Low-Level Image Cues in the Perception
of Translucent Materials
ROLAND W. FLEMING and HEINRICH H. BÜLTHOFF
Max Planck Institute for Biological Cybernetics
When light strikes a translucent material (such as wax, milk or fruit flesh), it enters the body of the object, scatters and reemerges
from the surface. The diffusion of light through translucent materials gives them a characteristic visual softness and glow. What
image properties underlie this distinctive appearance? What cues allow us to tell whether a surface is translucent or opaque?
Previous work on the perception of semitransparent materials was based on a very restricted physical model of thin filters
[Metelli 1970; 1974a,b]. However, recent advances in computer graphics [Jensen et al. 2001; Jensen and Buhler 2002] allow us
to efficiently simulate the complex subsurface light transport effects that occur in real translucent objects. Here we use this
model to study the perception of translucency, using a combination of psychophysics and image statistics. We find that many of
the cues that were traditionally thought to be important for semitransparent filters (e.g., X-junctions) are not relevant for solid
translucent objects. We discuss the role of highlights, color, object size, contrast, blur, and lighting direction in the perception
of translucency. We argue that the physics of translucency are too complex for the visual system to estimate intrinsic physical
parameters by inverse optics. Instead, we suggest that we identify translucent materials by parsing them into key regions and
by gathering image statistics from these regions.
Categories and Subject Descriptors: I.3.7 [Computer Graphics]: Three-dimensional Graphics and Realism—Color, shading,
shadowing, and texture; I.4.8 [Image Processing and Computer Vision]: Scene analysis—Shading; J.4 [Social and
Behavioural Sciences]: Psychology
General Terms: Human Factors, Experimentation
Additional Key Words and Phrases: Human visual perception, material perception, image statistics, Metelli, transparency,
translucency, illumination
1.
1.1
INTRODUCTION
Visual Perception of Material Properties
One of the most vivid aspects of our visual experience is our sensitivity to the material attributes of
objects. We can easily distinguish between materials such as wax, chalk, or bronze across wide variations
in illumination and object shape. Without handling an object, we can usually tell with ease whether it
will be wet or dry, friable or spongy, rough or smooth to the touch. Despite this, we understand very
little about how the human visual system recognizes materials.
One reason why prior research into the perception of materials has been limited is that it is difficult
to systematically manipulate the material qualities of real objects. However, recent advances in computer graphics make it much easier to generate a wide range of realistic stimuli. It is now possible to
Author’s address: R. Fleming, Max Planck Institute for Biological Cybernetics, Spemannstraße 38, Tübingen, 72076,
Germany.
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parametrically vary the material qualities of a simulated object, while holding all other aspects of the
scene (e.g., lighting, viewpoint, object shape, etc.) absolutely constant.
In this work, we use a recently developed computer simulation of subsurface light transport [Jensen
et al. 2001; Jensen and Buhler 2002] to study how we perceive translucent materials. We find that the
visual system does not use many of the cues that were traditionally thought to be important for the
perception of materials that transmit light.
1.2
Translucent Materials
Many of the materials that we encounter on a daily basis are partially permeable to light. For example,
fruit flesh, wax, cheese, and human skin are all somewhat translucent. The light that bleeds through
these objects gives them a characteristic visual softness and glow that plays a major role in their distinctive appearance. Here, we study some of the cues that give translucent materials their characteristic
“look.”
Translucency is potentially a very important physical property for an organism to identify. It can help
us to distinguish between materials, such as milk and white paint, and can even inform us about the
functional state of an object. For example, proteins, such as albumen or meat flesh, become more opaque
when cooked, while fruits become increasingly translucent as they ripen, growing quite transparent
as they begin to rot. Absinthe acquires a distinctive opalescent louche when mixed with water and
transparent plastic becomes white and opaque when subjected to repeated stresses. How do we recognize
translucent objects? What image cues do we use to distinguish translucent from opaque?
1.3
Metelli’s “Episcotister” Model
There has been a large body of previous work on the perception of materials that transmit light [Adelson
1993, 1999; Anderson 1999, 2003; Beck 1972, 1978; Beck and Ivry 1988; Beck et al. 1984; Chen and
D’Zmura 1998; D’Zmura et al. 1997, 2000; Fuchs 1923a,b; Gerbino 1994; Gerbino et al. 1990; Heider
1933; von Helmholtz 1867/1962; Hering 1874/1964; Hunter 1975; Kanizsa 1955; Katz 1935; Kersten
1991; Kersten et al. 1992; Khang and Zaidi 2002a,b; Koffka 1935; Lindsey and Todd 1996; Masin 1997,
1999a,b; Metelli 1967, 1970, 1974a,b; Metelli et al. 1985; Metzger 1953; Nakayama and Shimojo 1992;
Nakayama et al. 1990; Plummer and Ramachandran 1993; Robilotto et al. 2002; Robilotto and Zaidi
2004; Singh 2004; Singh and Anderson 2002a,b; Somers and Adelson 1997; Stoner et al. 1990; Tommasi
1999; Tudor-Hart 1928; Watanabe and Cavanagh 1992, 1993a,b. For an excellent review see Singh and
Anderson 2002a].
Almost all of this research is based on a very simple physical model of semitransparent materials,
the most famous incarnation of which is the “episcotister” model of Metelli [1967, 1970, 1974a,b].1 The
basic concept behind this model is that the object of interest is a thin filter or screen, through which
some background pattern is visible. As depicted in Figure 1, the episcotister consists of an opaque disk
of cardboard with a wedge cut out. When the episcotister is spun at high speed (above the “flicker-fusion
threshold”) there is a linear mixing of the color of the disk with the background that is visible through
it. This leads to the impression of a thin transparent screen or filter lying in front of the background
pattern. The properties of the filter—its opacity and lightness—are determined by the size of the sector
that is cut out of the disk, α, and the shade of grey that the disk is painted, t.
By varying t and α, the episcotister can generate a continuous range of semitransparent materials. Furthermore, simple algebraic relations hold between the properties of the episcotister and the
luminances that are present in the resulting display [Gerbino 1994; Metelli 1970, 1974a,b; Singh and
1 To
our knowledge, the only exceptions to this trend are to be found in the work of Koenderink and colleagues [e.g., Koenderink
2003; Koenderink and van Doorn 2001] and some ongoing projects of Adelson and colleagues [unpublished].
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Fig. 1. (a) The episcotister is a disk of cardboard that is painted a certain shade of grey, t, with a wedge of angle α cut out.
(b) When rotated at high speed, the episcotister produces the impression of a transparent filter. The lightness and opacity of this
filter are controlled by varying α and t. We argue below that this is a poor model of real translucent materials, such as wax or
jade.
Anderson 2002a]. This has lead to a good understanding of some of the factors that are important in
the perception of transparency. For the purposes of the current arguments, we will now review three
aspects of Metelli-type displays that are traditionally thought to be important in the perception of
transparency. To anticipate, we will argue that these three cues generally do not apply to images of real
translucent materials, such as alabaster or marmalade.
First, a number of authors [Adelson 1993; Adelson and Anandan 1990; Anderson 1997, 2001; Beck and
Ivry 1988] have noted the possible importance of local image features, called X-Junctions, which occur
whenever the boundary of the filter crosses a contour in the background pattern, as depicted in Figure 2.
Metelli [1970] observed that we perceive a region to be transparent only when certain luminance and
figural relations hold between the various regions in the display. Some of these constraints can be
reexpressed in terms of the luminance structure of X-junctions. It has been suggested that junctions
could provide the visual system with a local signature for decomposing the image into transparent
layers.
