Perception and misperception of surface opacityPhillip J. Marlowa,1, Juno Kimb, and Barton L. Andersona,1

aSchool of Psychology, University of Sydney, NSW 2006, Sydney, Australia; and bSchool of Optometry and Vision Science, NSW 2052, Sydney, Australia

Edited by Wilson S. Geisler, University of Texas at Austin, Austin, TX, and approved November 7, 2017 (received for review June 29, 2017)

A fundamental problem in extracting scene structure is distinguish-ing different physical sources of image structure. Light reflected byan opaque surface covaries with local surface orientation, whereaslight transported through the body of a translucent material doesnot. This suggests the possibility that the visual system may use thecovariation of local surface orientation and intensity as a cue to theopacity of surfaces. We tested this hypothesis by manipulating thecontrast of luminance gradients and the surface geometries to whichthey belonged and assessed how these manipulations affected theperception of surface opacity/translucency. We show that (i) identi-cal luminance gradients can appear either translucent or opaquedepending on the relationship between luminance and perceived3D surface orientation, (ii) illusory percepts of translucency can beinduced by embedding opaque surfaces in diffuse light fields thateliminate the covariation between surface orientation and intensity,and (iii) illusory percepts of opacity can be generated when trans-parent materials are embedded in a light field that generates imageswhere surface orientation and intensity covary. Our results provideinsight into how the visual system distinguishes opaque surfaces andlight-permeable materials and why discrepancies arise between theperception and physics of opacity and translucency. These resultssuggest that the most significant information used to compute theperceived opacity and translucency of surfaces arise at a level ofrepresentation where 3D shape is made explicit.

visual perception | 3D shape | material perception | reflectance | translucency

Afundamental goal of vision research is to understand howthe brain derives the appearance of objects and materials

from image structure. This problem is difficult because imagestructure arises from a number of distinct physical sources: 3Dshape, reflectance, transmittance and/or subsurface scattering,and the light field. Our ability to perceive the color, lightness,gloss, translucency, and shape of materials implies that theremust be information available to perform these computations,although such processes are just beginning to be understood.Recent work on opaque surfaces has shown that the perception

of reflectance depends on both physical (1–8) and perceived (9–12) 3D shape. The 3D shape of surfaces modulates the pattern ofspecular reflections projected to the eyes, which induces corre-sponding variations in the perception of gloss (1–8). Perceived 3Dshape can also alter the apparent reflectance of identical lumi-nance gradients (9–12). When a fixed image gradient appears tobe generated by a shaded surface with a high curvature, it appearsmore matte than when the same gradient appears to be generatedby a lower surface curvature (10–12). These results suggest thatthe reflectance properties of surfaces are derived at a level ofrepresentation where 3D shape is made explicit.The physics characterizing the interaction of light and trans-

lucent materials is also affected by its 3D shape and is morecomplicated than the physics of surface reflectance. The lightprojected from a translucent material depends on its 3D surfacegeometry, reflectance properties, and how light is transportedinto and out of its volume. The amount, spectral content, anddirection of the light crossing the surface of the material dependon its refractive indices, the viewing direction, and angle of in-cident light. The light scattered within a material depends onthe density and reflectance of the particles suspended within itsbody (13–15). The amount of light transmitted through atranslucent object also depends on its thickness, which may not

be computable from the images because it requires informationabout surface geometry that is not in view. The complexity of lightinteractions with translucent materials has motivated the sugges-tion that the perception of translucency may depend entirely onheuristic “rules of thumb,” similar to those employed by artists todepict such attributes (16).There may, however, be some general generative constraints that

