The "False Colour" Problem

The emergence of new data in multidimensional function lattices is studied. A typical example is the apparition of false colours when (R,G,B) images are processed. Two lattice models are specially analysed. Firstly, one considers a mixture of total and marginal orderings where the variations of some components are governed by other ones. This constraint yields the “pilot lattices”. The second model is a cylindrical polar representation in n dimensions. In this model, data that are distributed on the unit sphere of n − 1 dimensions need to be ordered. The proposed orders, and lattices are specific to each image. They are obtained from Voronoi tesselation of the unit sphere The case of four dimensions is treated in detail and illustrated.