A new and fast method for dominant point detection and polygonal representation of a discrete curve is proposed. Starting from results of discrete geometry [1, 2], the notion of maximal blurred segment of width has been proposed, well adapted to possibly noisy and/or not connected curves [3]. For a given width, the dominant points of a curve C are deduced from the sequence of maximal blurred segments of C in O(n log2 n) time. Comparisons with other methods of the literature prove the efficacity of our approach.