Toward a new axiomatic for hyper-connections

Benjamin Perret (1) , Sébastien Lefèvre (2) , Christophe Collet (1)

1 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection
2 VALORIA - Laboratoire de Recherche en Informatique et ses Applications de Vannes et Lorient

We propose an evolution of the hyper-connection axiomatic in order to improve the consistency of hyper-connected filters and to simplify their design. Our idea relies on the principle that the decomposition of an image into h-components must be necessary and sufficient. We propose a set of three equivalent axioms to achieve this goal. We show that an existing h-connection already fulfills these axioms and we propose a new h-connection based on flat functions that also fulfills these axioms. Finally we show that these new axioms bring several new interesting properties that simplify the use of h-connections and guarantee the consistency of h-connected filters as they ensure that: 1) every deletion of image components will effectively modify the filtered image 2) a deleted component can not reappear in the filtered image.

Domaines: Traitement des images [eess.IV]

Benjamin Perret, Sébastien Lefèvre, Christophe Collet. Toward a new axiomatic for hyper-connections. International Symposium on Mathematical Morphology (ISMM), 2011, Intra, Italy. pp.85-95. ⟨hal-00663811⟩