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Karin Petrini, Alexander Logvinenko; Multidimensional scaling (MDS) analysis of achromatic transparency. Journal of Vision 2006;6(6):394. doi: https://doi.org/10.1167/6.6.394.
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As an object is always viewed through some media (atmosphere), the intensity of light coming to the eye (L) is affected by both the object reflectance (r), and the media transmittance (t): L= Itr+a. Here I is the incident light intensity; and a is the scattered light intensity.
A perceptual correlate of r is the object's lightness. A perceptual correlate of t is the apparent clearness (transmittance) of the media, a being experienced as “fogginess” of the media. The latter make up two perceptual dimensions of the media. When they are present in perception, achromatic transparency is said to be perceived.
Yet, Robilotto, Khang & Zaidi (2002) claimed that achromatic transparency was one-dimensional. This is in line with the classical study by Metelli who used only two dimensions (lightness and strength of transparency) to describe a percept with achromatic transparency. Since lightness is a perceptual attribute of object rather than media, we conclude that achromatic transparency in Metelli's model was also one-dimensional.
We used nine Adelson's tile patterns to produce an impression of achromatic transparency. The patterns simulated four different transmittances (t) and two levels of a. Pairs of the patterns were presented to five observers with an instruction to assign a rate of dissimilarity between the achromatic transparencies by a number on a 30 point-scale. The output configuration from the non-metric MDS was clearly two-dimensional, confirming the two-dimensionality of the achromatic transparency. One dimension correlated with t, the other one with a.
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