Abstract
We study some basic morphological operators acting on the lattice of all subgraphs of a (non-weighted) graph \(\mathbb{G}\). To this end, we consider two dual adjunctions between the edge set and the vertex set of \(\mathbb{G}\). This allows us (i) to recover the classical notion of a dilation/erosion of a subset of the vertices of \(\mathbb{G}\) and (ii) to extend it to subgraphs of \(\mathbb{G}\). Afterward, we propose several new erosions, dilations, granulometries and alternate filters acting (i) on the subsets of the edge and vertex set of \(\mathbb{G}\) and (ii) on the subgraphs of \(\mathbb{G}\).
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Cousty, J., Najman, L., Serra, J. (2009). Some Morphological Operators in Graph Spaces. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds) Mathematical Morphology and Its Application to Signal and Image Processing. ISMM 2009. Lecture Notes in Computer Science, vol 5720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03613-2_14
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DOI: https://doi.org/10.1007/978-3-642-03613-2_14
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