The second major assumption is that the visual system infers the optical qualities of a transparent
region by comparing it to the surrounding background. An example of this is demonstrated in Figure 3.
The central regions is identical in the two displays; however, depending on the context in which the
region is embedded, it can be made to appear transparent or not.2 The important idea is that the
visual system has to compare the transparent region with its background in order to determine how
transparent it is.
The third major assumption to emerge from Metelli’s simple model of transparency, is Adelson’s
[1999] concept of linear atmospheres. Adelson argued that transparent filters (and many other optical
processes) can be thought of as “atmospheres” that systematically modify the luminances that are
2 As
one anonymous reviewer noted, this particular example can also be predicted by looking at the local junctions. However,
while junction class can specify categorical properties of the scene (i.e., “transparent” versus “not transparent”), it cannot specify
metric attributes (i.e., the degree of transparency). Here, we are raising the common suggestion that the perceptual assignment of
a particular degree of transparency requires a comparison between the transparent region and its surround. Singh and Anderson
[2002a] discuss this distinction in greater depth.
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Fig. 2. X-Junctions occur where two contours intersect in the image. The ordinal relations between the intensities that form the
junction determine which percepts are possible. The S-shaped ordering leads to a bistable percept in which either square can be
seen as a transparent filter; the C-shaped ordering means that only the tilted square can be seen as transparent; the criss-cross
ordering is inconsistent with either of the squares appearing transparent. Adapted from Beck and Ivry [1988].
Fig. 3. The central regions in (a) and (b) are pixel-for-pixel identical. However, the apparent quality of the regions depends
crucially on the context in which they are placed. In (a) the region is surrounded by higher contrast stripes and, consequently,
appears transparent; in (b) the surround is lower contrast and, thus, the central region does not appear transparent.
visible through them. Specifically, a Metelli-type filter subjects the luminances in the background to
a simple linear (affine) transformation, called the atmospheric transfer function (ATF), as depicted in
Figure 4. We discuss this concept in greater detail below; for now, the important point is that the object
of interest is linear.
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Fig. 4. (a) Two “atmospheres” modify the intensities in the background in a linear way. The images of the two filters are also
linearly related to one another. (b) The atmospheric transfer function (ATF) shows the linear mapping from the background
through an atmosphere. Note that the mapping has both an additive and a multiplicative component. Figure modified from
Adelson [1999].
A large range of optical phenomena can be thought of as “linear atmospheres.” For example, cast
shadows behave like an ideal black episcotister, because surfaces inside the shadow are darker than
their counterparts outside the shadow by a constant multiplicative factor. In fact, all of the following
processes can be approximated quite well by Metelli-type transparency:
1.
2.
3.
4.
5.
6.
7.
illumination effects, such as shadows, spot-lights, and caustics,
highlights on glossy surfaces,
stains or patches of dye,
synthetic patterns, such as gingham plaid,
screens such as muslin or gauze,
rotating fan blades or propellors,
thin, neutral-density filters.
However, although Metelli displays apply to a large range of optical phenomena, we argue here
that, ironically, they provide a very poor model of generic lumps of real translucent material, such as
wax or cheese. The main reason for this is that the episcotister excludes many of the physical effects
that occur in real scenes, such as graded changes in lighting across the scene; interreflections between
the object and its background; and specular reflections from the surface of the object.3 Most importantly
of all, the simple models ignore crucial aspects of light transport within the body of the object itself:
refraction and subsurface light scatter. We have found that these limitations of the generative model
have profound consequences for the image cues that the visual system can use for the perception of
translucency.
3 Specular
reflections add a veiling luminance to the image transmitted by a transparent object. Thus, specular reflections
themselves behave like an additional Metellilike filter (with its own parameters) superimposed on the image. We have been
unable to find any example of previous work where this effect has been incorporated into the generative model.
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Fig. 5. The optical behavior of reflective and translucent materials.
1.4
Subsurface Scattering and the BSSRDF
When light strikes a real translucent object, it passes through the surface, refracts and scatters multiple times within the body of the medium, before emerging at some other location on the surface. This
phenomenon, called subsurface scattering, causes light to spread out into a diffuse region around the
point of illumination. In contrast, traditional models for light scattering based on the Bidirectional
Reflectance Distribution Function (BRDF) assume that materials are opaque and that all light is
reflected from the point that is illuminated. This difference is depicted in Figure 5.
Recent advances in computer graphics [Jensen et al. 2001; Jensen and Buhler 2002] allow us to
simulate subsurface scatter realistically and efficiently. A full simulation of translucency requires solving the radiative transport equation [Chandrasekhar 1960]. Jensen et al. [2001] simplified the light
scattering by assuming that the translucent material is homogeneous. In this case the scattering of
light can be approximated by a diffusion equation plus a term for single scattering. Together, these
terms form a Bidirectional Scattering Surface Reflectance Distribution Function (BSSRDF).
The parameters in the BSSRDF are the refractive index of the material, the phase function (which
determines the directions in which light scatters), and the scattering and absorption coefficients. The
absorption and scattering coefficients specify the probability that a photon will be absorbed or scattered
when traveling a given distance within the material. By adjusting these parameters it is possible to
emulate a range of different translucent materials, as shown in Figure 6.
Koenderink and van Doorn [2001] pointed out that translucent materials have an appearance that
differs from traditional Lambertian materials and they investigated the diffusion of light in simple
geometric shapes in order to analyze the shape from shading characteristics of translucent objects.
They observed that the shape of translucent objects is difficult to analyze as the appearance depends
not only on the location of the lighting and the observer, but also on the shape of the object, since much
of the lighting is due to scattering within the translucent object.
For the current argument, the most important observation is that subsurface scatter has dramatic
consequences for the perception of translucent materials. Many of the cues that were traditionally
thought to be important for the perception of Metelli-type transparency simply do not apply to these
more realistic materials. Consider, for example, the translucent dragon shown in Figure 7.
The image has the characteristic visual softness and glow that we associate with translucent materials. The way that light diffuses through the thinner parts of the object gives us a distinct impression
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Fig. 6. The laughing Buddha rendered with different settings of the BSSRDF. The scattering coefficient progressively increases
from left to right all other parameters are held constant. The apparent material quality ranges from glassy, through jadelike to
porcelain. Model courtesy of the Stanford 3D scanning repository.
Fig. 7. A translucent dragon that was rendered using Jensen’s [2001] BSSRDF algorithm. Note that the image contains no
X-Junctions and the background is not visible through the object. Despite this, we have a vivid impression that the material is
permeable to light.
of its translucency. However, this percept of translucency occurs even though we cannot see any background pattern through the object. The image does not contain salient X-junctions and there is no clear
sense of figural continuity between the background and the region of the dragon. Clearly, if we wish
to understand how we perceive this class of materials, we must consider a new range of image cues.
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Although Metelli displays have informed us about many aspects of perception, they cannot tell us how
we recognize generic lumps of translucent stuff.
2.
IMAGE CUES FOR THE PERCEPTION OF TRANSLUCENCY
2.1
Inverse Optics Versus Image Statistics
It has commonly been suggested that the visual system could estimate surface reflectance by inverting
the physics of image generation. For example, von Helmholtz [1867/1962] famously conjectured that the
visual system recovers albedo by estimating and actively discounting the contribution of the illuminant
to the observed image intensity. Similar reasoning plays a role in many more recent theories of color
constancy [e.g., Brainard et al. 2003; Maloney and Yang 2003]. However, while such an approach may
be plausible for simple scenes consisting of point light sources and isolated Lambertian surfaces, in
more complex scenes, it becomes increasingly unlikely that the visual system is capable of modeling
the complex interactions of light with surfaces [although, see Doerschner et al. 2004; Delahunt and
Brainard 2004; Bloj et al. 2004].
