position relative to the luminance maxima in diffuse shading appears to contribute to perceived surface gloss. Thus, it would seem that both specular highlight position and orientation relative to diffuse shading are used to estimate surface gloss. In the last experiment to follow, we conducted a control experiment to verify that the effects of displacing specular highlights relative to diffuse shading were not caused by changes in the intensity of highlights. 
Experiment 4
One potential confound in the aforementioned experiments is that peak highlight intensity could change when highlights were additively combined with different intensities of diffuse shading. Displaced highlights added to darker regions of diffuse shading would have had greater contrast relative to the surrounding diffuse shading. Because perceived gloss is known to increase with increasing highlight contrast relative to surrounding surface shading (Beck & Prazdny, 1981), it appears that changes in highlight contrast cannot account for the declines in perceived gloss. However, it is possible that the decline in the peak intensity of the displaced highlights may have contributed to the decline in perceived gloss observed in the previous experiment. In Experiment 4, we replicated the previous experiment but multiplicatively controlled the intensity of the displaced specular highlights so that their average peak intensity was equated across conditions. 
Observers
Sixteen undergraduate psychology students with normal or corrected-to-normal color vision participated in the study. All were naive to the experimental procedures and research rationale. 
Stimuli
Surfaces were the same as those used in the previous experiment. However, each frame in the animation sequence was rendered in Blender 2.49 and linearly tone mapped from HDR to grayscale to ensure the specular highlights were predominantly restricted in intensity to the luminance range of the display. Importantly, we controlled highlight intensity by multiplicatively increasing the intensity of displaced highlights so that they had the same luminance on average as highlights in the correct positions and orientations. Sample stimulus images comparable to those used in Experiment 3 are shown in Figure 13 for three levels in phase offset (0°, 16°, and 46°) and the three diffuse illumination directions. 
Figure 13
 
Images with highlights multiplicatively matched in intensity were generated after combining different levels of phase offset between diffuse and specular shading (along rows) with different levels of counterclockwise displacement in the illumination field providing diffuse shading (down columns).
Figure 13
 
Images with highlights multiplicatively matched in intensity were generated after combining different levels of phase offset between diffuse and specular shading (along rows) with different levels of counterclockwise displacement in the illumination field providing diffuse shading (down columns).
Procedure
The procedure was identical to the previous experiment. At the end of the experiment, we presented the stimulus images for the 0° and 180° conditions with no phase offset and asked observers to indicate which image contained the highlights that appeared brightest. All but three observers indicated that the displaced highlights appeared to have the same or greater intensity as the aligned highlights. 
Results and discussion
The psychophysical responses we obtained with matched-intensity highlights closely replicated the findings of the previous experiment. Figure 14 plots means and 95% confidence intervals for the estimated probability that surfaces appeared glossy as a function of the phase offset between specular highlights and diffuse shading. Separate curves represent different parametric misalignments in diffuse illumination. As in Experiments 2 and 3, phase offsets reduced perceived gloss when the illumination fields for specular and diffuse shading were aligned (0°; black traces in Figures 14A and 14B). A three-way repeated-measures ANOVA showed a significant effect of phase offset on perceived gloss (F 4,60 = 3.97, p < 0.01). There was a significant effect of misalignment in diffuse illumination direction on perceived gloss (F 2,30 = 12.47, p < 0.0005), which is again evident in the vertical separation between the three colored curves in Figures 14A and 14B. There was a significant interaction effect between phase offset and diffuse illumination direction on perceived gloss (F 8,120 = 2.77, p < 0.01). This was again caused by an inverse relationship between perceived gloss and phase offsets, which diminished with static surfaces when the diffuse illumination direction was misaligned by 90° with the specular highlights (90°, red traces in Figures 14A and 14B). The effect of phase offsets on perceived gloss was abolished with static and dynamic surfaces when specular highlights were generated in the opposite direction to the most intense diffuse shading (180°, green traces in Figures 14A and 14B). No significant effects of highlight motion on perceived gloss were observed (F 1,15 = 1.94, p = 0.18). The similarity of these data to the data in the previous experiment suggest that the decline in perceived gloss observed when displacing highlights relative to diffuse shading was not due to attenuation of highlight intensity. We discuss below the apparent role of a highlight's position and orientation congruence with global and local patterns of diffuse shading in the perception of surface gloss. 
Figure 14
 
