On decomposition of structure element for mathematical morphology

The 1-D decomposition of a 2-D structure element has been solved. For the 2-D structures which have comparatively regular shapes or small sizes, especially for the convex sets, their PP (point pair) decompositions can be obtained by using the methods presented. For most structure elements used in practice, their best PP decompositions have been resolved. The discussions presented are based on a general lattice. Both square and hexagon lattices are therefore covered