Given the extreme physical complexity of light scatter within participating media, we suggest that
it is highly unlikely that the visual system estimates translucency using inverse optics. Instead, we
propose that the visual system relies on a number of relatively simple image measurements that reliably
correlate with changes in object translucency. Accordingly, we have studied a number of simple image
statistics that the visual system could exploit in the perception of translucency. Our approach is to
generate a series of images that differ only in the degree of translucency and to search for simple image
measurements that correlate with the resulting changes in the image. In this section, we present a
number of observations on the roles of various image cues in the perception of translucency.
2.2
Specular Highlights and the Perception of Translucency
Highlights occur when light is specularly reflected from the surface of an object. Note that specular
reflections are caused by the interface between two materials of different refractive index (i.e., the
surface itself). As such, highlights are not a direct consequence of light transport within the body of an
object. We might, therefore, expect the perception of translucency to be quite independent of specular
reflections.4 However, many translucent materials that we commonly encounter are somewhat glossy
(e.g., plastic, candle wax, or honey). This means that the human visual system may “expect” translucent
materials to exhibit specular reflections.
Interestingly, we have found that highlights can contribute to the visual impression of translucency.
Consider, for example, the images shown in Figure 8. Each pair of images is identical, except for the
addition of specular highlights to the right-hand images. Observers generally agree that the glossy
surfaces look more like canonical translucent materials than the surfaces without highlights.5
It is well known that adding localized highlights to the image of a matte object makes the object
appear more glossy [Beck and Prazdny 1981; Berzhanskaya et al. 2002].6 However, to our knowledge, it
4 Note,
however, that the binocular depth of highlights is generally not on the surface itself [Blake and Bülthoff 1990, 1991]. Here
we are dealing with monocular images, but it is possible that adding stereoscopic information would alter the effects described
here.
5 We are not suggesting that highlights affect the perceived degree of translucency (i.e., they do not make the objects appear more
or less opaque). Rather, they affect the realism of the depiction of translucency (i.e., how much the objects look like they are made
of real translucent materials).
6 In these works, the late Jacob Beck and colleagues emphasized the nonuniformity of the resulting gloss percept across the surface
(it appears to weaken with distance from the highlight). However, one of the most striking aspects of his famous demonstration
is just how far the impression of glossiness propagates away from the highlights: The entire surface appears somewhat more
glossy.
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Fig. 8. The role of highlights in the perception of translucency. Left images have no highlights; right images have highlights.
Most observers agree that the specularities make the impression of translucency more compelling.
has not been noted before that the resulting glossiness can have consequences for the apparent realism
of a material’s translucency.
It is worth noting that we can have a vivid impression of translucency even when the images are
not physically correct renditions of translucency. For example, although the image pair in (a) were
created using a full evaluation of the BSSRDF, the images in (b) are simply based on the depth data
from a synthetic object. Specifically, the intensity of each pixel specifies how close the surface is to
the observer at the corresponding location in the image. Although this is not a correct simulation of
translucency, we tend to see the depth map as somewhat translucent. This illusion is enhanced with
the addition of highlights. The specular component in the right-hand image of (b) was rendered under full-scene illumination from the Debevec [1998] panoramic light-probe database. Thus, there is no
meaningful consistency in the “illumination” of the two components of the image. However, despite
this inconsistency, we readily fuse the two components into a single percept of a glossy, translucent
object. The inconsistency in illumination does not hinder the sense of translucency. On the contrary,
observers generally agree that the inconsistently illuminated image looks more realistic than its consistent, but highlight-less, counterpart. Together these observations support the idea that perception of
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Fig. 9. Cubes exhibiting various color effects generated using the BSSRDF. (a) Opaque and uniform green; (b) mauve body color
with blue fringe; (c) mauve body with pink fringe; (d) a material unlike those commonly encountered in the real world: the color
varies continuously from pink through mauve to green. Note that within each cube, all parameters of the BSSRDF are constant;
the color variations are due to the progressive filtering of scattered light.
translucency depends on simple image heuristics rather than physically correct inverse optics. It also
suggests that for graphics applications, we may be able to induce a vivid percept of translucency without
having to simulate all of the physics correctly.
2.3
Color Cues in the Perception of Translucency
Can color cues influence our perception of translucency? When white light passes through a colored
translucent object, it is progressively filtered, and emerges colored. Interestingly, hue, saturation, and
intensity can all vary as a function of the distance traveled by a ray through a translucent material.
This suggests that perhaps the visual system can use color cues in the perception of translucency. The
BSSRDF can produce a wide range of color phenomena, depending on the color values of the scattering
and absorption coefficients. A few examples are shown in Figure 9.
We know that color is not necessary for the perception of translucency, because grey-scale images,
such as Figure 6 and 7, can nevertheless yield a strong impression of translucency. However, can color
modify the sense of translucency when present?
We have found that color saturation can affect the way a translucent object appears to “glow.” Consider
the two cubes in Figure 10. The hue and intensity components of the two images are identical. What
differs is the saturation component. In (a) the saturation is positively correlated with the intensity
image, while in (b) it is negatively correlated. The mean saturation is held constant. Observers generally
agree that (a) appears to have a “warmer” glow, while (b) appears more “icy” or “dilute.”
Although saturation variations can affect perceived translucency, they are insufficient on their own to
yield an impression of translucency. This is demonstrated in Figure 11. In (a), saturation is held constant
across the image, while intensity varies. In (b), intensity is held constant while saturation varies. Most
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Fig. 10. (a) Color saturation is positively correlated with intensity. (b) Saturation is negatively correlated with intensity. Mean
saturation is identical for the two images. Most observers agree that (a) appears “warmer” than (b).
Fig. 11. (a) Intensity varies across the image, but saturation is constant. (b) Intensity is constant, but saturation varies. Most
observers agree that (a) looks more translucent than (b).
subjects agree that (a) looks translucent, while (b) does not. This suggests that the saturation component
is neither necessary nor sufficient to yield an impression of translucency.
2.4
Important Image Regions
Not all regions of an object are equally informative about the degree of translucency. As a photon travels
through a translucent object, it engages in a sequence of interactions with the particles of the medium.
With each interaction, there is a certain chance that the light ray will be absorbed or scattered. Thus,
the further a light ray travels, the greater is the chance that it will not contribute to the light emerging
from the surface of the object. This means that wherever an object is thin, the transmitted light will
tend to have a large effect on image intensity; by contrast, wherever the object is thick, the transmitted
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Fig. 12. A translucent cube illuminated directly from behind. Note the bright fringes where light passes through the thin edges
of the cube.
Fig. 13. Differences between (a) opaque and (b) translucent versions of a cube. Image (c) shows the unsigned differences in pixel
intensities between (a) and (b). Although the perceived material qualities of (a) and (b) are very different, most image locations
are actually quite similar. Note, particular, that the surface that faces the bright light source carries very little information about
the degree of opacity. Almost all of the translucent appearance is determined by the bright, blurry fringes around the edges of
the cube.
light will be highly attenuated, resulting in only a weak increase in luminance. Figure 12 shows a cube
that is illuminated from directly behind. All visible points in the image result from light that has passed
through cube. Note the bright fringe around the edge of the cube, where light passes through the thin
edges and vertices.
