Shape Recognition, Prairie Fires, Convex Deficiencies and Skeletons

To every closed subset A of the Euclidean plane is associated its convex deficiency D and its skeletal pair (S,q). Extending a known result (A is convex iff S = phi iff D = phi) one can prove: different sets have the same skeletal pair iff they have the same convex deficiency. Several other results are presented concerning the correspondence A approaching (S,q) and the properties of S and q. The relevance of these notions and theorems for a mathematical model of visual perception is emphasized. (Author)