Identification and isotropy characterization of deformed random fields through excursion sets

Abstract : A deterministic application θ : R^2 → R^2 deforms bijectively and regularly the plane and allows to build a deformed random field X • θ : R^2 → R from a regular, stationary and isotropic random field X : R^2 → R. The deformed field X • θ is in general not isotropic, however we give an explicit characterization of the deformations θ that preserve the isotropy. Further assuming that X is Gaussian, we introduce a weak form of isotropy of the field X • θ, defined by an invariance property of the mean Euler characteristic of some of its excursion sets. Deformed fields satisfying this property are proved to be strictly isotropic. Besides, assuming that the mean Euler characteristic of excursions sets of X • θ over some basic domains is known, we are able to identify θ.
Type de document :
Pré-publication, Document de travail
MAP5 2017-15. 2017
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https://hal.archives-ouvertes.fr/hal-01495157
Contributeur : Julie Fournier <>
Soumis le : vendredi 24 mars 2017 - 15:50:39
Dernière modification le : mercredi 29 mars 2017 - 01:08:26

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  • HAL Id : hal-01495157, version 1

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Julie Fournier. Identification and isotropy characterization of deformed random fields through excursion sets. MAP5 2017-15. 2017. <hal-01495157>

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