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Refractive Index and Perceived Transparency


Fleming,  RW
Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Fleming, R. (2007). Refractive Index and Perceived Transparency. Poster presented at 10th Tübinger Wahrnehmungskonferenz (TWK 2007), Tübingen, Germany.

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.