We study a variational framework to compare shapes, modeled as Radon measures on ℝN, in order to quantify how they differ from isometric copies. To this purpose we discuss some notions of weak deformations termed reformations as well as integral functionals having some kind of isometries as minimizers. The approach pursued is based on the notion of pointwise Lipschitz constant leading to a matric space framework. In particular, to compare general shapes, we study this reformation problem by using the notion of transport plan and Wasserstein distances as in optimal mass transportation theory.

A Metric Approach to Elastic Reformations / Granieri, L; Maddalena, Francesco. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - 133:1(2014), pp. 153-185. [10.1007/s10440-013-9862-z]

A Metric Approach to Elastic Reformations

MADDALENA, Francesco
2014-01-01

Abstract

We study a variational framework to compare shapes, modeled as Radon measures on ℝN, in order to quantify how they differ from isometric copies. To this purpose we discuss some notions of weak deformations termed reformations as well as integral functionals having some kind of isometries as minimizers. The approach pursued is based on the notion of pointwise Lipschitz constant leading to a matric space framework. In particular, to compare general shapes, we study this reformation problem by using the notion of transport plan and Wasserstein distances as in optimal mass transportation theory.
2014
A Metric Approach to Elastic Reformations / Granieri, L; Maddalena, Francesco. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - 133:1(2014), pp. 153-185. [10.1007/s10440-013-9862-z]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/6752
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