Mathematical morphology, initially devoted to binary and grey-level image processing, also offers opportunities to develop efficient tools for multivalued – and in particular, colour – images. In this context, connected operators are increasingly considered as a relevant way to obtain such tools, mainly for image filtering and segmentation purposes. In this article, we focus on connected operators based on component-trees and their extension to multivalued images, namely component-graphs. Beyond the classical colour-handling strategies, we show how component-graphs can be algorithmically used to efficiently handle the whole structural information gathered by colour spaces, in order to finally design original image filtering tools.