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If the spectrum is filtered through a filter 𝑇(𝜆), the map 𝑔 must be replaced by a map 𝑔𝑇 that accounts for the filter 𝑇. The derivation is otherwise identical; metameric spectra are given by the set 𝑔𝑇−1(𝑆0) ∩ 𝐶0. If the spectrum is filtered through 𝑇1(𝜆) for one eye and 𝑇2(𝜆) for the other eye, spectra are only counted if they are metameric for both eyes. This results in the set 𝑔−1(𝑆 ) ∩ 𝑔−1(𝑆 ) ∩ 𝐶 . We can compare configurations (e.g. natural human vision versus vision augmented by our device, or vision augmented by two different filters sets) by comparing the volumes of their respective metameric spectra. For example, to compare the unfiltered case (natural human vision) to the case of vision modified by our two-filter passive multispectral device, we would compute the ratio: 𝜌 = Vol(𝑔−1(𝑆0) ∩ 𝐶0) Vol(𝑔−1(𝑆 )∩𝑔−1(𝑆 )∩𝐶 ) 𝑇1 0 𝑇2 0 0 A ratio of 𝜌 = 20 would signify that metameric spectra are 20 times less abundant when the two-filter passive multispectral device is used as compared to the unfiltered case. Specifically, if spectra are sampled from a uniform distribution on intensities, a spectrum is 20 times less likely to be metameric. Computing the ratio 𝜌 is challenging because the volumes involved have irregular shapes; they are intersections of degenerate (high-dimensional) ellipsoids with box constraints. In order to approximate the ratio 𝜌, we approximate each volume by the volume of its max-volume inscribed ellipsoid. An illustration of a max-volume inscribed ellipsoid is shown below (Fig. S4). 𝑇1 0 𝑇2 0 0 Figure S4: The shaded region is the intersection of ellipsoids and box constraints. The area is approximated by the max-area inscribed ellipsoid (dotted curve). 6PDF Image | Enhancing color vision by breaking binocular redundancy
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