In Mathematical Morphology, the reconstruction of images from markers has proven to be useful in morphological filtering and image segmentation. This work investigates the utilization of a criterion in the reconstruction process, whose utilization in the problem of the image reconstruction from an image marker has been partially treated elsewhere. This work further investigates this idea and extends it to the problem of image reconstruction from labelled markers. In the binary case, this allows us to compute the modified influence zones associated to the set of labelled markers. A significant difference with the usual case (i.e., the ”normal” influence zones) is that we generally do not obtain a whole partition of the space, because the criterion added to the reconstruction process causes that some points or pixels are not recovered. In addition, in this paper we consider the gray-level case, and we use the reconstruction with criterion to separate regions from a non-binary input image. This input image is considered as a topographic relief (similarly as in a normal watershed); however, the flooding mechanism is modified by the reconstruction criterion. The benefit is that we can control to some extent how the flooding proceeds and, therefore, how image region shapes are recovered.