Polygonal approximation is often involved in many applications of computer vision, image processing and data compression. In this context, we are interested in digital curves extracted from contours of objects contained in digital images. In particular, we propose a fully discrete structure, based on the notion of blurred segments, to study the geometrical features on such curves and apply it in a process of polygonal approximation. The experimental results demonstrate the robustness of the proposed method to local variation and noise on the curve.