Topology-preserving ordering of the RGB space with an evolutionary algorithm

Mathematical morphology (MM) is broadly used in image processing. MM operators require to establish an order between the values of a set of pixels. This is why MM is basically used with binary and grayscale images. Many works have been focused on extending MM to colour images by mapping a multi-dimensional colour space onto a linear ordered space. However, most of them are not validated in terms of topology preservation but in terms of the results once MM operations are applied. This work presents an evolutionary method to obtain total- and P-orderings of a colour space, i.e. RGB, maximising topology preservation. This approach can be used to order a whole colour space as well as to get a specific ordering for the subset of colours appearing in a particular image. These alternatives improve the results obtained with the orderings usually employed, in both topology preservation and noise reduction.