Multiresolution connectivity: An axiomatic approach

In this paper, we introduce all axiomatic framework for the notion of multiresolution connectivity on complete lattices. This framework extends the notion of connectivity classes, introduced by Serra in the late eighties. We introduce multiresolution connectivities by means of two equivalent notions: connectivity measures and connectivity pyramids. Wie present examples of multiresolution connectivities based on pyramids of dilations and of morphological sampling operators. We study the application of multiresolution connectivity to various image analysis tasks, such as pyramid decompositions, hierarchical segmentations, and multiresolution features.