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Monte Carlo Simulation Reflectance spectra were calculated by generating random values at a defined number of sampling numbers (ππ ) within the visible wavelengths (400 β 720 nm) using Matlabβs rand function; ππ was varied between 4-35 points to define the sharpness of spectral features, and the spectra were interpolated using a cubic spline. CIE 1931 2Β° matching functions were used to calculate tristumlus values for illuminant D65 reflected from the objects. Illuminant D65 was used as the white-point for conversion to the CIELAB space. A threshold of ΞπΈ < 2.3 was used to define indistinguishable tristimulus values25. The simulation was performed for several number of iterations (ππ ), from 1,000-20,000,000, to determine if the defined metric π converged for a given π . For π greater than 1,000,000 values for π converged to values within ππ ππ ~20% of each other within a given ππ . More-abstract calculation of metamer frequency The volume approximation ratios were computed using CVX, a package for specifying and solving convex programs37. Reference points [πΏ0, π0, π0] were chosen by uniformly sampling discretized spectra and mapping them to LAB tristimulus values. The computation was performed for various wavelength binning values (ππ), between 7-18, to vary the broadness/sharpness of spectra, and 500 reference points were computed for each binning value. A detailed summary of this calculation, including a formalized mathematical treatment, can be found in the Supplementary information. 17PDF Image | Enhancing color vision by breaking binocular redundancy
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