Shape-Based Analysis on Component-Graphs for Multivalued Image Processing

Connected morphological operators based on hierarchical image models have been increasingly considered to provide efficient image segmentation and filtering tools in various application fields, e.g. (bio)medical imaging, astronomy or satellite imaging. Among hierarchical image models, component-trees represent the structure of grey-level images by considering their nested binary level-sets obtained from successive thresholds. Recently, a new notion of component-graph was introduced to extend the component-tree to model any grey-level or multivalued images. The notion of shaping was also recently introduced as a way to improve the anti-extensive filtering of grey-level images by considering a two-layer component-tree for grey-level image processing. In this article, we study how component-graphs (that extend the component-tree from a spectral point of view) and shapings (that extends the component-tree from a conceptual point of view) can be associated for the effective processing of multivalued images. We provide structural and algorithmic developments. The relevance and usefulness of such association are illustrated by applicative examples. This study opens the way to new paradigms for connected filtering based on hierarchies.