The Hausdorff distance, the Gromov–Hausdorff, the Fréchet and the natural pseudodistance are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as inf_ρ F(ρ) where F is a suitable functional and ρ varies in a set of correspondences containing the set of homeomorphisms. Our main result states that the set of homeomorphisms cannot be enlarged to a metric space K, in such a way that the composition in K (extending the composition of homeomorphisms) passes to the limit and, at the same time, K is compact.
No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit
Frosini P;
2011-01-01
Abstract
The Hausdorff distance, the Gromov–Hausdorff, the Fréchet and the natural pseudodistance are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as inf_ρ F(ρ) where F is a suitable functional and ρ varies in a set of correspondences containing the set of homeomorphisms. Our main result states that the set of homeomorphisms cannot be enlarged to a metric space K, in such a way that the composition in K (extending the composition of homeomorphisms) passes to the limit and, at the same time, K is compact.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