Means and 95% confidence intervals showing estimated probabilities of gloss for surfaces with matched-intensity highlights. Data shown for (A) static images and (B) dynamically rotating presentations of stimuli. Results are shown for gloss percepts obtained with surfaces rendered with different angles of diffuse illumination: 0° (black), 90° (red), and 180° (green). (C) Model output from orientation field correlations between matte and glossy stimuli is shown as a function of phase offset for each of the three directions of diffuse illumination. (D) The prediction-based local diffuse intensity around specular highlights relative to the peak intensity of diffuse shading is also shown for the test conditions.
Figure 14
 
Means and 95% confidence intervals showing estimated probabilities of gloss for surfaces with matched-intensity highlights. Data shown for (A) static images and (B) dynamically rotating presentations of stimuli. Results are shown for gloss percepts obtained with surfaces rendered with different angles of diffuse illumination: 0° (black), 90° (red), and 180° (green). (C) Model output from orientation field correlations between matte and glossy stimuli is shown as a function of phase offset for each of the three directions of diffuse illumination. (D) The prediction-based local diffuse intensity around specular highlights relative to the peak intensity of diffuse shading is also shown for the test conditions.
General discussion
In Experiment 1, we found that misaligning specular highlights relative to diffuse surface shading reduced perceived gloss for highlights that were compatible with physical 3D surface geometry. The decline in perceived gloss was consistent with the corresponding decline in the correlation between the orientation fields of specular highlights and the surrounding diffuse shading. However, the decline in perceived gloss also appeared to depend on the presence of large anisotropies in global diffuse shading; perceived gloss only declined when highlights were misaligned with respect to diffuse shading generated by strongly anisotopic illumination fields. This suggests that perceived gloss depends on the global brightness congruence between specular highlights and the luminance maxima of diffuse shading. In Experiment 2, specular highlights were phase offset from their natural position and orientation congruence with the surface's meso-structure but were constrained to appear near the global luminance maxima in diffuse shading. Phase offsets reduced perceived gloss and generated large declines in the correlation between local orientation fields for specular highlights and adjacent diffuse shading. In Experiments 3 and 4, phase offsets were parametrically combined with changes in the direction of diffuse illumination, and both manipulations were found to influence perceived gloss. This suggests that the visual system computes surface gloss by assessing the position and orientation congruence of specular highlights with diffuse shading. 
The results of the current study are consistent with the view that perceived gloss depends on the orientations of specular highlights relative to surrounding diffuse shading (Anderson & Kim, 2009; Beck & Prazdny, 1981; Todd et al., 2004). In our earlier study, perceived gloss was reduced by rotating or translating the specular highlight map for an image of St. Matthew relative to the surface's diffuse shading (Anderson & Kim, 2009). We found that the decline in perceived gloss could be reasonably well modeled as a decline in the correlation between local orientation fields for the displaced specular highlights and the underlying diffuse shading at corresponding locations in the image. In the experiments reported above, we computed the local orientation fields at the edges of specular highlights added to diffuse shading and correlated these values with the adjacent orientation fields for diffuse shading pooled over a small regional neighborhood. We found that the correlation in orientation fields between highlight edges and adjacent diffuse shading provided an excellent account of the changes in perceived gloss caused by imposing phase offsets (Experiment 2) and also provided a good account of perceived gloss when displacing highlights from the luminance maxima in diffuse shading (Experiment 1). 
The orientation field models predicted gloss judgments in Experiments 1 and 2 but were not sufficient to account for the perception of gloss when we combined phase offsets with illumination field offsets in Experiments 3 and 4. We found that perceived gloss depended on the proximity of highlights to the peak luminance generated by diffuse shading, consistent with specular highlights tending to appear near luminance maxima in diffuse shading (Fleming et al., in press; Koenderink & van Doorn, 1980). We found that displacing highlights from their natural positions reduced perceived gloss, even though the displaced highlights remained compatible with physical 3D surface shape. The declines in perceived gloss caused by rotating the diffuse illumination field were robust against adding phase offsets between specular highlights and diffuse shading (Experiments 3 and 4). This finding provides further support for the view that perceived gloss is highly dependent on highlight proximity to apparent luminance maxima in diffuse shading. The falloff in perceived gloss was much steeper in Experiment 2 when highlights were constrained to appear near the global luminance maxima in diffuse shading, compared to the gradual linear falloff in perceived gloss observed in Experiment 1. These differences in the perceptual responses to different highlight displacements support the view that the perception of surface gloss depends on both highlight congruence with global and local patterns in a surface's diffuse shading profile. Based on the findings from the current study, it is unclear to what extent local position and orientation congruence of highlights with diffuse surface shading influences perceived gloss. However, in a companion study, we found that parametric changes in both highlight orientation and position relative to local diffuse shading accounted for perceived gloss ratings (Marlow et al., in press). 
Although the local position and orientation congruence between specular highlights and diffuse shading appears to be important for perceiving gloss, it is important to note that the pattern of specular highlights alone can provide a rich source of information about 3D shape and surface gloss. In Experiment 1, surfaces rendered with the St. Peter's Basilica light field appeared glossy even though they lacked prominent variations in diffuse shading. The efficacy of specular reflections in providing information about 3D shape and gloss can be seen by presenting the specular highlights alone (see Figure 15). This purely specular surface appears as a very glossy, black, 3D surface. Note that when the specular reflections are presented alone, there is no meaningful notion of highlight congruence, since diffuse shading is absent in the image. While we preserved the compatibility of displaced highlights with physical 3D surface shape in our experiments, it is possible that the highlights themselves may have carried sufficient shape information to influence perceived 3D surface shape (and gloss) when they were displaced to very dark regions of diffuse shading. Two observers participating in Experiment 4 noted that the specular highlights displaced to darker regions of diffuse shading occasionally appeared like small “shiny” pieces of tin foil attached to a completely matte surface, particularly in the motion sequences. They voluntarily made a categorical material distinction between the displaced highlights appearing as shiny reflections on a metallic surface and the undisplaced highlights appearing as glossy reflections on a polished non-metallic opaque material. However, the percept was isolated to the immediate neighborhood around a displaced highlight and did not propagate over the surface as in the case of highlights in the correct position and orientation. Our results suggest that the visual system estimates the glossiness of natural non-metallic surfaces by assessing the placement of specular highlights relative to global and local luminance variations in diffuse shading. 
Figure 15
 