the visual system may use to compute the opacity of surfaces. Onecharacteristic feature of opaque surfaces is that the intensity oflight projected to the image covaries with surface orientation inlight fields with a dominant illumination direction, which generatespatterns of surface shading. The intensity of diffuse reflectancedeclines with increasing angle between the surface normal and il-lumination direction. Although this covariation can be reduced bycast shadows and interreflections, the covariation of intensity andsurface orientation will not be completely eliminated, particularlyfor locally convex surface patches. In contradistinction, the sub-surface scattering that arises with translucent materials can pro-duce smooth image gradients that completely eliminate thesystematic covariation of intensity and surface orientation. Thissuggests that the covariation of intensity and surface orienta-tion could provide information that the visual system uses toevaluate the opacity of surfaces: If intensity covaries smoothlywith local surface orientation, it provides evidence that thislight has been reflected by the surface (i.e., shading); however,if intensity varies smoothly but independently of local surfaceorientation, then it could provide information that the lightprojected to a vantage point is generated by light–material in-teractions that occur within the body of an object.One of the primary assumptions shaping the work described

herein is that surface opacity constitutes a physical and percep-tual dimension, rather than distinct categories of materials. Thesame assumption is embodied in models of transparency. Theendpoints of this dimension can be illustrated by plotting intensityas a function of surface orientation for an opaque and translu-cent material with the same 3D shape (Fig. 1A). In this example,the translucent surface is illuminated by a punctate source

Significance

One of the most perplexing problems in vision science is to un-derstand how the visual system computes the reflectance andtransmittance properties of differentmaterials despite variability in3D shape and illumination. We show that 3D shape can play adecisive role in the perception of surface opacity and that grossmisperceptions of surface opacity can arise for specific surfacegeometries and light fields. We argue that the perception of sur-face opacity depends on the relationship between intensity and 3Dsurface orientation and show that this relationship can play a de-cisive role in modulating the perception of surface opacity, in-dependently of the true physical characteristics of materials.

Author contributions: P.J.M., J.K., and B.L.A. designed research; P.J.M. and B.L.A. per-formed research; P.J.M. analyzed data; and P.J.M. and B.L.A. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.1To whom correspondence may be addressed. Email: phillip.marlow@sydney.edu.au orbarton.anderson@sydney.edu.au.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1711416115/-/DCSupplemental.

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located inside the object, whereas the opaque (Lambertian) surfaceis illuminated externally by four rectangular area lamps. Local sur-face orientation is depicted by a circular base tangent to the surfaceand a line depicting the outward pointing surface normal (Fig. 1B).The intensity of each pixel is plotted as a function of the angularseparation (slant) of surface normals with respect to the illuminationdirection that generates the strongest intensity–orientation co-variation (see Methods). Note that the translucent object exhibits noclear dependence of intensity on surface orientation. In contradis-tinction, the opaque surface exhibits a low-dimensional (∼1D) de-pendence of intensity on surface orientation. The specific shape ofthis “contour” depends primarily on the diffuse and specular re-flectance of the surface as well as the locations of shadows. In this(Lambertian) example, intensity declines as a cosine function of theangular difference between the primary illumination direction until∼90° from the dominant overhead light source; orientations greaterthan 90° generate an attached shadow, and the intensities of theseregions depend on illumination from the illuminants from below andto its sides. The “thickness” or spread along the contour depends onfactors that weaken intensity–orientation covariation (here, the dif-ferent directions and intensities of the multiple light sources).The experiments described below were designed to assess whether

the covariation of intensity with 3D surface orientation modu-lates the perception of surface opacity. Most previous studies (13–21) into the perception of translucency have attempted to identifycues that provide information about the relative opacity/translucencyof a material by holding 3D shape fixed and either identifying ormanipulating image properties that modulate perceived surfaceopacity (such as contrast). Here, we take the complementary ap-proach and fix the luminance gradients in the images and vary the3D shapes that appear to generate them. Thus, any differences inperceived translucency that arise from modulating 3D shape cannotbe explained by differences in 2D image properties but must arise ata level of representation where 3D shape is made explicit.

