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ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
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This paper generalizes the notion of symmetrical neighbourhoods, which have been used to define connectivity in the case of sets, to the wider framework of complete lattices having a sup-generating family. Two versions (weak and strong) of the notion of a symmetrical dilation are introduced, and they are applied to the generation of "connected components" from the so-called "geodesic dilations". It turns out that any "climbing" "weakly symmetrical" extensive dilation induces a "geodesic" connectivity. When the lattice is the one of subsets of a metric space, the connectivities which are obtained in this way may coincide with the usual ones under some conditions, which are clarified. The abstract theory can be applied to grey-level and colour images, without any assumption of translation-invariance of operators.