Lie Methods in Color Signal Processing: Illumination Effects

In this paper we describe illumination changes with the help of elements in the Lorentz group SU(1,1). We show how Lie-theoretical methods can be applied to solve problems related to illumination changes. We derive partial differential equations that describe the changes in the space of color signals. We show how these changes effect the induced variations in the space of RGB vectors. We illustrate the application of these methods with two examples: In the first example we derive a simple linear equation system that links the pointwise pixel changes to the parameters of the illumination change. In the second example we construct operators in the RGB space that either compensate illumination changes or predict the effects of illumination changes