A completely black surface lacking diffuse shading can appear glossy. Rendering produced using image-based lighting with a light probe composited from two 180° fish-eye views of the Main Quadrangle at the University of Sydney on an overcast morning.
Figure 15
 
A completely black surface lacking diffuse shading can appear glossy. Rendering produced using image-based lighting with a light probe composited from two 180° fish-eye views of the Main Quadrangle at the University of Sydney on an overcast morning.
As noted in the Introduction section, specular surfaces generate particular patterns in velocity that are determined by surface geometry and the illumination field. Surfaces in motion only appear glossy if the highlights they generate move differentially according to the surface's 3D curvature (Hartung & Kersten, 2002). In the current study, we found similar declines in perceived gloss across static and dynamic viewing conditions for all experiments. The displacements of highlights would have generated changes in the velocity of specular highlights relative to the surface's diffuse shading, which may have contributed to the sustained declines in perceived gloss of moving surfaces. This is consistent with recent evidence suggesting that highlight velocities are used to estimate the surface gloss of purely specular or diffuse objects (Doerschner et al., 2011). However, in our experiments there exists a persistent notion of congruence that needs to be satisfied because surfaces contained both specular and diffuse shading. Globally coherent percepts of gloss were only observed in moving and stationary surfaces when highlights exhibited position and orientation congruence with respect to the diffuse shading. Thus, for the types of surfaces and illumination fields used herein, it would appear that the visual system primarily relies on the relationship between geometric and photometric information to estimate surface gloss. 
Although the correlation models implemented in the current study appear to account for the changes in perceived gloss of both stationary and moving surfaces, the visual system does not have explicit access to the specular and diffuse components in images of natural surfaces. We chose to correlate highlight edges with the underlying diffuse shading for computational efficiency. Because the diffuse shading varied relatively smoothly across the surfaces in our experiments, it is highly likely that similar correlation profiles would be obtained when considering the orientation fields for the visible regions of diffuse shading immediately adjacent to the highlights' edges in similar surfaces. The data obtained from these models suggest that the visual system could perform a low-level photogeometric analysis of images to estimate surface gloss. 
In summary, the results reported here and previously (e.g., Anderson & Kim, 2009; Kim & Anderson, 2010) suggest that perceived gloss depends on the structural relationship between surface highlights and the pattern of diffuse luminance variation in images. Our previous work generated highlight incongruence by simultaneously displacing the position and orientation of highlights in the image. However, the manipulations we performed herein displaced highlights relative to diffuse shading while preserving their consistency with physical 3D surface shape (Experiment 1) or disrupting their consistency with physical surface curvature (Experiments 24). These findings together provide further support for the view that the perception of surface gloss depends on highlight congruence with the structure of diffuse luminance variations in images and not just their consistency with surface shape. 
