| Summary: | Connected operators based on hierarchical image models have been increasingly considered for the design of efficient image segmentation and filtering tools in various application fields. 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 any grey-level or multivalued images. The notion of shaping was also introduced as a way to improve the anti-extensive filtering 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 extend 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. Although the contributions of this article are theoretical and methodological, we also provide two illustration examples that qualitatively emphasize the potential use and usefulness of the proposed paradigms for image analysis purposes.
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