Soft color morphology

Morphological operators have been used extensively when dealing with binary or grayscale images, but there is no general-purpose approach for multivariate images that meets the expectactions of practitioners under diferent circumstances. Although several approaches have been proposed, state-of-the-art applications tend to process channels independently, obviating interchannel correlation. In this work, we introduce a new definition of erosion and dilation that can handle images with any number of channels, study their theoretical properties and analyse its behaviour. It is based on the Fuzzy Mathematical Morphology, from which it inherits essential theoretical properties. Our operators consider the first channel to evaluate a pixel's importance, but handles all channels to generate coherent outputs. It successfully processes natural images in the L*a*b* space and can also avoid the creation of new chromatic values, specially important for hyperspectral imagery. We provide, thus, a general and well-founded framework to process color images with morphological operators.