A new very efficient linear algorithm for the segmentation of 8-connected digital curves is given. The simplicity comes from a definition of digital lines using a linear double diophantine inequality. A complete Pascal source code is given.

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We propose two fast methods for dominant point detection and polygonal representation of noisy and possibly disconnected curves based on a study of the decomposition of the curve into the sequence of maximal blurred segments [2]. Starting from results of discrete geometry [3,4], the notion of maximal blurred segment of width ν [2] has been proposed, well adapted to possibly noisy curves. The first method uses a fixed parameter that is the width of considered maximal blurred segments. The second method is deduced from the first one based on a multi-width approach to obtain a non-parametric method that uses no threshold for working with noisy curves. Comparisons with other methods in the literature prove the efficiency of our approach. Thanks to a recent result [5] concerning the construction of the sequence of maximal blurred segments, the complexity of the proposed methods is O(n log n). An application of vectorization is also given in this paper.

An algorithm of estimation of the curvature at each point of a general discrete curve in O(nlog 2 n) is proposed. It uses the notion of blurred segment, extending the definition of segment of arithmetic discrete line to be adapted to noisy curves. The proposed algorithm relies on the decomposition of a discrete curve into maximal blurred segments also presented in this paper.