A closed curve in the plane can be described in several ways. We show that a simple representation in terms of radius of curvature versus normal direction has certain advantages. In particular, convolutional filtering of the extended circular image leads to a closed curve. Similar filtering operations applied to some other representations of the curve do not guarantee that the result corresponds to a closed curve. In one case, where a closed curve is produced, it is smaller than the original. A description of a curve can be based on a sequence of smoothed versions of the curve. This is one reason why smoothing of closed curves is of interest.