Abstract
In this paper the relationship of hyperconnected filters with path openings and attribute-space connected filters is studied. Using a recently developed axiomatic framework based on hyperconnectivity operators, which are the hyperconnected equivalents of connectivity openings, it is shown that path openings are a special case of hyperconnected area openings. The new axiomatics also yield insight into the relationship between hyperconnectivity and attribute-space connectivity. It is shown any hyperconnectivity is an attribute-space connectivity, but that the reverse is not true.
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Wilkinson, M.H.F. (2009). Hyperconnectivity, Attribute-Space Connectivity and Path Openings: Theoretical Relationships. 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_5
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DOI: https://doi.org/10.1007/978-3-642-03613-2_5
Publisher Name: Springer, Berlin, Heidelberg
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