One important consequence of this is that some image regions vary considerably with changes in
translucency, while other regions remain roughly the same. Thus, different regions are more or less
informative about how translucent the object is. This can be quantified by looking at the pixel-by-pixel
difference between translucent and opaque versions of the same object, as shown in Figure 13.
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Fig. 14. A procedure for generating the impression of translucency from a Lambertian object using simple image manipulations.
The opaque cube (a) and translucent cube (b) have quite different material appearances. Despite this,
the images are actually surprisingly similar on a pixel-by-pixel basis. Image (c) shows the unsigned
differences between the two images. Dark regions in the difference map vary by only a small amount
with the change from opaque to translucent, which means that they carry little information about the
degree of translucency. Note, for example, that the leftward pointing surface (which faces a bright light
source), is almost identical in the two images and, thus, bears little information about the degree of
translucency. Almost all of the apparent translucency of (b) is caused by the bright, blurry fringes close
to the edges of the cube. One is reminded of Beck’s demonstration of the effects of local highlights on
apparent glossiness. Subtle image differences can lead to large changes in apparent material quality.
In principle, this could be exploited in an efficient procedure for imitating translucent materials
without a full evaluation of the BSSRDF. The system would first render a Lambertian version of the
object. This is easy to implement and extremely quick to compute. Then, using information about object
geometry and light source position, bright fringes could be added to the Lambertian image around
thin regions of the object. By tweaking the brightness and blurriness of the fringes, the apparent
translucency of the object could be varied. This may be sufficient for applications that do not require
a high degree of physical realism. Indeed, Figure 14, shows how very basic image modifications can
endow a Lambertian surface with a moderately acceptable translucent appearance.
The key to the procedure is the introduction of bright fringes around the corners of the cube using a
high-pass filter with a fairly large convolution kernel. The fact that such primitive image manipulations
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Fig. 15. Scale dependency effects in translucency. The first image shows three cubes of different sizes, all made out of the same
material. From left to right shows progressive zooms into the image. Note that the smaller cubes appear more translucent than
the larger ones, as light spreads through a greater proportion of their volume.
can affect our sense of material qualities further supports our suggestion that the visual system does
not use inverse optics to estimate translucency.
2.5
Dependency on Physical Scale
The fact that light reduces in intensity as it travels deeper into a translucent medium has a second
important consequence. For a given degree of translucency, the amount of light that bleeds through an
object depends on its size. Thus, smaller objects tend to appear more translucent than larger objects
that are made out of the same material. This is demonstrated in Figure 15, which shows three cubes
of different sizes. As we zoom into the smaller cubes, we can see that light spreads through a larger
proportion of their bodies, increasing their apparent translucency. Note that there is no equivalent
effect for smooth diffuse objects. Subsurface light scatter can, in principle, carry information about an
object’s scale. This has been exploited to represent the small size of computer-animated characters in
movies [Jensen and Buhler 2002].
2.6
Image Contrast
Arguably the most important cue in the perception of light-permeable materials is image contrast.
Historically, researchers have usually argued that the visual system estimates the properties of Metellitype filters by comparing some measure of image contrast (e.g., luminance range, Michelson contrast)
between the transparent region and its surround [Beck et al. 1984; Gerbino 1994; Metelli 1970, 1974a,b;
Singh and Anderson 2002a; although see also Robilotto et al. 2002]. However, as demonstrated in many
of the figures in this paper, we can enjoy a powerful percept of translucency even when the object of
interest is suspended in a black void. Thus, comparisons of image contrast between an object and its
surround, do not seem to be necessary for the perception of translucency. Nevertheless, as we will now
explain, the physics of subsurface light scatter mean that contrast does vary systematically with opacity
and is, therefore, likely to serve as a visual cue for translucency.
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Fig. 16. Contrast in the perception of materials that transmit light. (a) Three tori of increasing opacity. Note that the internal
contrast increases with opacity. (b) Three Metelli-type filters of increasing opacity. Here the contrast of the filter region decreases
with opacity.
Light diffuses through translucent materials, much like dye diffusing through a fluid. Translucent
objects become “filled” with light when illuminated. An important consequence of this is that points on
the surface that do not receive any direct illumination (i.e., they are in shadow) can nevertheless receive
light from within the body of the object. Conversely, regions that receive strong direct illumination tend
to dissipate the incident light by transmitting it to other parts of the object. This has the effect of
reducing the overall contrast of translucent objects, as shown in Figure 16(a). Three objects are shown
under the same lighting. Torus A is the most translucent, Torus B is of intermediate translucency, while
Torus C is relatively opaque. We will refer back to these three tori a number of times in the subsequent
discussion. Note that the range of intensities in the images progressively increases from A to C. It seems
reasonable, then, that the human visual system might use image contrast to estimate the opacity of
translucent objects, as has been suggested previously.
Note, however, that the mapping from image contrast to object opacity is radically different from
what would be expected from a Metelli-type display. This is demonstrated in Figure 16(b), which shows
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Fig. 17. The nonlinear relationship between intensity values in torus A and torus C.
a series of thin filters of increasing opacity. The contrast of a filter depends on the extent to which
the background pattern passes through it. When the filter is very transparent, the contrast is high
because the background shines through clearly. As the filter becomes more opaque, less of the background shows through and the contrast of image progressively decreases from A to C. This is the
exact opposite of the tori in (a). This means that the visual system cannot use contrast to estimate the
translucency of solid objects in the same way as it does to estimate the properties of thin semitransparent filters.7 Nevertheless, it seems quite likely that contrast is an important cue, especially given
that it is the “basic currency” of early visual processing [Anderson 2003; Cornsweet 1970; Hartline
1940; Hering 1874/1964]. In the rest of this section, we explore the role of contrast in the perception of
translucency.
So far we have used the term “contrast” loosely to mean the extent of intensity variations in an image.
However, there are many ways to quantify contrast, such as luminance range [Singh and Anderson
2002a], Michelson-, RMS-, or Weber-contrast, as well as a variety of more elaborate measures [Moulden
et al. 1990; Peli 1990]. Which measures of contrast are relevant for the perception of translucency? How
does contrast vary with translucency?
One possibility is that translucent objects are linear. As mentioned above, episcotister displays are
linear atmospheres [Adelson, 1999]. This means that if we place two different filters against the same
background, the two images will be linear transformations of one another. Stated another way, if we
want to adjust the apparent properties of a filter, we can simply subject the image intensities to a linear
(affine) transformation. To adjust the contrast, intensities are multiplicatively scaled, while to adjust
brightness, image intensities are additively scaled. These adjustments have predictable effects on the
apparent qualities of the filter. Can we use the concept of linear transformations to understand the
relationship between opaque and translucent objects?
In Figure 17, we put the linearity assumption directly to the test by comparing torus A with torus C.
If we plot the intensities of the translucent torus A on the x-axis and the intensities of corresponding
locations in the opaque torus C on the y-axis, we see that the two images are not linearly related to one
another.
7 Here,
as in the rest of the paper, we mean our analysis to apply to the generic case of a freely standing object of manipulable
size, with a nonnegligible degree of multiple subsurface scattering. It is, of course, possible to carefully arrange a scene so that
patterns shine through a real translucent material. However, under ordinary circumstances, even quite moderate subsurface
scattering tends to render background textures invisible when viewed through a chunk of translucent matter.
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Fig. 18. Intensity histograms of the three images. Note that the entire shape of the distribution changes as the torus becomes
more opaque.
