In this paper, we propose an affine-invariant method for describing and matching curves. This is important since affine transformations are often used to model perspective distortions. More specifically, we propose a new definition of the shape of a curve that characterizes a curve independently of the effects introduced by affine distortions. By combining this definition with a rotation-invariant shape descriptor, we show how it is possible to describe a curve in an intrinsically affine-invariant manner. To validate our procedure we built a database of shapes subject to perspective distortions and plotted the precision-recall curve for this dataset. Finally an application of our method is shown in the context of wide baseline matching.