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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)
Calabi et al. (Mon,) studied this question.