ResultsThe Computation of Opacity and Translucency from 3D Intensity Gradients.In experiment 1, we rendered images of a translucent andopaque surface and generated an alternate shape interpretationfor each. The alternate shape was designed to change the relation-ship between image intensity and surface orientation relative to that

of the rendered surface. The physically translucent object had ashape resembling a bloated “snake” that varied in thickness along itsmedial axis. It was illuminated from behind (see Methods), whichresulted in intensity maxima at the narrower regions and intensityminima at the thicker regions. The projected intensities of the gra-dients generated by the translucent snake do not exhibit any sys-tematic covariation with surface orientation (Fig. 2B, Upper Left). Asecond shape—a twisted “ribbon”—was constructed so that the in-tensities generated by the snake would be mapped onto a surfacesuch that they covaried with local surface orientation (Fig. 2B, UpperRight). If the visual system uses this covariation to infer the opacity ofa surface, the ribbon should appear opaque even though the imagegradients were generated by an object that was translucent.The second pair of surfaces was created by first generating a

surface where intensity varies perfectly with surface orientation (a“bump”; Fig. 2B, Lower Right) and then mapping these gradientsonto a second shape that eliminated this covariation (a “torus”; Fig.2B, Lower Left). Note that neither of these surfaces/materials wasrendered; the gradients were texture mapped onto each of the twosurfaces to create the stimuli. The surfaces for both pairs of surfaceswere covered in a black dot or grid texture superimposed over theluminance gradients, and the two 3D shape percepts were generatingusing binocular disparity or structure from motion. The contrast ofthe luminance gradients of the two shapes was varied in seven stepsby multiplicatively scaling the range of image intensities. Observersperformed paired comparison experiments in which each combina-tion of the two 3D shapes and seven different values of imagecontrast were presented, and observers selected the surface thatappeared more translucent in each pair. Different groups of naïveobservers (n ≥ 10 in each experiment; see Methods) were used foreach pair of 3D shapes (snake versus ribbon or bump versus torus)and for each shape cue (binocular or structure from motion).The effect of perceived shape on perceived material can be

directly experienced by the reader by viewing Fig. 3 and Movies S1and S2. Movies S1 and S2 are example stimuli used in the ex-periments shown in Fig. 2. Example stimuli for the stereoscopicexperiments are shown in Fig. 3. The shape interpretations wheresurface orientation and intensity exhibit a low-dimensional co-variation appear opaque (the bump and ribbon), whereas theshape interpretations that do not exhibit this covariation appeartranslucent (the torus and snake). Note also that the perception ofillumination also differs for these two shapes. The shapes thatappear translucent appear to transmit light from a source locatedbehind or inside the object, whereas the shapes that appear opa-que appear to reflect light from above. The results of experiment1 are shown in Fig. 2A, which plots the proportion of trials thateach stimulus was chosen as appearing more translucent than theother surfaces. The contrast of the luminance gradients increasesfrom left to right in each graph. The large, vertical separationbetween the white and black data points demonstrates that ob-servers are sensitive to the relationship between intensity andapparent surface orientation when judging translucency: Thesnake and torus appear more translucent than the ribbon andbump. Main and interaction effects of 3D shape and contrast weretested using planned within-subject contrasts. The effect of shapeon perceived translucency is statistically significant for both sets ofstimuli [counterclockwise from Fig. 2 A, Top Left: F(1, 13) = 60;F(1, 13) = 18; F(1, 9) = 255; F(1, 10) = 18, P << 0.01, for each]. The3D shape interpretation also influences the effect of image contraston perceived translucency, producing a significant interaction be-tween the main effects of shape and contrast [counterclockwisefrom Fig. 2 A, Top Left: F(1, 9) = 12, P < 0.01; F(1, 10) = 12,P < 0.01; F(1, 13) = 60, P << 0.01; F(1, 13) = 18, P << 0.01].Decreasing contrast increases perceived translucency for thebump surface, consistent with the view that low contrast is a cueto translucency (18–20). However, the torus, snake, and ribbonshapes appear most translucent for moderate contrast values.This interaction suggests that 3D shape can change the way thatimage contrast influences the perception of surface opacity.