Acknowledgments
This research was supported by an Australian Research Council (ARC) grant awarded to B. L. Anderson and an ARC Discovery Project awarded to B. L. Anderson, J. Kim, and R. Fleming. We thank R. Fleming for sharing his extensive knowledge and advice on rendering techniques used in this study. 
Commercial relationships: none. 
Corresponding authors: Juno Kim and Barton L. Anderson. 
Emails: juno@psych.usyd.edu.au; barta@psych.usyd.edu.au. 
Address: School of Psychology, 526 Griffith Taylor Building (A19), The University of Sydney, NSW 2006, Australia. 
References
Anderson B. L. Kim J. (2009). Image statistics do not explain the perception of gloss and lightness. Journal of Vision, 9, (11):10, 1–17, http://www.journalofvision.org/content/9/11/10, doi:10.1167/9.11.10. [PubMed] [Article] [CrossRef] [PubMed]
Beck J. Prazdny K. (1981). Highlights and the perception of glossiness. Perception & Psychophysics, 30, 407–410. [CrossRef] [PubMed]
Ben-Shahar O. Zucker S. (2001). On the perceptual organization of texture and shading flows: From a geometrical model to coherence computation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 1048–1055). Kauaii, HI.
Blake A. Bülthoff H. (1990). Does the brain know the physics of specular reflection? Nature, 343, 165–168. [CrossRef] [PubMed]
Breton P. Zucker S. W. (1996). Shadows and shading flow fields. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 782–789). San Francisco, CA.
Debevec P. (2002). Image-based lighting. IEEE Computer Graphics and Applications, 22, 26–34. [CrossRef]
Doerschner K. Kersten D. Schrater P. R. (2011). Rapid classification of surface reflectance from image velocities. Pattern Recognition, 44, 1874–1884. [CrossRef]
Fleming R. W. Torralba A. Adelson E. H. (2004). Specular reflections and the perception of shape. Journal of Vision, 4, (9):10, 798–820, http://www.journalofvision.org/content/4/9/10, doi:10.1167/4.9.10. [PubMed] [Article] [CrossRef]
Fleming R. W. Torralba A. Adelson E. H. (in press). Shape from sheen. In Zaidi Q. (Ed.), Three‐dimensional shape perception. New York: Springer‐Verlag.
Hartung B. Kersten D. (2002). Distinguishing shiny from matte [Abstract]. Journal of Vision, 2, (7):551, 551a, http://www.journalofvision.org/content/2/7/551, doi:10.1167/2.7.551. [CrossRef]
Kim J. Anderson B. L. (2010). Image statistics and the perception of surface gloss and lightness. Journal of Vision, 10, (9):3, 1–17, http://www.journalofvision.org/content/10/9/3, doi:10.1167/10.9.3. [PubMed] [Article] [CrossRef]
Koenderink J. J. van Doorn A. J. (1980). Photometric invariants related to solid shape. Optica Acta, 27, 981–996. [CrossRef]
Marlow P. Kim J. Anderson B. L. (in press). The role of brightness and orientation congruence in the perception of surface gloss. Journal of Vision.
Motoyoshi I. Nishida S. Sharan L. Adelson E. H. (2007). Image statistics and the perception of surface qualities. Nature, 447, 206–209. [CrossRef] [PubMed]
Sharan L. Li Y. Motoyoshi I. Nishida S. Adelson E. H. (2008). Image statistics for surface reflectance perception. Journal of the Optical Society of America, 25, 846–865. [CrossRef] [PubMed]
Todd J. T. Norman J. F. Mingolla E. (2004). Lightness constancy in the presence of specular highlights. Psychological Science, 15, 33–39. [CrossRef] [PubMed]
Ward G. J. (1994). The RADIANCE lighting simulation and rendering system. Computer Graphics, 28, 459–472.
Wendt G. Faul F. Ekroll V. Mausfeld R. (2010). Disparity, motion, and color information improve gloss constancy performance. Journal of Vision, 10, (9):7, 1–17, http://www.journalofvision.org/content/10/9/7, doi:10.1167/10.9.7. [PubMed] [Article] [CrossRef] [PubMed]
Figure 1
 
