Openings and closings with reconstruction criteria: a study of a class of lower and upper levelings

A study of a class of openings and closings is investigated using reconstruction criteria. The main goal in studying these transformations consists of eliminating some inconveniences of the morphological opening (closing) and the opening (closing) by reconstruction. The idea in building these new openings and closings comes from the notions of filters by reconstruction and levelings. In particular, concerning the notion of levelings, a study of a class of lower and upper levelings is carried out. The original work of levelings is due to Meyer, who proposes this notion and introduces some criteria to build the levelings in the general case (extended levelings and self-dual transformations). We see the criteria proposed by Meyer as reconstruction criteria during the reconstruction process from a marker image into the reference image. We show that new openings and closings are obtained, enabling intermediate results between the traditional opening (closing) and the opening (closing) by reconstruction. Some applications are studied to validate these transformations. © 2005 SPIE and IS&T. [DOI: 10.1117/1.1866149]