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The Misperception of Opacity. The intensity of an opaque surface willonly covary with surface orientation in light fields that contain apredominant illumination direction. It is the variation in the 3D poseof a surface with respect to this illumination direction that is re-sponsible for the coupling between surface orientation and intensityof shaded surfaces. Purely diffuse illumination (i.e., illumination in aGanzfeld) eliminates intensity gradients due to shading and henceeliminates this source of covariation. The intensity variations of auniform albedo surface embedded in a purely diffuse light field willdepend on the pattern of interreflections and the area of theGanzfeld that illuminates each point on a surface (“vignetting”). Thisarea is smaller for deep concavities due to self-occlusion than pro-truding convexities, which are fully exposed to ambient lighting.Since interreflections and vignetting depend more on the directionand magnitudes of surface curvature than surface orientation, opa-que surfaces in a Ganzfeld will exhibit inconsistencies between

surface orientation and intensity. If the visual system interprets theinconsistency between surface orientation and intensity as a cue totranslucency, then an opaque surface containing a distribution ofconvexities and deep concavities should appear translucent whenrendered in a diffuse illumination. To test this prediction, Lamber-tian and translucent variants of a bumpy surface [similar to that ofKim et al. (22)] were rendered in either a Ganzfeld or natural illu-mination. Observers viewed the surfaces along the direction of sur-face relief in structure-from-motion displays similar to our previousexperiments (Movies S3 and S4). Observers matched the materialappearance of each surface by adjusting the material parameters of acube rendered in a natural light field (Fig. 4). In one experiment, thecube was rendered without specular reflections, and observers onlyadjusted the density of subsurface scattering (Fig. S1A). In a secondexperiment, the cube was rendered with specular reflections, andobservers adjusted both the density of subsurface scattering and in-tensity of specular reflections (Fig. S1B). The results of both ex-periments show the Lambertian surface rendered in a Ganzfeldappears translucent. The vertical axis represents the density of sub-surface scattering particles; the correct match for a Lambertiansurface is the highest density on the graph (256); the graphical set-tings for each surface is depicted in Fig. S1D. The results show thatthe Lambertian surface rendered in the natural light field appearsopaque and matte, whereas the match for the same surface in theGanzfeld is very translucent and glossy [F(1, 4) = 1,005, P << 0.01, inFig. S1A; F(1, 4) = 576, P << 0.01, in Fig. S1B; and F(1, 4) = 1,931,P << 0.01, for the specular parameter in Fig. S1B]. This result im-plies that the visual system misattributes the diffuseness of the lightfield to the subsurface scattering of a translucent material in theabsence of any covariation in surface orientation and intensity,presumably because such materials occur more generically in naturalscenes than completely diffuse light fields.Our hypothesis also predicts that translucent materials should

fail to appear translucent if the light transported through thematerial accidentally preserves the covariation of intensity andsurface orientation. Fig. 5 depicts two shapes designed to test thishypothesis, which are variants of the translucent snake from Fig. 3.In one shape, the diameter of the circular cross-section varies alongthe snake’s medial axis; for the other, the diameter of the cross-section remains constant and appears as a curved cylinder. Forspecific combinations of illumination and subsurface scatteringdensity, the intensity of the light transported through the cylindercovaries with surface orientation. Both shapes were rendered asidentical translucent materials and were embedded in a light fieldwith a predominant direction of illumination from behind (seeMethods). Seven different levels of physical translucency wererendered by varying the density of subsurface scattering particles.Lambertian variants of these objects were also rendered withinthe same light field rotated 180° so the predominant direction ofillumination was along the line of sight. Seven albedos of theLambertian surfaces were chosen to produce the same maximalluminance as that generated by the translucent surfaces. Nine ob-servers ranked the surfaces from most to least translucent in apaired comparison experiment. Fig. S3B shows the proportion oftrials that each surface was chosen as appearing more translucentthan the other surfaces as a function of the maximal intensity in theimage. The open symbols depict the translucent renders, and thesmall gray symbols depict the Lambertian renders. The resultsreveal a large discrepancy between perceived and physical trans-lucency for the translucent cylinder. The cylinder appears lesstranslucent than the snake even though they are physically thesame material for all values of subsurface density, F(1, 8) = 30, P <0.01. Moreover, perceived translucency varies with the density ofsubsurface particles differently for the snake and cylinder, F(1, 8) =18.7, P < 0.01. The perceived translucency of the snake increases asdensity declines (and is hence physically more translucent), whereasthe cylinder appears less translucent as physical translucency in-creases. The misperception of translucency for the cylinder is wellpredicted by the emergence of a spurious relationship betweensurface orientation and the intensity of light passing through thetranslucent volume (Fig. S3C). These results provide further support

