This paper presents a method to compute a partition intended to be used in a region-based coding system where the number of regions is a design constraint. A new flat zone approach is introduced that (a) selects a subset of those flat zones (regions) that are present in the output of a multiscale connected filter, and that (b) assigns the rest of the regions to one among those selected by using flat zone merging procedures. The filters used are connected sequential alternating filters and a new connected filter recently presented. These are flat operators, invariant under anamorphosis, that act on a function by extending its flat zones exclusively. A new theoretical proposition is stated. Our segmentation approach behaves like a connected operator and it preserves the flat zone inclusion property between the input and the output partition. Moreover, regions computed at the highest resolution level can be imposed in successive coarser levels. Among the flat zones which are present at the output of a connected filter, the most significant ones with respect to several criteria are distinguished. This region selection is based solely on an ordering of the regions. Absolute thresholding is avoided, and the proposed approach computes with linear dynamic changes.
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