In recent papers, a new notion of component-graph was introduced. It extends the classical notion of component-tree initially proposed in mathematical morphology to model the structure of gray-level images. Component-graphs can indeed model the structure of any—gray-level or multivalued—images. We now extend the antiextensive filtering scheme based on component-trees, to make it tractable in the framework of component-graphs. More precisely, we provide solutions for building a component-graph, reducing it based on selection criteria, and reconstructing a filtered image from a reduced component-graph. In this paper, we first consider the cases where component-graphs still have a tree structure; they are then called multivalued component-trees. The relevance and usefulness of such multivalued component-trees are illustrated by applicative examples on hierarchically classified remote sensing images.