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Fig. 2. The perception of translucency depends on luminance contrast andapparent 3D shape. (A) Translucency judgments for the two possible 3D shapeinterpretations of each intensity gradient pattern. Error bars are SEMs of all ob-servers. The contrast of the gradient increases from left to right in each graph, andImax and Imin refer to the maximum and minimum intensity. B plots the re-lationship between intensity and surface orientation for each shape. Orientation isthe angle in degrees between the surface normal and illumination direction.

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for the hypothesis that the perception of translucency requires in-consistencies between intensity and 3D surface orientation.

DiscussionThe goal of the work presented herein was to gain insight into howthe visual system distinguishes luminance gradients generated bysurface shading from gradients generated by subsurface scattering.This problem is computationally difficult because shading and sub-surface scattering can generate similar luminance gradients if illu-mination and 3D shape are free to vary. We hypothesized that thecovariation of intensity with surface orientation is a source of in-formation that links projected light to 3D surface geometry andtherefore can be used to distinguish image structure generated byoptical interactions with surfaces from optical structure generated bysubsurface scattering. In support of this hypothesis, we showed that(i) identical luminance gradients can appear either as light trans-mitted through a light-permeable material or as light reflected froman opaque surface depending on perceived 3D surface geometry,

(ii) illusory percepts of translucency can be induced by embeddingopaque surfaces in diffuse light fields that eliminate the covariationbetween surface orientation and intensity, and (iii) illusory perceptsof opacity can be generated when transparent materials are illumi-nated in a manner that generates images where surface orientationand intensity covary. Thus, opaque materials can appear translucentand translucent materials can appear opaque when they are em-bedded in light fields that either eliminate or generate systematiccovariation in 3D surface orientation and intensity, respectively.Our hypothesis can also provide insight into illusory percepts

of translucency induced by depth map textures (18) and rampshading (23), where image brightness is determined by the dis-tance of the surface relative to some reference point. These il-lusory percepts of translucency also appear to depend on therelationship between intensity and local surface orientation.Images that exhibit stronger inconsistencies between intensityand surface normals appear more translucent (the left object inFig. S4) than those that generate spurious correlations betweenintensity and surface normals (the sphere in Fig. S4).The general insight shaping our theoretical approach is that the

computation of surface opacity is derived by the way that lightcovaries with 3D surface geometry. The hypothesis explored hereinonly considers how intensity varies as a function of local 3D surfaceorientation because this is the primary generative source of intensityvariations generated by opaque surfaces in a directional light field(“shading”). Our hypothesis does not exclude the possibility thathigher order 3D shape variables may also be used to compute theopacity/translucency of surfaces or may be used to weight the extentto which the surface orientation/intensity covariation cue is used insuch computations. Deep surface concavities can generate shadows,vignetting, and interreflections, all of which disrupt the relationshipbetween surface orientation and intensity (23, 24). Surface con-vexities, by contrast, are much less subject to these influences andwill generally preserve the surface orientation/intensity covariationcharacteristic of opaque surfaces. This suggests that the pattern ofintensity variations across a surface may not all be weighted equallyin the visual system’s computation of surface opacity. This can beseen in Fig. S2, which depicts surface normal-intensity plots for abumpy Lambertian surface in natural illumination. Despite thepresence of extensive cast shadows and interreflections present inmany regions of the surface, intensity covaries with surface normalson locally convex surface patches where cast shadows and interre-flections are less likely. In contradistinction, this covariation is notobserved in the same regions for the variants of the surface in Fig.S2 that appear translucent (i.e., that were either rendered as

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Fig. 3. A and B show two possible stereoscopic shape interpretations forthe same luminance gradients. The upper shape interpretation in each panel(i.e., the snake and torus) appears as a translucent volume illuminated fromwithin, whereas the lower shape interpretation (ribbon and bump) appearsas an opaque surface reflecting light from above. The two eyes’ views arearranged for crossed free fusion.

