This paper describes the use of viewpoint-invariant representations for shape-based retrieval in image databases. In particular, we focus on a class of man-made 3D objects, whose planar surfaces contain some distinctive patterns. For this class of objects we introduce a representation scheme for parametric curves, whose reference frame is constructed using consecutive sets of points that are invariant to affine and projective transformations. In particular, we employ intersections between line segments, bitangents, and cusp tangents. In order to reduce the computational complexity of this representation, we propose an ordering algorithm for the invariant points, which reduces the number of reference frames for each curve to the number of invariant points. We then propose a two-step retrieval method. First, an indexing procedure compares the query shape to all shapes of the database using only the first-order moments of the invariant points. Once a small set of candidate shapes has been selected, the Euclidean distance between the two curves in the invariant reference frame is used to compute a detailed similarity measure. Experimental results are reported for a database of trademark patterns subject to affine transformations.