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Blurred (previously named fuzzy) segments were introduced by Debled-Rennesson et al [1,2] as an extension of the arithmetical approach of Reveillès [11] on discrete lines, to take into account noise in digital images. An incremental linear-time algorithm was presented to decompose a discrete curve into blurred segments with order bounded by a parameter d. However, that algorithm fails to segment discrete curves into a minimal number of blurred segments. We show in this paper, that this characteristic is intrinsic to the whole class of blurred segments. We thus introduce a subclass of blurred segments, based on a geometric measure of thickness. We provide a new convex hull based incremental linear time algorithm for segmenting discrete curves into a minimal number of thin blurred segments.

Optimal Blurred Segments Decomposition in Linear Time