Abstract
The recognition of digital shapes is a deeply studied problem. The arithmetical framework, initiated by J.P. Reveilles in [1], provides a great theoretical basis, as well as many algorithms to deal with discrete objects. Among the many available tools, the tangential cover is a powerful one. First presented in [2], it computes the set of all maximal segments of a digital curve and allows either to obtain minimal length polygonalization, or asymptotic convergence of tangent estimations. Nevertheless, the arithmetical approach does not tolerate the introduction of irregularities, which are however inherent to the acquisition of digital shapes. In this paper, we propose a new definition for a class of so-called digital that applies well to a large class of discrete objects boundaries. We then propose an extension of the tangential cover to thick digital curves and provide an algorithm with a O(n log n) complexity, where n is the number of points of specific subparts of the thick digital curve.
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