The description of the relation between the one-parameter subgroups of a group and the differential operators in the Lie-algebra of the group is one of the major topics in Lie-theory. In this paper, we use this framework to derive a partial differential equation which describes the relation between the time-change of the spectral characteristics of the illumination source and the change of the color pixels in an image. In the first part of the paper, we introduce and justify the usage of conical coordinate systems in color space. In the second part we derive the differential equation describing the illumination change and in the last part we illustrate the algorithm with some simulation examples.