Constructing 2D Curve Atlases

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 dynamicprogramming 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