Quantization of color spaces and processing of color images by fibonacci lattices

Methods for processing gray scale images cannot be simply extended to color images because they rely on the fact that each gray level is described by a single number and the fact that a relation of full order can be easily established on the set of those numbers. Color spaces (such as RGB or Lab) are on the other hand three dimensional. To make them more amenable to the type of processing used for one-dimensional gray level pictures, we propose a particular space sampling and numbering of sampled points. The sampling scheme provides a uniform quantization of the Euclidean Lab space, and a way to establish a partial order relation on the set of points. The idea is based on several results from number theory and phyllotaxy. We illustrate possible processing of color images by first introducing the basic average and difference operations and then implementing edge detection and compression of color quantized images.