(A) An elongated surface region generates a congruent specular highlight that is stretched along lines of minimal change in diffuse shading (left), which also conforms to the direction of minimal surface curvature (right). (B) Rotating the specular highlight by 90° relative to the surface makes it incongruent with surrounding diffuse shading gradients (left) and 3D surface curvature (right).
Figure 1
 
(A) An elongated surface region generates a congruent specular highlight that is stretched along lines of minimal change in diffuse shading (left), which also conforms to the direction of minimal surface curvature (right). (B) Rotating the specular highlight by 90° relative to the surface makes it incongruent with surrounding diffuse shading gradients (left) and 3D surface curvature (right).
Figure 2
 
Anisotropy in diffuse shading profiles of the same 3D surface placed in the three different illumination fields. The global pattern of diffuse surface shading is more circularly symmetric in the illumination context of the St. Peter's Basilica light field compared to the outdoor illumination fields of the Uffizi and Eucalyptus Grove.
Figure 2
 
Anisotropy in diffuse shading profiles of the same 3D surface placed in the three different illumination fields. The global pattern of diffuse surface shading is more circularly symmetric in the illumination context of the St. Peter's Basilica light field compared to the outdoor illumination fields of the Uffizi and Eucalyptus Grove.
Figure 3
 
Method used to render specular highlights consistent with surface geometry while altering diffuse shading. Specular highlights rendered for the upright light probe were added to different radial profiles of diffuse shading produced by counterclockwise rotation of the light probe used for diffuse illumination (e.g., 0°, 45°, 90°, and 180°). The specular highlight map generated by the Eucalyptus Grove illumination field is shown in the center.
Figure 3
 
Method used to render specular highlights consistent with surface geometry while altering diffuse shading. Specular highlights rendered for the upright light probe were added to different radial profiles of diffuse shading produced by counterclockwise rotation of the light probe used for diffuse illumination (e.g., 0°, 45°, 90°, and 180°). The specular highlight map generated by the Eucalyptus Grove illumination field is shown in the center.
Figure 4
 
Effect of rendering specular reflections consistent with the geometry of a 3D surface where the orientation of the illumination field providing diffuse shading is the same (0°) or rotated counterclockwise by 90° (middle row) and 180° (lower row).
Figure 4
 
