Bounds on filters by reconstruction

This paper treats the problem of establishing bounds for the morphological filter by reconstruction class. Morphological filters by reconstruction, which are composed of openings and closings by reconstruction, are useful filters for image processing because they do not introduce discontinuities. The main contributions of this paper are: (a) to establish when the combination of openings by reconstruction is an opening by reconstruction (similarly for closing by reconstruction), and (b) to establish, for any filter by reconstruction, upper and lower bounds that are respectively a closing by reconstruction and an opening by reconstruction