Compact representation of W-operators
Júnior Barrera, Ronaldo F. Hashimoto · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
It is well known that the family of hit-miss operators constitutes a sup-generating family for W-operators, that is, any W-operator can be represented as the supremum of hit-miss operators. We present here a new sup-generating family for W- operators: compositions of hit-miss operators with dilations. The representation based on this sup-generating family is called compact, since it may use less sup-generating operators than the hit-miss representation. Considering the W-operators that are both anti-extensive and idempotent (in a strict sense), we have also gotten a simplification of the compact representation. Furthermore, adding the hypothesis of increasingness, we have shown that the simplified compact representation reduces to a minimal realization of the classical representation of Matheron for translation invariant openings.