Effect of rendering specular reflections consistent with the geometry of a 3D surface where the orientation of the illumination field providing diffuse shading is the same (0°) or rotated counterclockwise by 90° (middle row) and 180° (lower row).
Figure 5
 
Edge detection was used to identify edges of specular highlights generated by glossy surfaces. The insets on the right show the corresponding orientation fields for the diffuse shading and the edge of a highlight for the same surface region.
Figure 5
 
Edge detection was used to identify edges of specular highlights generated by glossy surfaces. The insets on the right show the corresponding orientation fields for the diffuse shading and the edge of a highlight for the same surface region.
Figure 6
 
Means and 95% confidence intervals showing the estimated probabilities of a surface being selected as glossier after different levels of angular offset in diffuse illumination relative to the natural specular highlights rendered with each of the three illumination fields (across columns). Results obtained with static images (blue) and dynamically rotating movies (red) in separate axes down each column.
Figure 6
 
Means and 95% confidence intervals showing the estimated probabilities of a surface being selected as glossier after different levels of angular offset in diffuse illumination relative to the natural specular highlights rendered with each of the three illumination fields (across columns). Results obtained with static images (blue) and dynamically rotating movies (red) in separate axes down each column.
Figure 7
 
Means and 95% confidence bands of correlations between local orientation fields at the edges of specular highlights in images of a glossy surface and the corresponding locations on purely diffuse surface with identical 3D structure. Correlation between local orientation fields for specular highlight edges and adjacent diffuse shading is seen reduced with increasing angle of misalignment in diffuse illumination.
Figure 7
 
Means and 95% confidence bands of correlations between local orientation fields at the edges of specular highlights in images of a glossy surface and the corresponding locations on purely diffuse surface with identical 3D structure. Correlation between local orientation fields for specular highlight edges and adjacent diffuse shading is seen reduced with increasing angle of misalignment in diffuse illumination.
Figure 8
 
Means and 95% confidence bands for the average intensity of diffuse shading around specular highlights represented as a ratio of the maximum intensity of diffuse surface shading in the image. The intensity of diffuse shading around specular highlights is seen to reduce with increasing angle of misignment in diffuse illumination.
Figure 8
 
Means and 95% confidence bands for the average intensity of diffuse shading around specular highlights represented as a ratio of the maximum intensity of diffuse surface shading in the image. The intensity of diffuse shading around specular highlights is seen to reduce with increasing angle of misignment in diffuse illumination.
Figure 9
 
Schematic showing the method used to add specular highlights to the diffuse shading profile rotated out of phase by known angles around the vertical axis (θ). Resulting stimulus images taken from the side of the surface with phase offsets in specular highlights of 0° (i.e., no offset) and 46° are shown against the black background.
Figure 9
 
Schematic showing the method used to add specular highlights to the diffuse shading profile rotated out of phase by known angles around the vertical axis (θ). Resulting stimulus images taken from the side of the surface with phase offsets in specular highlights of 0° (i.e., no offset) and 46° are shown against the black background.
Figure 10
 
Means and 95% confidence intervals showing estimated probabilities of surface highlights being perceived as glossy reflections were found to decrease with increasing angle of phase offset around the vertical axis. Effects of phase offset are shown based on data obtained with both dynamically rotating (red) and statically viewed surfaces (blue). Similar falloff in the mean correlation between diffuse and specular orientation fields (green) and diffuse shading intensity around highlights (black) is also observed in the model predictions with increasing level of phase offset (green). The 95% confidence band denoted by dotted lines is based on 18 different views around the surface (i.e., 20° steps).
Figure 10
 
Means and 95% confidence intervals showing estimated probabilities of surface highlights being perceived as glossy reflections were found to decrease with increasing angle of phase offset around the vertical axis. Effects of phase offset are shown based on data obtained with both dynamically rotating (red) and statically viewed surfaces (blue). Similar falloff in the mean correlation between diffuse and specular orientation fields (green) and diffuse shading intensity around highlights (black) is also observed in the model predictions with increasing level of phase offset (green). The 95% confidence band denoted by dotted lines is based on 18 different views around the surface (i.e., 20° steps).
Figure 11
 