Fig. 4. Misperception of surface opacity in diffuse illumination. Two images ofthe same bumpy, opaque (lambertian) surface rendered in either a natural lightfield (Left) or diffuse illumination (Right). The diffuse illumination elicits an il-lusory percept of gloss and translucency. The cubes show the appearance of thematch surface at PSE in subsurface scattering and specular reflectance (Fig. S1).

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translucent or rendered as opaque in a diffuse light field). Apromising line of future work will be to assess how well materialproperties are predicted by different regions of surfaces character-ized by higher order shape descriptors (such as convexities, con-cavities, or saddles), in conjunction with the surface orientation–intensity analysis proposed herein.Previous studies (13–21) that have investigated cues to per-

ceived translucency have held 3D shape fixed and either variedthe amount of simulated translucency (subsurface scattering) ordirectly manipulated image properties in an attempt to modulateperceived opacity/translucency. Here, we took the complemen-tary approach and held image properties fixed and varied 3Dshape. A related approach was taken by Kim et al. (22), whoreported that the percept of “glow” is also coupled to repre-sentations of 3D shape. They constructed bumpy surfaces ren-dered in a diffuse light field similar to those depicted in Fig. 4and found that a percept of glow could be induced by invertingthe depth of the peaks and valleys while holding the intensitygradients fixed. They mentioned a possible link between trans-lucency and their (inverted) glowing stimulus but did not assessperceived translucency in either of their stimuli. The experimentsreported herein demonstrate that variants of their noninverted

stimulus also appear translucent. Thus, the experiments pre-sented herein show that 3D shape plays a decisive role in de-termining whether a surface appears translucent or opaque.A number of studies have suggested that image contrast is a

significant cue to subsurface scattering, which tends to be re-duced by translucent materials by softening shading gradientsand shadows (18–20). Our results also show that contrast mod-ulates perceived translucency but revealed that the effects ofcontrast depended on the particular shape used: The bumpappeared most translucent at low contrast, whereas the effect ofcontrast on the torus was nonmonotonic, appearing most trans-lucent for midlevel values of contrast. To assess whether thisresult was specific to the contrast manipulation we performed inour experiments (multiplicative scaling), we performed additionalexperiments to assess a variety of nonlinear contrast transforma-tions, similar to those found to be effective in eliciting percepts oftranslucency in previous work (18). We observed the same generalpattern of results for all forms of contrast tested; the effect of 3Dshape had a larger influence on perceived surface opacity thancontrast (Fig. S5).Previous work has also shown that the perception of trans-

lucency can be significantly enhanced by the addition of specularreflections (18, 19). The luminance gradients in our experimentswere texture mapped onto different shapes and therefore did notcontain specular reflections. We conducted an additional experi-ment using the same two sets of shape stimuli used in experiment1 (Movies S1 and S2) and rendered these surfaces with a specularcomponent of reflection (Fig. S6 andMovies S5 and S6). We againobserved large effects of 3D shape on perceived opacity andcomparatively smaller effects of contrast. Our results thereforegeneralize to stimuli with or without specular reflections.There is continuing debate about the level of representation