This is important because it affects our concept of contrast. Specifically, it excludes any definition
that assumes linearity. Instead, we must seek alternative measures of contrast that capture the ways
that intensity variations change with changes in translucency.
When we gradually alter an object from translucent to opaque, the entire distribution of image
intensities changes shape, as shown in Figure 18. Here, the mode shifts to lower intensities, while the
whole distribution becomes more skewed. This suggests that our concept of contrast should take into
account the complete distribution of intensities, or at least some summary statistics (e.g., mode and
skew), that capture these changes. In Figure 19, we show how mean, variance, skew and kurtosis vary
as the torus changes continuously from translucent to opaque. Note that all four summary statistics
vary considerably with changes in object opacity. It seems that the distribution of brights and darks in
the image can carry a wealth of information about the material qualities of objects.
If human visual estimates of translucency incorporate information that is captured by intensity
histograms, then we ought to be able to alter the apparent translucency of objects simply by manipulating their intensity histograms. Considering how basic this image manipulation is, we have found that
intensity histograms provide a surprisingly powerful means for adjusting the apparent translucency
of objects. For example, as we show in Figure 20, we can take an object of intermediate opacity (torus
B) and adjust its intensity histogram so that it closely approximates the histogram of a more translucent object (torus A) or a more opaque object (torus C). This is achieved by passing the image through
carefully chosen nonlinearities. The results of this histogram matching process are shown at the bottom of Figure 20. When we match the histogram of torus B to A, we endow torus B with a compelling
translucent appearance. Conversely, matching to torus C makes torus B appear more opaque.
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Fig. 19. Summary statistics of the intensity distribution as a function of opacity. Note that (a), (c), and (d) are all nonmonotonic
functions. This becomes important in our later analysis.
It is important to note that histogram matching preserves the ordinal relationship between pixels, so
the spatial structure of the image is not affected by the nonlinear transformation. Histogram matching
cannot, for example, introduce blurriness to the image, or change the position of highlights. Subsurface
scatter does introduce blur to the image, as we discuss below. Thus, it is all the more surprising we can
make a translucent object appear opaque (or vice versa) simply by changing the intensity histogram.
This is, once again, consistent with our suggestion that the visual system uses simple image heuristics to
identify translucent appearance, rather than using inverse optics to estimate parameters of subsurface
scatter.
However, although the intensity histogram captures something important about translucent objects,
we should emphasize that it is insufficient alone. For example, in Figure 21, the pixels in torus A have
been scrambled (in a way that keeps the image quite smooth) to create a pattern of random noise with
the same intensity histogram as torus A. Unsurprisingly, this transformation destroys the impression
of translucency. It is worth noting that the scrambling also destroys the sense of three-dimensional (3D)
shape. It is possible that by using a different scrambling procedure that preserves the sense of threedimensionality, the impression of translucency would persist. Clearly it is not just the distribution of
lights and darks, but their spatial relations that inform us that something is translucent.
Furthermore, intensity distributions can, of course, be affected by factors other than the degree of
translucency. For example, moving the light source alters the proportion of the object that is in shadow,
which naturally changes ratio of light to dark in the image. Below we show that perceived translucency
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Fig. 20. Using histogram matching to modify apparent translucency. Here we adjust the intensity histogram of torus B so that
it matches either of the target images: torus A or C. This is achieved by passing the original image through carefully chosen
nonlinearities. The output images are modified versions of the original, which are endowed with the apparent translucency or
opacity of the target images.
does change when the light source moves. However, we find that these changes cannot be easily predicted
solely from the changes in the intensity histogram.
In summary, a simple linear concept of contrast cannot account for the different appearances of
translucent and opaque objects. If, instead, we consider the full intensity distribution, we can traverse
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Fig. 21. A noise pattern that has the same intensity histogram as torus A. The image does not appear translucent.
the space of translucent and opaque objects surprisingly successfully, as long as the lighting conditions
are held constant. However, the intensity distribution fails to capture crucial information about the
spatial structure of translucent images.
2.7
Spatial Structure: Blur, Haze, and Isophotes
We have argued that it is not solely the proportion of light and dark in an image, but their spatial
relationships that make an object look translucent. In this section we discuss how translucency affects
the spatial structure of images.
Subsurface scatter causes light rays to spread out into diffuse puffs as they pass through a translucent
medium. This has the effect of blurring out sharp details in the image of a translucent object. Consider,
for example, the images in Figure 6. Details that are visible in the most opaque Buddha become softened
or even invisible in the more translucent objects. Note also the edges of the shadows cast across the tori
in Figure 22(a). These are crisp and pronounced in torus C, but blurry and diffuse in torus A.
It seems reasonable, then, that blur could play an important role in the distinctive soft appearance of
translucent materials. Indeed, it has been suggested previously that blur can influence our perception
of transparency in Metelli-like displays. Singh and Anderson [2002b] showed that blurring the pattern
that is visible through a filter, as shown in Figure 22(b), makes the filter appear more opaque. Note,
however, that this is in direct contrast with our intuitions about the physics of solid translucent objects.
As an object becomes more translucent, we expect sharp edges to become diffused out by the bleeding
of light through the medium. Thus, we would generally expect blurriness to be correlated with translucency not with opacity. As with image contrast, this inconsistency between Metelli-type displays and
more realistic renderings is due to the fact that the appearance of a thin filter is determined by the way
it modifies the background that is visible through it. This is generally not the case for solid translucent
bodies.
Although blur clearly appears to be related to translucency, we have found that it is insufficient, on
its own, to produce a vivid percept of translucency. If the intensity distribution is held roughly constant,
then adding blur by itself has little effect on perceived translucency, as shown in Figure 23. Here, torus
B has been subjected to a rotational transformation that blurs out details within the body of the torus
but does not cause any blurring across the boundary of the torus. Inspecting the close-up reveals that
the shadow boundary, for example, has been considerably diffused. Nevertheless, this has very little
effect on the overall appearance of the torus. Certainly it does not mimic the apparent translucency of
torus A.
There are a number of reasons why blur may have such a weak effect in this demonstration. First,
there are many processes that can produce blur in images, including depth of field effects and shadow
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Fig. 22. Relationship between blur and perceived opacity. (a) A series of tori ranging from translucent to opaque. Note that the
image features generally become sharper (less blurry) from left to right. By contrast, Singh and Anderson [2002b] have shown
that adding blur to a Metelli display, as shown in (b), makes the filter appear more opaque.
penumbras. Thus, in the absence of additional cues to translucency, the visual system may not be able
to attribute the blur to subsurface light scattering.
Second, it is possible that the way that light spreads through a translucent object does not have the
same effect on the image as a simple blurring operation. In Figure 24, we plot what happens to image
details as the material varies continuously from translucent to opaque.
We rendered a large number of tori, ranging from highly translucent to highly opaque. From each
torus, we measure how the intensity varies along a circular path around the image (shown in red).
This is like plotting a single raster line from the image, except that the line curves around the object.
In Figure 24(b), we plot how the intensities along the “raster line” vary as a function of opacity. The
x-axis is the degree of opacity, while the y-axis is the position along the “raster line” that passes around
the torus. Stated another way, we have “unwrapped” the tori and plotted the image intensities as the
degree of translucency varies. Thus allows us to visualize more directly how translucency smears out
details in the image.
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Fig. 23. Effects of blur on perceived translucency. (a) Original version of torus B. (b) Blurred version of torus B. (c) Blurriness
in the more translucent torus A. Note that the blur has almost no effect on the apparent translucency of (b), although the blur
is clearly visible in the close-up.
