Image segmentation and filtering based on transformations with reconstruction criteria

In this paper, a class of transformations with reconstruction criteria, derived from the reconstruction transformations, is investigated. The idea to build these transformations consists in stopping the reconstruction process according to a size criterion. This class of transformations was initially proposed for obtaining intermediate results between the morphological opening and the opening by reconstruction. Here, the transformations are presented in the general case, as in the reconstruction transformations case, by imposing some conditions on the marker. We show that the set of markers for the transformations with reconstruction criteria is given by the set of dilated images. The interest of these transformations in image segmentation is shown, and in particular, the form of selecting the markers for segmenting images is described for binary images. Also, the use of the opening and closing with reconstruction criteria to build other morphological tools is illustrated to show the performance of these transformations. In particular, the notion of granulometry and the alternating sequential filters using openings and closings with reconstruction criteria are investigated.