Abstract
In this paper the notion of hyperconnectivity, which is an extension of connectivity is explored in the lattice theoretical framework. It is shown that a fourth axiom is needed when moving from connections to hyperconnections, in order to define hyperconnected components meaningfully, which is important for the definition of, e.g., viscous levellings. New hyperconnectivity openings, which are the hyperconnected equivalents of connectivity openings are then defined. It then shown that all algebraic openings which are translation and grey-scale invariant can be described as hyperconnected attribute filters. This means that hyperconnectivity lies at the heart of a vast range of morphological filters.
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Wilkinson, M.H.F. (2011). Hyperconnections and Openings on Complete Lattices. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds) Mathematical Morphology and Its Applications to Image and Signal Processing. ISMM 2011. Lecture Notes in Computer Science, vol 6671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21569-8_7
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DOI: https://doi.org/10.1007/978-3-642-21569-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21568-1
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