Note that the shadow boundaries (indicated by the red dots) are not simply more or less blurred
depending on the opacity. Instead, they remain quite sharp except at the most translucent end of the
scale. The apparent blurriness of the translucent tori is due to a veil of superimposed “haze,” which
glows into the shadows from the neighboring bright regions. This suggests that the relevant cue for
translucency may not be simple image blur, but rather the superimposition of sharp and blurred versions
of image features. We call this the “shadow-haze” effect.
There are other ways of visualizing the structure of images. For example, the spatial organisation of
lights and darks can be made visible by plotting the isophotes (contours of equal luminance), as shown
in Figure 25. Many researchers have found isophotes to be invaluable for studying how illumination and
3D shape determine image structure in the case of opaque materials [e.g., Koenderink and van Doorn,
1980; Mamassian and Kersten 1996; Mingolla and Todd 1986; Todd and Mingolla 1983]. It seems likely
that they could also be a useful tool for understanding translucency.
Note the fact that the isophotes are closer together in torus B than in torus A. This is related to the
smoothness of torus A, which is yet another way of conceiving of blur.
It is important to note that spatial organization alone does not tell us whether an object is translucent
or not. This is demonstrated in Figure 26, which shows the photographic negative of torus A. The
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Fig. 24. In order to visualize the blurring of image features by subsurface light scatter, we have rendered a series of tori of
different opacities. Here we show how image intensity varies along a particular circular path around the torus (red circle) as a
function of the opacity of the torus. Note that the shadow boundaries (red dots) remain sharp for all but the most translucent tori.
What varies is the amount of “haze” that is superimposed on this sharp boundary. Accordingly, we call this the “shadow-haze”
effect.
photographic negative has exactly the same pattern of isophotes as its positive counterpart and yet the
image does not appear translucent. This is important as it suggests that the visual system attends to
the direction in which intensity is varying and not just to the spatial layout of the intensity variations.
Isophotes and intensity histograms capture complementary properties of the image. Isophotes patterns carry information about local spatial relations between image intensities, but exclude information
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Fig. 25. Isophotes of torus A and B. Note the bunching up around the edge of the shadow in torus B.
Fig. 26. The photographic negative of torus A has the same isophote pattern, but does not appear translucent.
about the actual intensities that makeup these patterns. By contrast, intensity histograms carry
information about the distribution of brights and darks in the image, but exclude information about the
spatial locations of the intensities. We suggest that the visual system relies on both classes of information to identify translucent materials. Several authors have previously suggested that simple textural
image statistics may be important in the perception of surface reflectance properties [Adelson 2001;
Fleming et al. 2003; Nishida and Shinya 1998]. Here, we argue that related image measurements are
exploited in the perception of subsurface scattering properties.
3.
EFFECTS OF ILLUMINATION DIRECTION ON PERCEIVED TRANSLUCENCY: TESTING
CANDIDATE CUES
So far we have informally studied how a number of image cues influence perceived translucency. In
this section we report the results of a quantitative psychophysical experiment on the perception of
translucent materials across changes in the conditions of illumination. To anticipate, we find that
perceived translucency varies considerably depending on the position of the light source. Importantly,
changes in the lighting also cause numerous measurable properties of the image to also change. Thus,
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Fig. 27. A translucent torus illuminated from six different directions. Top row: illumination from behind. Bottom row: illumination from the front. Note that the apparent opacity of the torus changes depending on the direction of illumination.
this experiment allows us to compare how well a variety of image cues can predict human visual percepts
of translucency.
The motivation for the experiment is the informal observation that objects tend to look more translucent when illuminated from behind. Anyone who has spent time playing with translucent materials as
a child, will have noticed that they look more translucent when held up to the light. When illuminated
from behind, a gemstone or slice of fruit is filled with a distinctive glow, which enhances the sense of
the object’s translucency.
An example of this effect is shown in Figure 27. A torus is illuminated from six different orientations
(three behind and three in front). Note that the apparent translucency of the torus changes depending on
the light direction. We studied this effect systematically, using a psychophysical translucency-matching
task.
3.1
Methods
Subjects were presented with images of two translucent tori simultaneously. On each trial, the image on
the left (the “Test” image) was selected by the computer, while the image on the right (the “Match”) could
be adjusted by the subject. The two objects were illuminated from different directions. The subject’s
task was to adjust the translucency of the match image until the torus appeared to be made out of the
same material as the test torus, despite differences in the illumination.
3.1.1 Subjects. Fifteen paid subjects performed the experiment. All were naive to the goals of the
research program and had normal or corrected-to-normal vision.
3.1.2 Stimuli. Stimuli were rendered using Dali, a photon mapping-based global illumination software package written by Henrik Wann Jensen, which includes an implementation of the BSSRDF
algorithm described in Jensen [2001] and Jensen and Buhler [2002]. The images were rendered and
tone-mapped beforehand and stored in image buffers for presentation during the experiment.
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The translucency of the test object was one of three different values, ranging from highly translucentlike jade to highly opaquelike a cue ball. Specifically, the absorption coefficient was held fixed at 0.1,
while the scattering coefficient was set to 2.00, 7.13, or 20.0. We tested the appearance of these three
objects under 12 different illumination directions around the object. The illumination consisted of a
single point light source whose position varied around a horizontal circle located somewhat above the
torus.
The illumination direction for the match object was held constant (above, back left). The subject could
adjust the apparent translucency through 128 different values, which spanned a range greater than
the three values used for the test objects. Specifically, the absorption coefficient was held fixed at 0.1
(i.e., the same as the test objects), while the subject adjusted the scattering coefficient through 128
steps from 0.4 to 60. The step sizes were nonlinear to create a more uniform perceptual scale. Subjects
readily agreed with the statement “when I move the mouse to the right, the torus appears to change
from being relatively translucent to relative opaque, while everything else about the scene appears to
stay the same.” Therefore, for subsequent discussion, we refer to this modified scattering coefficient
scale as “perceived opacity” (even though we have not calibrated it to ensure that it is a truly linear
scale). A number of analyses in the earlier sections of this paper were based on these match tori.
3.1.3 Procedure. Before the experiment, subjects were briefed with a series of slides that featured
example stimuli from the experiment. The subjects were tested to ensure that they understood the
relevant perceptual dimension of translucency. Our plan was to exclude any subjects that failed to rank
seven test stimuli in order of translucency; however, all subjects were able to do this with ease.
All test images were shown to the subjects twice in a randomly interleaved sequence. Subjects were
given unlimited time to adjust the match stimulus using the mouse and, once satisfied with the match,
could move onto the next trial in the sequence by pressing a button on the keyboard.
Before the main experiment, subjects were given practice trials consisting of the same three test
objects illuminated from nine different directions. During practice, subjects were asked to say out loud
a numerical rating of the perceived opacity on a scale from 1 to 7 before adjusting the mouse. No
feedback was given, the practice was simply intended to help subjects orient to the task.
3.2
Results
The mean data across all subjects is shown in Figure 28. The x-axis represents the position of the
light source, varying from behind the torus (<180◦ ), to in front (>180◦ ). The y-axis shows which match
stimulus was chosen by the subjects as appearing to be made of the same material as the test stimulus.
Note that if the observers were able to accurately estimate the intrinsic parameters of the BSSRDF,
irrespective of the illumination, the data would fall along the three horizontal lines. This is not the case.
