We present an approach to computing a curve atlas based on deriving a correspondence between two curves. This correspondence is based on a notion of an alignment curve and on a measure of similarity between the intrinsic properties of the curve, namely, length and curvature. The optimal correspondence is found by an efficient dynamic-programming method. This is then used to compute an average for a set of curves and applied to computing the averages of bone shapes and corpus callosum as examples, towards constructing a computational atlas. The proposed notion of alignment also leads to a registration method, which is illustrated with several examples.