Abstract
Almost everything that we think we know about the perception of transparent materials is
derived from Metelli’s “episcotister model”, or some subtle variant thereof. An opaque disk
with a missing wedge is rotated at high-speed (above the flicker-fusion threshold), so that its
colour mixes linearly with that of the background. And indeed, we have learnt an immense
amount about mid-level vision using this model: it applies well to shadows, specularities,
stains, black smoke, gauzes, infinitely thin neutral density filters, or any system that generates
the linear superposition of two images. However, ironically, it is hopeless as a model of real
chunks of transparent stuff, such as ice cubes, quartz crystals, or even a common glass of water.
Most real transparent things (i) have non-zero volume, (ii) obey Fresnel’s equations (and thus
exhibit specular reflection and refraction), and consequently (iii) can elicit the vivid impression
of transparency without containing any of the cues traditionally thought to be important (e.g.
X-junctions or reduction of contrast in the transparent region).
Here we report the results of several experiments on the perception of refractive index
using physically-based computer simulations of light transport through refractive dielectrics.
The first experiments use maximum likelihood difference scaling (MLDS) to measure the perceptual
scale of refractive index. We find that the scale is positively bowed for all subjects,
which means that smaller refractive indices appear more different from one another than larger
refractive indices. The shape of the function is not well predicted by simple measures of imagedifferences.
One of the more obvious potential cues is the pattern of distortions created by refraction of
the background through a transparent object. We provide a theoretical analysis of this cue, and
derive a measure of the pattern of distortions that the visual system could plausibly perform,
called the ‘distortion field’. The distortion field, D = div(d), where d is the field of vectors measuring
the spatial displacement of features caused by refraction through the object. Although
the distortion field varies systematically with refractive index, it is also affected by the object
shape, the distance to the background, and the distance to the viewer, so it is an ambiguous cue.
In a set of matching experiments, we find that observers make large systematic errors in the
estimation of refractive index when these irrelevant scene factors are varied, suggesting that
subjects are unable to overcome this ambiguity.