Instead, perceived opacity undergoes a dramatic change when the lighting is altered. All three objects
appeared significantly more opaque when illuminated from the front than from behind. The effect is
most marked for the object of intermediate translucency.
Thus, for the conditions used in our experiment, the visual system seems poor at “discounting” the
effects of light source direction. Objects tend to appear more translucent when illuminated from behind.
It is interesting to contrast this with previous work on the perception of other material attributes. For
example, Fleming et al. [2003] found that the perception of gloss remains relatively stable across change
in illumination, as long as the pattern of illumination is realistic.
3.3
Discussion
Throughout this paper, we have argued that the visual system does not estimate translucency through
inverse optics. Instead, we believe that the visual system relies on simple image heuristics that correlate
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Fig. 28. Mean data across 15 subjects for the three test objects. Perceived opacity varies as a function of light source direction.
Angles less than 180◦ corresponding to lighting from behind the object, while angles greater than 180◦ are illuminated from the
front. Error bars represent standard error (SE).
with translucency. The fact that subjects were unable to correctly incorporate lighting changes into their
estimates of translucency is consistent with this proposal. It suggests that subjects use image cues that
are reliable when objects are illuminated from behind, but which somehow break down when objects
are illuminated from the front. However, we are left with the deeper question: which image cues do
subjects rely on? Can we find image measurements that vary with light source position in the same way
that perceived translucency does? This experiment allows us to test how well a number of image cues
can predict human performance. In the following section, we show the predictions made by a number of
different matching strategies. To anticipate, we find no single simple cue that can predict the qualitative
structure of the entire data set. However, a slightly more sophisticated approach, based on segmenting
the image into important regions, does somewhat better (although not perfectly).
3.3.1 Pixel-Wise Image Similarity. The simplest imaginable matching strategy would be to pick the
match image that is most similar to the test image on a pixel-by-pixel basis. We know a priori that
this would not be a good matching strategy because differences in the lighting will cause differences in
the position of shadows and highlights. Figure 29 shows the curves that would be obtained if subjects
matched by picking the match image that correlates most strongly with the presented test image.
Correlation places particular emphasis on the spatial position of image features, rather than their
absolute intensities.
It is clear from this graph that subjects certainly did not use pixel-wise correlation to perform the
task. The only aspect of the data that is successfully captured is the ordering from high to low opacity.
This leads to the following conclusion: rather than focusing on the spatial positions of image features,
subjects abstract something about the appearance of the pattern as a whole. This is consistent with our
suggestion that subjects represent the overall look of a translucent substance using summary statistics,
like those used to classify textures [Heeger and Bergen 1995; Portilla and Simoncelli 2000].
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Fig. 29. Predicted matching performance if subjects used pixel-wise intensity correlations to select a Match.
3.3.2 Summary Statistics of the Intensity Histogram. A more plausible strategy would be for
the subjects to match the brightness, contrast, and other higher-order properties of the intensity distribution. As discussed above, there are a number of simple intensity statistics that vary systematically
with translucency. Because these measures are (1) easy to estimate from the image and (2) correlate
with translucency, it seems plausible that subjects could use them as heuristic indicators of translucency. In other words, instead of performing a full-blown inverse optics computation, perhaps subjects
selected their matches simply by equating low-level intensity statistics (e.g., picking the match torus
that has the same mean intensity as the test torus).
If we believe that this is how subjects performed the task, the natural question is how intensity
statistics vary with changes in illumination direction. Can we use these variations to predict variations
in subjects’ performance?
In Section 2.6 (“Image contrast”), we considered four summary statistics: mean, variance, skew and
kurtosis. In Figure 30, we show how each of these statistics vary depending on the lighting direction.
Given that these intensity statistics do, indeed, vary as the illumination changes, it seems possible that
these might be the cues that subjects use to estimate opacity.
It is important to note, however, that these graphs are not direct predictions of matching performance.
They simply show how each statistic varies with lighting direction. In order to derive a quantitative
prediction, we must find which match stimulus has the corresponding value of the given statistic. The
resulting prediction curves are shown in Figure 31.
These prediction curves were generated as follows. We have three test tori with different degrees of
translucency. We progressively rotated the light around each torus in steps of 2◦ to create 180 images
of each torus, nine of which (per torus) were the test stimuli used in the experiment. For each image
we then searched the set of 128 match stimuli for the image whose mean, variance, skew, or kurtosis
was closest to the corresponding test image. This image was taken to be the predicted match.
Note that the graphs for mean, skew, and kurtosis contain two curves for each of the three test
conditions (one is always close to the bottom of the graph). This is because, as we saw in Figure 19, each
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Fig. 30. Variations in the intensity distribution as light source position changes. Red lines are the most opaque torus, while
pinker lines are progressively more translucent. Note that all four summary statistics undergo complex variations as we move
the light source.
of these statistics varies nonmonotonically as a function of the translucency of the match stimulus.
Thus, for example, if the test stimulus has a given mean intensity, there are actually two different
match stimuli with the corresponding mean; in other words, two predicted matches.
It is clear from these figures that these statistics are spectacularly poor predictors of subjects’ performance. None of the curves capture the basic qualitative features of the psychophysical data: The almost
uniform appearance of objects when illuminated from behind and the large increase in apparent opacity when illuminated from the front. This is especially important for the mean and variance statistics.
Mean intensity is closely related to perceived brightness and variance is closely related to perceived
contrast. It seems very unlikely that subjects matched the stimuli based solely on their percepts of
brightness or contrast.
We saw above that by modifying the intensity distribution we can navigate through a continuous
space of different translucent percepts. However, the results of this experiment show that this applies
only when the lighting is held constant. Changes in lighting direction alter the proportion of the object
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Fig. 31. Predicted matching performance based on each of the four intensity statistics (a) mean, (b) variance, (c) skew, and
(d) kurtosis. As in the original data plot, pink represents the least opaque test tori, while redder curves represent increasing
opacity. Again, the three dashed lines show the predictions of perfect “translucency constancy” (i.e., performance that is invariant
irrespective of the lighting).
that is in shadow. This has a substantial, but irrelevant, effect on the intensity distribution, introducing
an additional source of variability that has nothing to do with the intrinsic material properties of the
object.
3.3.3 Brightness of Shadowed Regions. We have seen that simple, low-level intensity statistics do
not successfully predict matching performance in isolation. However, these measures weigh all portions
of the image with equal importance. A more sophisticated analysis would take into account how much
information is carried by the various image regions. As discussed above, parts of the object that are
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Fig. 32. Predicted matching performance based on the mean intensity of the shadowed region.
pointing at a light source do not vary much with changes in the degree of translucency and, thus,
do not carry reliable information about the degree of translucency. Thus, subjects would do better to
attend to image regions that do not receive direct illumination (viz., the shadows). The subjects could
base their judgments of translucency on the light that glows out of the shadowed regions, having passed
through the object. This approach would require a more sophisticated segmentation of the image, which
includes an estimate of lighting variations. Thus, this strategy could be thought of as an intermediatelevel approach to translucency estimation, somewhere between simple low-level image statistics and
full-blown inverse optics.
In Figure 32, we plot the predictions if subjects used the mean intensity of the shadowed region to
select a match.
