Illumination Invariants

In this paper we show how tools from group theory can be used to find invariants for time-changing illumination changes. In the first part of the paper we give a brief overview over the theory of one-parameter groups and their invariants. In the second part we describe how the chromaticity coordinates of time-changing illumination spectra can be described by one-parameter curves. Examples for black-body radiators and measured illumination changes are presented. In the last section we describe the invariants for several selected one-parameter groups and the blackbody radiators. The derivation of the differential equations and their solution can be done with the help of symbolic mathematical software packages like Maple and we describe a simple Maple session in which the invariants are constructed.