The Kubelka-Munk theory for color image invariant properties

A fundamental problem in color image processing is the integration of the physical laws of light reflection into image processing results, the problem known as photometric invariance. The derivation of object properties from color images yields the extraction of geometric and photometric invariants from color images. Photometric invariance is to be derived from the physics of reflection. In this paper, we rehearse the results from radiative transfer theory to model the reflection and transmission of light in colored layers. We concentrate on the Kubelka-Munk theory for colored layers, which is posed as a general model for color image formation. The model is used for decades in the painting and printing industrie, and is proven to be valid for a wide range of materials. We relate the Kubelka-Munk theory to photometric models currently used in image processing. As a consequence, the wide range of materials for which Kubelka-Munk is proven valid may be inherited to algorithms based on newer models. Furthermore, photometric invariant properties proven for one model are, by using Kubelka-Munk, easily extended to related models.