Although these prediction curves exhibit marked deviations from the psychophysical data, they do
nevertheless capture a few important qualitative features of the subject’s matches. First, note that the
prediction curves are approximately flat and close to the objective values when the light arrives from
behind (roughly 30◦ –150◦ ). This is mirrored in the psychophysical data. Second, the predicted match
rises in opacity for all three curves as the light source direction approaches 180◦ . This also occurs in
the subjects’ performance. Finally, the three prediction curves are closer together when the lighting is
in front than when it is behind. In other words, the brightness of the shadowed region predicts that
the three test stimuli should appear more similar to each other when illuminated from the front. This
is also manifested in our subjective experience of translucency (Figure 27) and in the psychophysical
matching data. Thus, although these prediction curves deviate substantially from the psychophysical
data, they are considerably more successful than the low-level image statistics we have considered
so far.
The predictions are worst for the front-lit conditions (180◦ –360◦ ). It is worth noting that the shadow
takes up only a relatively small proportion of the image under these conditions. In Figure 33, we plot
the proportion of the image that is in shadow as a function of light source direction.
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Fig. 33. Proportion of torus that is in shadow as a function of light source direction. Note that when the torus is illuminated
from in front (180◦ –360◦ ), only a small proportion is in shadow.
Only a small amount of shadow is present in the image when the test stimuli are lit from the front
and thus under these conditions, the shadow provides a weak, unreliable cue. It seems reasonable
that subjects may have relied more on the shadow region when it filled a greater proportion of image.
By contrast, when the shadow cue was weak, the subjects may have resorted to a different matching
strategy.
There is a deeper insight to be gained from this. When the tori are illuminated from the front, the
image simply does not change very much with changes in the degree of translucency. Stated another
way, the image information is not diagnostic: using the image information alone, there is little basis for
a visual system to distinguish between translucent and opaque objects. This provides a more general
explanation of why human translucency matching performance degrades when the objects are illuminated from the front. In the absence of image information to specify that a surface is translucent, the
visual system seems to assume that it is opaque.
To summarize, we have found that without parsing the image, simple intensity statistics are very
poor predictors of the perception of translucency across changes in illumination. However, if we assume
that the visual system is able to separate the image into regions that receive light directly from external sources, versus regions that receive light from within the object, then we can use simple image
measurements to predict matching performance. When the image does not contain these important
regions, the visual system has no image cues that the surface is translucent and, therefore, assumes
that the object is opaque.
This strategy requires an intermediate level of analysis—neither raw image statistics nor full-blown
inverse optics are used to estimate translucency. Instead, the image is segmented intelligently and
simple image measurements are derived from the resulting image regions. In spirit, this proposal is
very similar to some recent theories of lightness perception [Adelson 1999; Gilchrist et al. 1999], which
also argue for segmenting images into regions based on lighting conditions and then gathering simple
image measurements from those regions. We still do not understand how this segmentation could be
performed. One possibility is that local image statistics themselves may carry cues that facilitate this
segmentation. However, which statistics can provide this information remains to be discovered.
One final issue is worthy of consideration. In our examples, the intensity of the shadow region is
diagnostic of translucency because the only way that light can get to this region is by passing through
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object—there are no other sources of illumination. Thus, when the object is translucent, the shadow
region is bright, but when the object is perfectly opaque, this region is in complete darkness. However,
under more natural illumination conditions it is rare to encounter an ideal shadow, such as this, which
receives no light at all from extrinsic sources. In the real world, a patch of surface that is shadowed
from one light source, will generally nevertheless receive some light from other directions. Under such
circumstances, the intensity of the shadow regions will be less diagnostic of translucency, because the
intensity will vary less with changes in the degree of translucency. This makes the testable prediction
that under more diffuse illumination conditions, variations in perceived translucency should be smaller
than in the current experiment. Under more diffuse lighting, opaque objects should appear visually
“softer,” while translucent materials should not appear to glow as fiercely as they do under a spotlight.
This issue suggests itself as an excellent topic for future research.
4.
CONCLUSIONS
What makes materials such as wax, cheese or marble look translucent? Here we have used a combination
of psychophysics and image analysis to study some of the factors that influence perceived translucency.
In contrast to most previous work on semitransparent materials, our findings are based on a realistic
model of subsurface light transport [Jensen et al. 2001; Jensen and Buhler 2002], rather than on
Metelli’s episcotister model. We have found that the change of the generative model has profound
consequences for the visual cues that we can use to estimate translucency. Many of the factors that
were traditionally thought to be important for the perception of thin transparent filters are not required
for the perception of translucency in solid objects. These factors include: (1) X-junctions, (2) visibility
of the background through the transparent region, and (3) comparisons of contrast between the object
and its surround.
Indeed, we have found that it is possible to enjoy a vivid impression of translucency when the object of
interest is an isolated body suspended in a black void. On the other hand, realistic translucent objects
contain a wealth of hitherto ignored cues that the visual system could use to identify translucent
materials. We have argued in this paper that the physics of translucency is simply too complex for the
visual system to run the generative equations “in reverse” and estimate intrinsic physical parameters
via inverse optics. Instead, we have focused on an array of simple image cues and the information they
can supply about translucent materials.
To summarize our main findings, we will conclude with a few suggestions for artists and animators
who wish to render translucent materials.
Translucent objects look most realistic when they are glossy. Although highlights are not a direct
consequence of subsurface light scatter, nevertheless, most translucent materials that we commonly
encounter (e.g., fruit flesh, gemstones, and mucos), are somewhat glossy. Thus, the visual system “expects” translucent objects to have specular highlights. Glossiness also aids the perception of shape, by
recovering detail that is lost by the softening effects of subsurface scatter.
Color can be used to modify the subjective quality of a translucent substance. If we wish translucent
objects to look “glowing” and “warm,” color saturation should be positively correlated with intensity. By
contrast, if we wish them to look “icy” or “dilute,” the correlation should be negative.
Translucent objects should generally be lower contrast than their opaque counterparts under similar
lighting conditions. However, the relationship between translucent and opaque versions of an object
is generally nonlinear. Thus, to portray a translucent object realistically, it is not sufficient simply to
reduce an opaque object’s contrast (using Photoshop, for example). It is necessary to modify the entire
distribution of intensities. As a simple heuristic, objects can be made to look somewhat more opaque
by passing them through a sigmoidal nonlinearity, or more translucent by passing them through the
inverse, i.e., an “N-shaped” nonlinearity.
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Sharp cast shadows should be avoided as they make objects appear hard and opaque, while blur and
loss of detail gives translucent objects their characteristic soft appearance. However, as with contrast,
we cannot make an opaque object appear translucent simply by blurring out the details. Attention must
be paid to the global effects of light bleeding through the shadowed region of an object if we wish to
portray a translucent material. Haze around the shadow boundary and blurry fringes around sharp
corners can add a sense of diffusion and glow.
Translucency can also be exploited to indicate physical size. The thinner or smaller an object is, the
more light bleeds through, providing information about physical scale.
Finally, we have found that translucent objects appear more translucent when illuminated from
behind, rather than from the front. One consequence of this is that if we wish to enhance or emphasize
the apparent translucency of an object, we should organize the scene lighting so that the object is illuminated predominantly from behind. It is the light that has traveled all the way through a translucent
medium (rather than scattering back in the direction of the light source) that is responsible for the
material’s characteristic visual appearance.
ACKNOWLEDGMENTS
This research was supported by a fellowship to RWF from the Max Planck Society. The authors wish to
thank Henrik Wann Jensen for the invaluable opportunity to use Dali and the BSSRDF shader, without
which this research would not have been possible; as well as for collaboration on the earlier report of
these findings, which appeared as Fleming, Jensen and Bülthoff [2004].
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VON
Received November 2004; revised April 2005; accepted April 2005
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