Abstract

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 $XYZ$s that would be possible under illuminant A.

© 2005 Optical Society of America

On calculating metamer sets for spectrally tunable LED illuminators

Graham Finlayson, Michal Mackiewicz, Anya Hurlbert, Bradley Pearce, and Stuart Crichton
J. Opt. Soc. Am. A 31(7) 1577-1587 (2014)

Metamer sets without spectral calibration

Ali Alsam and Graham Finlayson
J. Opt. Soc. Am. A 24(9) 2505-2512 (2007)

Metamer-set-based approach to estimating surface reflectance from camera RGB

Peter Morovic and Graham D. Finlayson
J. Opt. Soc. Am. A 23(8) 1814-1822 (2006)

Metamer mismatching in practice versus theory

Xiandou Zhang, Brian Funt, and Hamidreza Mirzaei
J. Opt. Soc. Am. A 33(3) A238-A247 (2016)

Spherical sampling methods for the calculation of metamer mismatch volumes

Michal Mackiewicz, Hans Jakob Rivertz, and Graham Finlayson
J. Opt. Soc. Am. A 36(1) 96-104 (2019)