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As further verification of the apparent decrease in metamer frequency, we also developed a more- abstract mathematical method (See Supplementary Information for a complete description of this calculation, abridged here for clarity). Rather than comparing stochastically generated spectra, as above, this method aims to calculate the overall number of spectra that map to perceptually indistinguishable tristimulus values (ΞE < 2.3). For a given reference point in LAB space, [Lo, ao, bo], the number of metamers (with respect to the reference point) was determined by counting the spectra, πΌ(π), that map to LAB coordinates within a sphere of radius 2.3 around the reference point. We determined the number of metamers by calculating the volume of spectra, represented by an ellipsoid in π-dimensional space, where π is the number of discrete wavelength bins that define a spectrum. However, calculating the exact volume of high dimensional ellipsoids in this case is difficult; instead, we calculate the volume of the max-inscribed ellipsoid subject to box constraints, which represents an upper-bound of the true value and is more computationally efficient31 (see Supplementary Information for more details). The volume of this ellipsoid represents the number of metamers, for a given reference point, for the unfiltered case (π ). For the filtered π’ case, the union of two ellipsoids, corresponding to each filter individually, represents the number of metamers (π ); this is equivalent to Condition 2 above, where we assume that monocular metamerism must be present in both eyes simultaneously to yield indistinguishable color percepts in the filtered case. Thus, the overall decrease in metamer frequency is given by: π π’ π π WhereπΉ =2,asanexample,representsatwo-folddecreaseinmetamerfrequency.Thisprocess π was repeated for 500 LAB reference points from randomly generated spectra to adequately sample the color space. The number of wavelength samples (π ) was also varied to again explore the effect of spectral sharpness; as in the Monte-Carlo simulation, the decrease in metamer frequency occurs around 12 β 16 bins. Using this metric, we estimate a decrease in metamer frequency by one-to-two orders of magnitude π πΉ= π π 12PDF Image | Enhancing color vision by breaking binocular redundancy
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