Calculating Metamer Sets without Spectral Calibration

The set of metamers for a given device response can be calculated given the device’s spectral sensitivities. Knowledge of the metamer set has been useful in practical applications such as colour correction and reflectance recovery; and also in furthering our understanding of aspects of colour science such as the tendency of metamers to cross at certain preferred wavelengths. Unfortunately, the device sensitivities of a camera or scanner are not known and they are difficult to estimate reliably outside the lab. The main contribution of this paper is to show how metamer sets can be calculated when a device’s spectral sensitivities are not known. The result is built on two observations: first, the set of all reflectance spectra are convex combinations of certain basic colours which tend to be very bright (or dark) and have high chroma. Second, the convex combinations which describe reflectance spectra result in convex combinations of RGBs. Thus, given an rgb it is possible to find the set of convex combination of the RGBs of the basic colours which generate the same rgb. The corresponding set of convex combinations of the basic spectra is precisely the metamers set