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of filters, a metamer pair is defined by two spectra with a color difference ΔE < 2.325. Condition 2: With the use of binocular filters, such as those in Fig. 2b, a metamer pair is defined by two spectra with a monocular color difference ΔE < 2.3 in each eye. That is, a pair of spectra is a metamer if and only if it is a metamer in each eye individually. We do not consider the possibility of other perceptual effects such as binocular rivalry or dichoptic color mixing. Our first metric uses a Monte Carlo simulation to probe the effect binocular filters have on the perception of pairs of spectra, given the conditions above (Fig. 4). To start, a pair of reflectance spectra is generated by stochastically sampling intensity values from a uniform distribution at regularly spaced intervals within the visible wavelength range. Particularly, samples were taken uniformly at points: 𝜆1, 𝜆2...𝜆𝑁𝑠−1, 𝜆𝑁𝑠 , where 𝑁𝑠 is the total number of sampling points. The sharpness of the reflectance spectra was adjusted by changing 𝑁𝑠 , with larger numbers leading to sharper features, and were interpolated at 10 nm intervals using a cubic spline to create smooth spectra. We assumed illuminant D65, and then filtered the reflected spectra by the filter transmission responses given in Fig. 2b. ΔE color differences were calculated between the pairs of spectra for the unfiltered case, and through Filter 1 and Filter 2. The method was performed for various number of iterations (𝑁𝑖), which varied from 1,000 to 20,000,000, and the number of unfiltered (𝑀𝑢) and filtered (𝑀𝑓) metamers were recorded for each trial. We then defined a metric that represents the decrease in metamer frequency upon filtering: 𝑃 = 𝑀𝑢 𝑚 𝑀 𝑓 Forexample,𝑃 =2representsatwo-folddecreaseinthenumberofmetamersusingthetwofilters. 𝑚 The results from this simulation, for several sampling values (𝑁𝑠 ) and iteration numbers (𝑁𝑖 ), are given in Fig. S5 of the Supplementary Information. Given the simulation conditions, the filters in this work result in up to a ~15× decrease in the number of metamers for randomly generated spectra; this effect appears to be greatest for moderately sharp spectral features (𝑁𝑠 = 15), and drops off for very broad or very sharp 10PDF Image | Enhancing color vision by breaking binocular redundancy
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