Metamer sets

If two different surfaces look the same when viewed under a particular light source, then they are called metamers. We show mathematically how one can solve for the whole set of physically realizable natural surface reflectances that relate to the same tristimulus, the metamer set. Our analysis is based on very general linear models of reflectances, coupled with constraints that reflectances should adhere to (e.g., positivity and boundedness). We show that we can recover metamer sets for linear models of an arbitrary high dimension. To illustrate our new algorithm, we provide an example of calculating the metamer set and its manifestation as a mismatch region. Given a single XYZ observed under illuminant D65, we can examine the set of XYZs that would be possible under illuminant A.