THEORETICAL ASPECTS OF MORPHOLOGICAL FILTERS BY RECONSTRUCTION

This paper investigates morphological connected filters and, in partic ular, the so-called filters by reconstruction. A brief background is o ffered on the theory of morphological filtering. Then, the concept of connectivity is introduced within the morphological framework, which m akes it possible to establish connected filters as those that do not i ntroduce discontinuities or, in other words, that extend the input ima ge flat zones. An important subset of connected filters is the class o f filters by reconstruction, which allows to build connected filters t hat treat both the peaks and valleys of an input image while possessin g a robustness property called the strong-property. The focus of our r esearch is on the combination, by means of the sup- and inf-operations , of alternating filters by reconstruction when their component filter s belong to a granulometry and an antigranulometry (by reconstruction) . These operators will be investigated by means of the study of their grain and pore properties. Some commutation properties are introduced that facilitate the manipulation of filters by reconstruction. An impo rtant theoretical result of this paper is the establishment of a new f amily of strong morphological filters. Although most theoretical expre ssions refer to set operators, results are automatically extendable fo r non-binary (gray-level) functions.