The natural pseudo-distance is a similarity measure conceived for the purpose of comparing shapes. In this paper we revisit this pseudo-distance from the point of view of quotients. In particular, we show that the natural pseudo-distance coincides with the quotient pseudo-metric on the space of continuous functions on a compact manifold, endowed with the uniform convergence metric, modulo self-homeomorphisms of the manifold. As applications of this result, the natural pseudo-distance is shown to be actually a metric on a number of function subspaces such as the space of topological embeddings, of isometries, and of simple Morse functions on surfaces.

The natural pseudo-distance as a quotient pseudo-metric, and applications / Cagliari, F.; Di Fabio, B.; Landi, Claudia. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - STAMPA. - 27:3(2015), pp. 1729-1742. [10.1515/forum-2012-0152]

The natural pseudo-distance as a quotient pseudo-metric, and applications

LANDI, Claudia
2015

Abstract

The natural pseudo-distance is a similarity measure conceived for the purpose of comparing shapes. In this paper we revisit this pseudo-distance from the point of view of quotients. In particular, we show that the natural pseudo-distance coincides with the quotient pseudo-metric on the space of continuous functions on a compact manifold, endowed with the uniform convergence metric, modulo self-homeomorphisms of the manifold. As applications of this result, the natural pseudo-distance is shown to be actually a metric on a number of function subspaces such as the space of topological embeddings, of isometries, and of simple Morse functions on surfaces.
28-mag-2013
27
3
1729
1742
The natural pseudo-distance as a quotient pseudo-metric, and applications / Cagliari, F.; Di Fabio, B.; Landi, Claudia. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - STAMPA. - 27:3(2015), pp. 1729-1742. [10.1515/forum-2012-0152]
Cagliari, F.; Di Fabio, B.; Landi, Claudia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/930889
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