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

Cagliari, Francesca ; Di Fabio, Barbara ; Landi, Claudia (2012) The natural pseudo-distance as a quotient pseudo-metric, and applications. [Preprint]

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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.

Document type:Preprint
Uncontrolled Keywords:Function space, Morse function, homeomorphism group action, isometry, shape comparison
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/03 Geometria
DOI:10.6092/unibo/amsacta/3499
Depositato da:Barbara Di Fabio
Depositato il:10 Oct 2012 10:31
Last modified:29 Jan 2013 11:24

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