An approach is presented for deriving qualitative descriptions of contours containing structures at different (unknown) scales. The descriptions are in terms of straight arcs, curved arcs with sign of curvature, corners, and points delimiting the arcs: inflexion points and transitions from straight to curved. Furthermore, the tangents at these points are derived. The approach is based on the construction of a hierarchic family of polygons, having the scale-space property of causality; structure can only disappear as scale goes from fine to coarse. Using the principle that structures that are stable over scale represent significant properties, the features of the descriptive representations are then derived.>