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Abstract: The concept of blurred segment is introduced, it allows the flexible segmentation of discrete curves, taking into account noise. Relying on an arithmetic definition of discrete lines [J.-P. Reveillès, Géométrie discrète, calculs en nombre entiers et algorithmique, Thèse d’état, Université Louis Pasteur, Strasbourg, 1991], it generalizes such lines, admitting that some points are missing. Thus, a larger class of objects is considered. A very efficient linear detection algorithm for blurred segments and its application to curve segmentation are presented. [Copyright &y& Elsevier]

The convexity of a discrete region is a property used in numerous domains of computational imagery. We study its detection in the particular case of polyominoes. We present a first method, directly relying on its definition. A second method, which is based on techniques for segmentation of curves in discrete lines, leads to a very simple, linear, algorithm whose correctness is proven. Correlatively, we obtain a characterisation of lower and upper frontiers of the convex hull of a discrete line segment. Finally, we evoke some applications of these results to the problem of discrete tomography. [Copyright &y& Elsevier]