Abstract. We propose a new complete method to extract significant description(s) of planar curves according to constant curvature segments. This method is based (i) on a multi-scale segmentation and curve approximation algorithm, defined by two grouping processes (polygonal and constant curvature approximations), leading to a multi-scale covering of the curve, and (ii) on an intra- and inter-scale classification of this multiscale covering guided by heuristically-defined qualitative labels leading to pairs (scale, list of constant curvature segments) that best describe the shape of the curve. Experiments show that the proposed method is able to provide salient segmentation and approximation results which respect shape description and recognition criteria.