Constructing multiscale connectivities

In a recent paper, we have proposed a novel theory that extends connectivity to a multiscale framework. Although we have presented several examples, we have not provided a systematic approach for constructing multiscale connectivities. In this paper, we introduce three general techniques for constructing multiscale connectivities. The first two start from a given base connectivity and produce multiscale connectivities by applying pyramids of clusterings or granulometries. The third technique starts from a given multiscale connectivity and constructs a new one by means of a clustering or an opening. Several examples illustrate the utility of the proposed techniques for constructing multiscale connectivities.