On morphological openings and closings of signals in shaped noise

We have shown previously that morphological openings and closings can be viewed as consistent MAP estimators of morphologically smooth binary image signals immersed in i.i.d. union (clutter) noise, or suffering from i.i.d. random dropouts. We revisit this viewpoint under a different set of assumptions, which allows the explicit incorporation of geometric and morphological constraints into the noise model, i.e., the noise may now exhibit a geometric structure; surprisingly, it turns out that this affects neither the optimality nor the consistency of these filters