Recent works with colour spaces in digital imagen processing are related to colour image segmentation, texture analysis, image morphology, colour image standardization, and object localization. Non-linear systems are frequently present in non-traditional colour spaces (Hering Space) since they help to enhance some specific image characteristics. The present work is related with the study and application of two colour theories: Opponent Colours and Tricromaticity (RGB) as tridimensional representations, using linear and non-linear transformations among these colour spaces. In addition, this paper presents two numeric solutions to solve the implicit non-linear equation system. Due to the positive results obtained with the proposed algorithms, they were implemented to develop a computerized license plate identification system with the introduction of illumination effects.