ABSTRACT
The usual approach to statistical shape recognition involves two successive steps: the shape to be recognized is transformed into a small number of parameters reflecting the interesting features of this shape. Then a classifier does the final identification of these parameters. This measurement step is crucial, and the overall performance of a recognition system generally depends on the quality of these measures. An explicit construction is given to retrieve the shape from the covariogram, up to a translation and a symmetry about the origin. The basic idea is to translate at the origin all the compact sets, that is, force the sets to have their circumscribed circle centered at the origin. In the convex polygonal case, an easy case allowing analytical computations, properties can be inferred. For instance, it can be shown that the number of edges cannot be computed from the granulometric curve.