where material properties are computed. Whereas previous workhas emphasized properties that can be directly computed fromimages, we have argued that the computation of opacity/trans-lucency occurs at a level where 3D shape of surfaces is made ex-plicit (10–12). This argument is grounded on two assumptions:(i) The concept of a surface entails some notion of shape (for-mally and perceptually), which in our environment is 3D; and(ii) opacity/translucency is a property of surfaces. If this is correct,then it follows that the computation of surface opacity must ariseat a level where surfaces are represented, which entails a repre-sentation of (3D) shape. In support of this view, we have shownthat 3D shape can play a decisive role in the perception of opacity/translucency. Moreover, all previous research into the perceptionof surface opacity/translucency used stimuli that evoked vividpercepts of 3D shape. Indeed, if our logic is correct, it should notbe possible to generate a percept of opacity or translucencywithout a percept of 3D shape. This does not imply that imageproperties (or statistics) do not provide inputs needed for thesecomputations; it simply implies that such inputs do not acquireperceptual meaning in specifying the opacity/translucency of amaterial until they are linked to a representation of 3D shape.There are a number of outstanding issues raised by the studies

reported herein. First, our orientation–intensity plots were de-rived using the ground truth surface orientations and intensitiesrather than any direct measurements of perceived shape. Al-though the orientation/intensity computations mush be derivedfrom perceived 3D shape, any distortions in perceived shaperelative to ground truth in our stimuli would likely be related by amonotonic transformation of surface orientation and illumina-tion direction [e.g., affine distortions (25, 26)], and hence do notaffect our main arguments. Second, although vivid percepts of3D shape and opacity/translucency can arise from static mon-ocular images, there is currently no explanation of how 3D shapecan be computed from such images. The stimuli and analysesdescribed herein exploited parallax cues to elicit a particular 3Dshape percept, and hence offer no insight into how the visualsystem solves this problem. Lastly, our experiments—like allprevious studies into the perception of opacity/translucency—have only investigated uniform albedo surfaces, so it is unclear

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Fig. 5. Misperception of translucency; a physically translucent surface illumi-nated from behind that appears opaque and illuminated from the front. Theimages are stereograms arranged for crossed free fusion and depict two objectsthat are physically the same translucent material and are rendered in the sameillumination (primarily from behind, i.e., back lit). Note that the lower shapeappears translucent whereas the upper shape is misperceived to be opaque andfrontally illuminated. The graph shows the results of a paired comparison ex-periment judging translucency. Error bars are SEMs of all observers. See also Fig. S3.

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whether our results generalize to stimuli containing densely varyingsurface albedo. We therefore performed additional experimentsusing stimuli containing variations is surface pigmentation, andobserved the same dramatic effect of 3D shape on perceived sur-face opacity/translucency (Fig. S7). It is clear from viewing thesestimuli that the visual system successfully segments the contribu-tions of texture from the smooth gradients generated by shading orsubsurface scattering, although it remains unknown how the visualsystem performs this decomposition. Thus, the same orientation/intensity analysis proposed herein can account for these texturedstimuli under the proviso that the intensity variations caused byalbedo (texture) are correctly identified as texture.The results presented herein and elsewhere indicate that the

perception of surface opacity/translucency, like the perception ofspecular and diffuse reflectance, depends on the apparent 3Dstructure of images (9–12, 23, 27–29). Indeed, we have arguedthe concept of a surface, both conceptually and perceptually,entails a notion of shape, which in our environment is 3D. If thisis correct, it suggests that the representations used to deriveproperties such as opacity/translucency occur at a level where 3Dshape is made explicit. Future research is required to develop a

more complete understanding of precisely how computations of3D shape and material properties are coupled, i.e., how the vi-sual system uses 3D shape to derive material properties, and howmaterial properties influence the computation of 3D shape.

MethodsThe experiments were approved by the University of Sydney and participantsprovided written informed consent and were debriefed about the aims inadherence with the Declaration of Helsinki. The three inputs to the surfaceorientation-intensity analysis were a RADIANCE high dynamic range (HDR)image of the surface, its depth map, and a list of illumination directions to beanalyzed, which covered the spherical space of possible illumination direc-tions. For each illumination direction, the image intensities were plottedagainst the angular separation of the surface normals relative to that di-rection. The plot shown for each surface was selected because it exhibits thestrongest negative correlation between intensity and surface orientation ofall of the illumination directions analyzed. See Fig. S8 and Supporting In-formation for the full methods.

ACKNOWLEDGMENTS. This research was supported by grants awarded (toB.L.A.) from the Australian Research Council.

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