Abstract : The extension of mathematical morphology to multivalued images is an important issue. This is particularly true in the context of connected operators based on morphological hierarchies, which aim to provide efficient image filtering and segmentation tools in various application fields, e.g.(bio)medical imaging, remote sensing, or astronomy. In this article, we propose a preliminary study that describes how two notions recently introduced for connected filtering, namely component-graphs (that extend component-trees from a spectral point of view) and shaping (that extend component-trees from a conceptual point of view) can be associated for the effective processing of multivalued images. Structural, algo-rithmic and experimental developments are proposed. This study opens the way to new paradigms for connected filtering based on hierarchies.