A new paradigm for the architecture of morphological machines: binary decision diagrams

A central paradigm in mathematical morphology (MM) is the representation of set operators in terms of erosions, intersection, union, complementation and composition. The hardware or software that implements this decomposition structure is called a morphological machine (MMach). The architecture of all known MMachs has as central characteristic: a small kernel with very fast procedures. Another well-known decomposition result in MM is the representation of W-operators (i.e. translation-invariant and locally defined) as an union of sup-generating (i.e. hit-or-miss) operators. In particular, erosion is a sup-generating operator. A remarkable property of this decomposition structure is that it can be represented efficiently by a binary decision diagram (BDD). In this paper, we propose a new architecture for a MMach that is based on BDDs and we compare it with the conventional architecture