Abstract: Component-trees are classical tree structures for grey-level image modelling. Component graphs are defined as a generalization of component trees to images taking their values in any (totally or partially) ordered sets. Similarly to component-trees, component-graphs are a lossless image model; then, they can allow for the development of various image processing approaches. However, component-graphs are not trees, but directed acyclic graphs. This makes their construction non-trivial, leading to non-linear time cost and resulting in non-linear space data structures. In this theoretical article, we discuss the notion(s) of component-graph, and we propose a strategy for their efficient building and representation, which are necessary conditions for further involving them in image processing approaches.

Keywords: Component-graph, algorithmics , mathematical morphology, multivalued images

Reference: Nicolas Passat, Benoît Naegel, Camille Kurtz. Component-graph construction. Journal of Mathematical Imaging and Vision, 2019.

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