Non-linearly tone-mapped images generated after combining different levels of phase offset between diffuse and specular shading (along rows) with different levels of counterclockwise displacement in the illumination field providing diffuse shading (down columns).
Figure 11
 
Non-linearly tone-mapped images generated after combining different levels of phase offset between diffuse and specular shading (along rows) with different levels of counterclockwise displacement in the illumination field providing diffuse shading (down columns).
Figure 12
 
Means and 95% confidence intervals showing probabilities of perceived gloss for tone-mapped surfaces presented in (A) static images and (B) dynamically rotating presentations of stimuli. Results are shown for gloss percepts obtained with surfaces rendered with different angles of diffuse illumination: 0° (black), 90° (red), and 180° (green). (C) Model output from orientation field correlations between matte and glossy stimuli is shown as a function of phase offset for each of the three directions of diffuse illumination. (D) The prediction-based local diffuse intensity around specular highlights relative to the peak intensity of diffuse shading is also shown for the test conditions.
Figure 12
 
Means and 95% confidence intervals showing probabilities of perceived gloss for tone-mapped surfaces presented in (A) static images and (B) dynamically rotating presentations of stimuli. Results are shown for gloss percepts obtained with surfaces rendered with different angles of diffuse illumination: 0° (black), 90° (red), and 180° (green). (C) Model output from orientation field correlations between matte and glossy stimuli is shown as a function of phase offset for each of the three directions of diffuse illumination. (D) The prediction-based local diffuse intensity around specular highlights relative to the peak intensity of diffuse shading is also shown for the test conditions.
Figure 13
 
Images with highlights multiplicatively matched in intensity were generated after combining different levels of phase offset between diffuse and specular shading (along rows) with different levels of counterclockwise displacement in the illumination field providing diffuse shading (down columns).
Figure 13
 
Images with highlights multiplicatively matched in intensity were generated after combining different levels of phase offset between diffuse and specular shading (along rows) with different levels of counterclockwise displacement in the illumination field providing diffuse shading (down columns).
Figure 14
 
Means and 95% confidence intervals showing estimated probabilities of gloss for surfaces with matched-intensity highlights. Data shown for (A) static images and (B) dynamically rotating presentations of stimuli. Results are shown for gloss percepts obtained with surfaces rendered with different angles of diffuse illumination: 0° (black), 90° (red), and 180° (green). (C) Model output from orientation field correlations between matte and glossy stimuli is shown as a function of phase offset for each of the three directions of diffuse illumination. (D) The prediction-based local diffuse intensity around specular highlights relative to the peak intensity of diffuse shading is also shown for the test conditions.
Figure 14
 
Means and 95% confidence intervals showing estimated probabilities of gloss for surfaces with matched-intensity highlights. Data shown for (A) static images and (B) dynamically rotating presentations of stimuli. Results are shown for gloss percepts obtained with surfaces rendered with different angles of diffuse illumination: 0° (black), 90° (red), and 180° (green). (C) Model output from orientation field correlations between matte and glossy stimuli is shown as a function of phase offset for each of the three directions of diffuse illumination. (D) The prediction-based local diffuse intensity around specular highlights relative to the peak intensity of diffuse shading is also shown for the test conditions.
Figure 15
 
A completely black surface lacking diffuse shading can appear glossy. Rendering produced using image-based lighting with a light probe composited from two 180° fish-eye views of the Main Quadrangle at the University of Sydney on an overcast morning.
Figure 15
 
A completely black surface lacking diffuse shading can appear glossy. Rendering produced using image-based lighting with a light probe composited from two 180° fish-eye views of the Main Quadrangle at the University of Sydney on an overcast morning.
×
×

This PDF is available to Subscribers Only

Sign in or purchase a subscription to access this content. ×

You must be signed into an individual account to use this feature.

×