The reconstruction of noisy digital shapes is a complex question and a lot of contributions have been proposed to address this problem, including blurred segment decomposition or adaptive tangential covering for instance. In this article, we propose a novel approach combining multi-scale and irregular isothetic representations of the input contour, as an extension of a previous work [Vacavant et al., A Combined Multi-Scale/Irregular Algorithm for the Vectorization of Noisy Digital Contours, CVIU 2013]. Our new algorithm improves the representation of the contour by 1-D intervals, and achieves afterwards the decomposition of the contour into maximal arcs or segments. Our experiments with synthetic and real images show that our contribution can be employed as a relevant option for noisy shape reconstruction.
With the definition of discrete lines introduced by Réveillès [REV91], there has been a wide range of research in discrete geometry and more precisely on the study of discrete lines. By the use of the linear time segment recognition algorithm of Debled and Réveillès [DR94], Vialard [VIA96a] has proposed a O(l) algorithm for computing the tangent in one point of a discrete curve where l is the average length of the tangent. By applying her algorithm to n points of a discrete curve, the complexity becomes O(n.l). This paper proposes a new approach for computing the tangent. It is based on a precise study of the tangent evolution along a discrete curve. The resulting algorithm has a O(n) complexity and is thus optimal. Some applications in curvature computation and a tombstones contours study are also presented.
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