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It turns out the max-volume inscribed ellipsoid can be efficiently computed using semidefinite programming techniques. See for example [S2]. We approximated the ratio 𝜌 by using the inner ellipsoid approximation for both the numerator and denominator. Volume approximation ratios were computed using CVX, a package for specifying and solving convex programs [S3]. We computed approximate volume ratios for the two-filter case as well as the one-filter case, using the transmission spectrum of a filter sold by EnChroma for alleviating some of the adverse effects of red-green color vision deficiency (EnChroma filter [S4]). In each case, we tried several different discretization points 𝑁𝑆 and we repeated the computation for 500 different reference points [𝐿0,𝑎0,𝑏0]. The reference points were selected by choosing discretized spectra at random, with reflectance values sampled from a uniform distribution between 0 and 1 (i.e., 𝑁𝑆 randomly sampled values per spectrum), and mapping them to LAB tristimulus values. A summary of the results is shown in Table S1. Using two filters results in a dramatic decrease in metamers, roughly consistent over the range of tested discretizations. In contrast, using a single filter (EnChroma in this case) has little effect on the number of metamers. Discretization points (𝑁 ) 𝑆 Two filters, mean Two filters, median EnChroma, mean EnChroma, median 7 22.977 17.251 0.945 0.945 9 115.823 80.690 0.887 0.870 12 120.580 57.4080 1.090 1.082 14 160.634 85.885 0.944 0.944 16 178.020 77.153 1.125 0.924 18 111.243 41.369 1.086 1.017 Table S1 – Results of the metamer ratio approximation. Mean and median 𝜌 values are 500 randomly generated spectra for each discretization. Using two filters reduces the frequency of metamers by a factor of about 50 on average, while using a single EnChroma filter has a negligible effect on the frequency of metamers 7 computed overPDF Image | Enhancing color vision by breaking binocular redundancy
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