Blurred segments were introduced by Debled-Rennesson et al. [Segmentation of discrete curves into fuzzy segments. In: 9th IWCIA, Electronic notes in discrete mathematics, vol. 12; 2003; Segmentation of discrete curves into fuzzy segments, extended version. Technical Report, INRIA Report RR-4989, http://www.inria.fr/rrrt/rr-4989.html; 2003] as an extension of the arithmetical approach of Reveille` s [Ge