Learning shape correspondence for n-D curves

We present a learning method that introduces explicit knowledge into the shape correspondence problem. Given two input curves to be matched, our approach establishes a dense correspondence field between them, where the characteristics of the matching field closely resemble those in an a priori learning set. We build a shape distance matrix from the values of a shape descriptor computed at every point along the curves. This matrix embeds the correspondence problem in a highly expressive and redundant construct and provides the basis for a pattern matching strategy for curve matching. We selected the previously introduced observed transport measure as a shape descriptor, as its properties make it particularly amenable to the matching problem. Synthetic and real examples are presented along with discussions of the robustness and applications of the technique.